From 9bd0266a70e01c2a1ba0f3badabd87840ac12ad5 Mon Sep 17 00:00:00 2001
From: Alexandre Guillemot <alexandre.guillemot@inria.fr>
Date: Wed, 10 Jul 2024 11:04:19 +0200
Subject: [PATCH] new test + corrections

---
 data/{eric_1.json => eric_1_start.json} |   2 +-
 data/eric_2_start.json                  |   2 +-
 data/eric_2_whole.json                  |  26 ++---
 data/eric_3_start.json                  | 129 ++++++++++++++++++++++++
 tests/track.rs                          |  11 +-
 5 files changed, 150 insertions(+), 20 deletions(-)
 rename data/{eric_1.json => eric_1_start.json} (63%)
 create mode 100644 data/eric_3_start.json

diff --git a/data/eric_1.json b/data/eric_1_start.json
similarity index 63%
rename from data/eric_1.json
rename to data/eric_1_start.json
index 44b5217..5b881ca 100644
--- a/data/eric_1.json
+++ b/data/eric_1_start.json
@@ -1,6 +1,6 @@
 {
   "system": [
-    "(1.58450893905961 - 1.04170241505670*I)*s*t^9 + (-0.380952380952381)*s*t^8 + (-1.57815973271041 + 1.04170241505670*I)*t^9 + 6.52936507936508*s*t^7 + (-39.6162698412698)*s*t^6 + 111.781770833333*s*t^5 + (-168.336929563492)*s*t^4 + 140.359523809524*s*t^3 + (-61.3142857142857)*s*t^2 + 10.9714285714286*s*t + (-1.57815973271041 + 1.04170241505670*I)*s + 1.57815973271041 - 1.04170241505670*I"
+    "(0.765427760068489 + 0.841213233952685*I)*s*t^9 + (-60.0000000000000)*s*t^8 + (0.234572239931511 - 0.841213233952685*I)*t^9 + 1028.37500000000*s*t^7 + (-6239.56250000000)*s*t^6 + 17605.6289062500*s*t^5 + (-26513.0664062500)*s*t^4 + 22106.6250000000*s*t^3 + (-9657.00000000000)*s*t^2 + 1728.00000000000*s*t + (0.234572239931511 - 0.841213233952685*I)*s - 0.234572239931511 + 0.841213233952685*I"
   ],
   "variables": [
     "t"
diff --git a/data/eric_2_start.json b/data/eric_2_start.json
index c3258c0..b8e3759 100644
--- a/data/eric_2_start.json
+++ b/data/eric_2_start.json
@@ -1,6 +1,6 @@
 {
   "system": [
-    "(4.40119621269103e21 + 2.07646704099341*I)*s*t^12 + (-2.48486206116244e21)*s*t^11 + (0.824232064010525 - 2.07646704099341*I)*t^12 + 7.15589489118275e20*s*t^10 + (-1.30064448518599e20)*s*t^9 + 1.61539042894445e19*s*t^8 + (-1.43200680558675e18)*s*t^7 + 9.29548157939717e16*s*t^6 + (-4.47126624045069e15)*s*t^5 + 1.59158752669684e14*s*t^4 + (-4.11861315573355e12)*s*t^3 + 7.41746656526445e10*s*t^2 + (-8.43481240927689e8)*s*t + (4.64883615508963e6 - 2.19330259059727e-15*I)*s - 8.70608724125354e-16 + 2.19330259059727e-15*I"
+    "(-0.987635189458098 + 1.49095595246224*I)*s*t^12 + (-0.564587884993002)*s*t^11 + (1.98763518945810 - 1.49095595246224*I)*t^12 + 0.162589772083972*s*t^10 + (-0.0295520677182155)*s*t^9 + 0.00367034404030069*s*t^8 + (-0.000325367635611767)*s*t^7 + 0.0000211203525818578*s*t^6 + (-1.01592067800968e-6)*s*t^5 + (3.61626123849565e-8)*s*t^4 + (-9.35794033416951e-10)*s*t^3 + (1.68532967102804e-11)*s*t^2 + (-1.91648179305316e-13)*s*t + (3.15573898907785e-15 - 1.57484683765430e-15*I)*s - 2.09947248096705e-15 + 1.57484683765430e-15*I"
   ],
   "variables": [
     "t"
diff --git a/data/eric_2_whole.json b/data/eric_2_whole.json
index ef9681e..852f56d 100644
--- a/data/eric_2_whole.json
+++ b/data/eric_2_whole.json
@@ -1,6 +1,6 @@
 {
   "system": [
-    "291.985913969380*u^12*t^12 + (-172.253693946150)*u^12*t^11 + (-10163.8441278618)*u^11*t^12 + 58.4771544057247*u^12*t^10 + 5892.08071342026*u^11*t^11 + 125207.932128093*u^10*t^12 + (-12.0622233541053)*u^12*t^9 + (-1485.65457868269)*u^11*t^10 + (-56139.6762089220)*u^10*t^11 + (-492123.339279936)*u^9*t^12 + 1.61506876694251*u^12*t^8 + 232.220637608697*u^11*t^9 + 12286.8660430127*u^10*t^10 + 233861.428850714*u^9*t^11 + 1.27617005484431e6*u^8*t^12 + (-0.148872550232955)*u^12*t^7 + (-25.6948084219751)*u^11*t^8 + (-1733.68963604658)*u^10*t^9 + (-51689.9410854231)*u^9*t^10 + (-615141.936304683)*u^8*t^11 + (-2.30573334589703e6)*u^7*t^12 + 0.00982506912639265*u^12*t^6 + 2.12515641577215*u^11*t^7 + 176.881236619930*u^10*t^8 + 7193.12032649030*u^9*t^9 + 138673.311736711*u^8*t^10 + 1.14847707770907e6*u^7*t^11 + 3.20796676811084e6*u^6*t^12 + (-0.000474117882517914)*u^12*t^5 + (-0.133710936691851)*u^11*t^6 + (-13.7952094951460)*u^10*t^7 + (-714.061025623088)*u^9*t^8 + (-19420.3009899726)*u^8*t^9 + (-262013.986098494)*u^7*t^10 + (-1.57926394917992e6)*u^6*t^11 + (-3.23403418622649e6)*u^5*t^12 + 0.0000168039676174565*u^12*t^4 + 0.00639407755872646*u^11*t^5 + 0.839853920099805*u^10*t^6 + 54.0248028708399*u^9*t^7 + 1913.08448243550*u^8*t^8 + 36837.9261643420*u^7*t^9 + 360811.360754331*u^6*t^10 + 1.59648680324767e6*u^5*t^11 + 2.34969224634977e6*u^4*t^12 + (-4.31322938390615e-7)*u^12*t^3 + (-0.000229497541899682)*u^11*t^4 + (-0.0398143059021635)*u^10*t^5 + (-3.21602598213524)*u^9*t^6 + (-142.441930680931)*u^8*t^7 + (-3615.22541226700)*u^7*t^8 + (-50704.3370076243)*u^6*t^9 + (-363474.573069933)*u^5*t^10 + (-1.15951903625212e6)*u^4*t^11 + (-1.19167130391349e6)*u^3*t^12 + (7.69416621612847e-9)*u^12*t^2 + (6.02695623133855e-6)*u^11*t^3 + 0.00144264039485390*u^10*t^4 + 0.151272689609132*u^9*t^5 + 8.35102034269374*u^8*t^6 + 266.601150727094*u^7*t^7 + 4957.28022017498*u^6*t^8 + 50977.8361390672*u^5*t^9 + 264523.815367909*u^4*t^10 + 592561.739987215*u^3*t^11 + 415000.624178551*u^2*t^12 + (-8.66759901708900e-11)*u^12*t + (-1.10342545670943e-7)*u^11*t^2 + (-0.0000386596206854883)*u^10*t^3 + (-0.00552016340235600)*u^9*t^4 + (-0.390294381835101)*u^8*t^5 + (-15.4706886651686)*u^7*t^6 + (-363.206085719017)*u^6*t^7 + (-4970.18981901736)*u^5*t^8 + (-37092.0851731318)*u^4*t^9 + (-135581.915933998)*u^3*t^10 + (-204943.763707541)*u^2*t^11 + (-90855.5111987490)*u*t^12 + (4.73987584658319e-13)*u^12 + (1.27428098029711e-9)*u^11*t + (7.25368271341722e-7)*u^10*t^2 + 0.000150570433859259*u^9*t^3 + 0.0143207881833988*u^8*t^4 + 0.719754731153476*u^7*t^5 + 20.9407116318188*u^6*t^6 + 362.768959346817*u^5*t^7 + 3614.55889446789*u^4*t^8 + 19067.2226605129*u^3*t^9 + 46907.1782951051*u^2*t^10 + 44294.2870402311*u*t^11 + 10768.3513804891*t^12 + (-7.10981376987479e-12)*u^11 + (-8.58290199271221e-9)*u^10*t + (-2.89062791916756e-6)*u^9*t^2 + (-0.000396691532018399)*u^8*t^3 + (-0.0265346695050781)*u^7*t^4 + (-0.971968343573428)*u^6*t^5 + (-20.8491315640085)*u^5*t^6 + (-263.619013577278)*u^4*t^7 + (-1861.77663245723)*u^3*t^8 + (-6608.08613721770)*u^2*t^9 + (-10015.5622381694)*u*t^10 + (-4792.53243141695)*t^11 + (4.88799696678892e-11)*u^10 + (3.50213426911742e-8)*u^9*t + (7.77834713980322e-6)*u^8*t^2 + 0.000744979144291756*u^7*t^3 + 0.0360017851026920*u^6*t^4 + 0.967761965850788*u^5*t^5 + 15.1492869450978*u^4*t^6 + 136.058275532946*u^3*t^7 + 647.324631359211*u^2*t^8 + 1403.58028327981*u*t^9 + 1032.32964209279*t^10 + (-2.03666540282872e-10)*u^9 + (-9.64141699107585e-8)*u^8*t + (-0.0000148915555624384)*u^7*t^2 + (-0.00102282847182166)*u^6*t^3 + (-0.0360328890015286)*u^5*t^4 + (-0.704816796697397)*u^4*t^5 + (-7.83869514929689)*u^3*t^6 + (-47.4741256805995)*u^2*t^7 + (-137.438487268286)*u*t^8 + (-140.936844999634)*t^9 + (5.72812144545576e-10)*u^8 + (1.88661627005179e-7)*u^7*t + 0.0000208022002618112*u^6*t^2 + 0.00103464231217503*u^5*t^3 + 0.0263984296858160*u^4*t^4 + 0.366180387121713*u^3*t^5 + 2.74606380513530*u^2*t^6 + 10.1069110324016*u*t^7 + 13.6464402810444*t^8 + (-1.14562428909115e-9)*u^7 + (-2.69055083192061e-7)*u^6*t + (-0.0000213673832402054)*u^5*t^2 + (-0.000765392166159378)*u^4*t^3 + (-0.0138041794067677)*u^3*t^4 + (-0.128897354475157)*u^2*t^5 + (-0.586530445050743)*u*t^6 - t^7 + (1.67070208825793e-9)*u^6 + (2.81762814644537e-7)*u^5*t + 0.0000160203048122468*u^4*t^2 + 0.000403851865560491*u^3*t^3 + 0.00489043815058762*u^2*t^4 + 0.0276363325521584*u*t^5 + 0.0580210368812289*t^6 + (-1.79003795170493e-9)*u^5 + (-2.15040879585164e-7)*u^4*t + (-8.55203666123908e-6)*u^3*t^2 + (-0.000144265715693558)*u^2*t^3 + (-0.00105404987150739)*u*t^4 + (-0.00273488383020088)*t^5 + (1.39846714976947e-9)*u^4 + (1.16641422349601e-7)*u^3*t + (3.08611493549191e-6)*u^2*t^2 + 0.0000313236719466755*u*t^3 + 0.000104563262646765*t^4 + (-7.76926194316374e-10)*u^3 + (-4.26808835152920e-8)*u^2*t + (-6.76106151166632e-7)*u*t^2 + (-3.12555466755856e-6)*t^3 + (2.91347322868640e-10)*u^2 + (9.45937128397352e-9)*u*t + (6.80224937710337e-8)*t^2 + (-6.62153006519637e-11)*u + (-9.60264767605940e-10)*t + 6.89742715124622e-12"
+    "u^12*t^12 + (-0.589938369301655)*u^12*t^11 + (-34.8093645672499)*u^11*t^12 + 0.200273888595383*u^12*t^10 + 20.1793320551694*u^11*t^11 + 428.814974071741*u^10*t^12 + (-0.0413109769239422)*u^12*t^9 + (-5.08810359543059)*u^11*t^10 + (-192.268440096083)*u^10*t^11 + (-1685.43520675296)*u^9*t^12 + 0.00553132425118246*u^12*t^8 + 0.795314522032215*u^11*t^9 + 42.0803383148858*u^10*t^10 + 800.933941201145*u^9*t^11 + 4370.65623301998*u^8*t^12 + (-0.000509862096459102)*u^12*t^7 + (-0.0880001643663865)*u^11*t^8 + (-5.93757970197284)*u^10*t^9 + (-177.028886026480)*u^9*t^10 + (-2106.75209616170)*u^8*t^11 + (-7896.72801181369)*u^7*t^12 + 0.0000336491202360638*u^12*t^6 + 0.00727828403391748*u^11*t^7 + 0.605786882714072*u^10*t^8 + 24.6351621169116*u^9*t^9 + 474.931512453896*u^8*t^10 + 3933.33042028015*u^7*t^11 + 10986.7175594205*u^6*t^12 + (-1.62376970886216e-6)*u^12*t^5 + (-0.000457936257520536)*u^11*t^6 + (-0.0472461472802167)*u^10*t^7 + (-2.44553244338345)*u^9*t^8 + (-66.5110885863115)*u^8*t^9 + (-897.351459652846)*u^7*t^10 + (-5408.69909685277)*u^6*t^11 + (-11075.9938459416)*u^5*t^12 + (5.75506105380778e-8)*u^12*t^4 + 0.0000218985822699549*u^11*t^5 + 0.00287635080981296*u^10*t^6 + 0.185025373780549*u^9*t^7 + 6.55197525260114*u^8*t^8 + 126.163367484245*u^7*t^9 + 1235.71495572957*u^6*t^10 + 5467.68431923428*u^5*t^11 + 8047.27945402249*u^4*t^12 + (-1.47720461075340e-9)*u^12*t^3 + (-7.85988401905405e-7)*u^11*t^4 + (-0.000136356940514393)*u^10*t^5 + (-0.0110143189389352)*u^9*t^6 + (-0.487838364339276)*u^8*t^7 + (-12.3815062278864)*u^7*t^8 + (-173.653366761184)*u^6*t^9 + (-1244.83598584844)*u^5*t^10 + (-3971.14717107110)*u^4*t^11 + (-4081.26298872918)*u^3*t^12 + (2.63511554770938e-11)*u^12*t^2 + (2.06412567969651e-8)*u^11*t^3 + (4.94078764020508e-6)*u^10*t^4 + 0.000518082148390882*u^9*t^5 + 0.0286007644312920*u^8*t^6 + 0.913061685417646*u^7*t^7 + 16.9778060618871*u^6*t^8 + 174.590052807866*u^5*t^9 + 905.947180026119*u^4*t^10 + 2029.41892617928*u^3*t^11 + 1421.30357775434*u^2*t^12 + (-2.96849902766129e-13)*u^12*t + (-3.77903660388611e-10)*u^11*t^2 + (-1.32402348318564e-7)*u^10*t^3 + (-0.0000189055811881901)*u^9*t^4 + (-0.00133668907698071)*u^8*t^5 + (-0.0529843664540301)*u^7*t^6 + (-1.24391646426172)*u^6*t^7 + (-17.0220191496586)*u^5*t^8 + (-127.033817038933)*u^4*t^9 + (-464.344029788425)*u^3*t^10 + (-701.896063825300)*u^2*t^11 + (-311.164021454393)*u*t^12 + (1.62332346178872e-15)*u^12 + (4.36418648753973e-12)*u^11*t + (2.48425775572786e-9)*u^10*t^2 + (5.15677046924423e-7)*u^9*t^3 + 0.0000490461611271444*u^8*t^4 + 0.00246503237559930*u^7*t^5 + 0.0717182255374646*u^6*t^6 + 1.24241938391884*u^5*t^7 + 12.3792235225667*u^4*t^8 + 65.3018578920641*u^3*t^9 + 160.648771228136*u^2*t^10 + 151.700081822701*u*t^11 + 36.8796947568449*t^12 + (-2.43498519268309e-14)*u^11 + (-2.93949179809142e-11)*u^10*t + (-9.89988825101572e-9)*u^9*t^2 + (-1.35859818244520e-6)*u^8*t^3 + (-0.0000908765397082158)*u^7*t^4 + (-0.00332881929254764)*u^6*t^5 + (-0.0714045800380454)*u^5*t^6 + (-0.902848394271934)*u^4*t^7 + (-6.37625496088990)*u^3*t^8 + (-22.6315237176498)*u^2*t^9 + (-34.3015253784457)*u*t^10 + (-16.4135740874114)*t^11 + (1.67405231996962e-13)*u^10 + (1.19941891083303e-10)*u^9*t + (2.66394602193683e-8)*u^8*t^2 + (2.55142151949796e-6)*u^7*t^3 + 0.000123299732556508*u^6*t^4 + 0.00331441319444017*u^5*t^5 + 0.0518836225321694*u^4*t^6 + 0.465975476978707*u^3*t^7 + 2.21697212224797*u^2*t^8 + 4.80701368158121*u*t^9 + 3.53554604076226*t^10 + (-6.97521799987343e-13)*u^9 + (-3.30201442254742e-10)*u^8*t + (-5.10009382301916e-8)*u^7*t^2 + (-3.50300621669345e-6)*u^6*t^3 + (-0.000123406257896767)*u^5*t^4 + (-0.00241387259787919)*u^4*t^5 + (-0.0268461414550255)*u^3*t^6 + (-0.162590465530395)*u^2*t^7 + (-0.470702457525739)*u*t^8 + (-0.482683712661608)*t^9 + (1.96178006246440e-12)*u^8 + (6.46132631675388e-10)*u^7*t + (7.12438486467286e-8)*u^6*t^2 + (3.54346652586647e-6)*u^5*t^3 + 0.0000904099424761438*u^4*t^4 + 0.00125410291936245*u^3*t^5 + 0.00940478178486127*u^2*t^6 + 0.0346143788068540*u*t^7 + 0.0467366390916906*t^8 + (-3.92356012492880e-12)*u^7 + (-9.21465969143551e-10)*u^6*t + (-7.31795001674162e-8)*u^5*t^2 + (-2.62133250112758e-6)*u^4*t^3 + (-0.0000472768676375781)*u^3*t^4 + (-0.000441450591649683)*u^2*t^5 + (-0.00200876281008628)*u*t^6 + (-0.00342482274711672)*t^7 + (5.72185851552117e-12)*u^6 + (9.64987696886243e-10)*u^5*t + (5.48667043367263e-8)*u^4*t^2 + (1.38312105563709e-6)*u^3*t^3 + 0.0000167488838214999*u^2*t^4 + 0.0000946495403715144*u*t^5 + 0.000198711766922131*t^6 + (-6.13056269520125e-12)*u^5 + (-7.36476895963256e-10)*u^4*t + (-2.92892096915877e-8)*u^3*t^2 + (-4.94084504736371e-7)*u^2*t^3 + (-3.60993397653397e-6)*u*t^4 + (-9.36649235239366e-6)*t^5 + (4.78950210562598e-12)*u^4 + (3.99476196518964e-10)*u^3*t + (1.05693966312893e-8)*u^2*t^2 + (1.07278024206196e-7)*u*t^3 + (3.58110640425383e-7)*t^4 + (-2.66083450312554e-12)*u^3 + (-1.46174460730211e-10)*u^2*t + (-2.31554372598102e-9)*u*t^2 + (-1.07044707228114e-8)*t^3 + (9.97812938672079e-13)*u^2 + (3.23966699467752e-11)*u*t + (2.32964983982642e-10)*t^2 + (-2.26775667880018e-13)*u + (-3.28873661935158e-12)*t + 2.36224654041685e-14"
   ],
   "variables": [
     "t"
@@ -18,40 +18,40 @@
   ],
   "fiber": [
     [
-      "0.0205897428271471 - 0.0273902295785671*I"
+      "0.04378452575702442 + 0.016584014026303013*I"
     ],
     [
-      "0.0205897428271471 + 0.0273902295785671*I"
+      "0.04554167336171262 - 0.025684325093511744*I"
     ],
     [
-      "0.0295835550629069 - 0.0265235215165480*I"
+      "0.05834770831962616 + 0.02681735053453036*I"
     ],
     [
-      "0.0295835550629069 + 0.0265235215165480*I"
+      "0.04554167336171262 + 0.025684325093511744*I"
     ],
     [
-      "0.0437845257544986 - 0.0165840140292292*I"
+      "0.08444673716824383 + 0.12620770713329416*I"
     ],
     [
-      "0.0437845257544986 + 0.0165840140292292*I"
+      "0.02058974282715596 + 0.027390229578642646*I"
     ],
     [
-      "0.0455416733656628 - 0.0256843250910521*I"
+      "0.029583555062738357 + 0.02652352151585309*I"
     ],
     [
-      "0.0455416733656628 + 0.0256843250910521*I"
+      "0.029583555062738357 - 0.02652352151585309*I"
     ],
     [
-      "0.0583477083180423 - 0.0268173505337788*I"
+      "0.02058974282715596 - 0.027390229578642646*I"
     ],
     [
-      "0.0583477083180423 + 0.0268173505337788*I"
+      "0.04378452575702442 - 0.016584014026303013*I"
     ],
     [
-      "0.0844467371682436 - 0.126207707133294*I"
+      "0.08444673716824402 - 0.1262077071332945*I"
     ],
     [
-      "0.0844467371682436 + 0.126207707133294*I"
+      "0.05834770831962616 - 0.02681735053453036*I"
     ]
   ]
 }
\ No newline at end of file
diff --git a/data/eric_3_start.json b/data/eric_3_start.json
new file mode 100644
index 0000000..6f381a6
--- /dev/null
+++ b/data/eric_3_start.json
@@ -0,0 +1,129 @@
+{
+  "system": [
+    "(1.43621950898151 - 0.0849554776350988*I)*s*t^36 + (-50.1616420216288)*s*t^35 + (-0.436219508981506 + 0.0849554776350988*I)*t^36 + 1251.93590131808*s*t^34 + (-20748.8448560575)*s*t^33 + 257278.698267398*s*t^32 + (-2.54990772033343e6)*s*t^31 + 2.10685091473558e7*s*t^30 + (-1.49365084077861e8)*s*t^29 + 9.27430029295417e8*s*t^28 + (-5.11930509193850e9)*s*t^27 + 2.53991348041017e10*s*t^26 + (-1.14199767970257e11)*s*t^25 + 4.68176746987365e11*s*t^24 + (-1.75801860947412e12)*s*t^23 + 6.06638715238621e12*s*t^22 + (-1.92800438048173e13)*s*t^21 + 5.65148879686506e13*s*t^20 + (-1.52890456073221e14)*s*t^19 + 3.81735954397990e14*s*t^18 + (-8.79138949028448e14)*s*t^17 + 1.86541839850739e15*s*t^16 + (-3.64094951996787e15)*s*t^15 + 6.52317774427379e15*s*t^14 + (-1.06999387183811e16)*s*t^13 + 1.60180975262251e16*s*t^12 + (-2.18014674468066e16)*s*t^11 + 2.68515315397655e16*s*t^10 + (-2.97528531315906e16)*s*t^9 + 2.94414064604463e16*s*t^8 + (-2.57700442914174e16)*s*t^7 + 1.97019512226299e16*s*t^6 + (-1.29313228053815e16)*s*t^5 + 7.10973950539588e15*s*t^4 + (-3.15577231981498e15)*s*t^3 + 1.06460991180845e15*s*t^2 + (-2.43737048404679e14)*s*t + (1.60932952959566e13 + 2.42508141088874e12*I)*s + 1.24520260699589e13 - 2.42508141088874e12*I"
+  ],
+  "variables": [
+    "t"
+  ],
+  "parameters": [
+    "s"
+  ],
+  "path": [
+    [
+      "0.0"
+    ],
+    [
+      "1.0"
+    ]
+  ],
+  "fiber": [
+    [
+      "-2.36463906111158"
+    ],
+    [
+      "2.36463906111158"
+    ],
+    [
+      "-2.32871488045820 - 0.410615263802068*I"
+    ],
+    [
+      "-2.32871488045820 + 0.410615263802068*I"
+    ],
+    [
+      "-2.22203387654867 - 0.808754190594859*I"
+    ],
+    [
+      "-2.22203387654867 + 0.808754190594859*I"
+    ],
+    [
+      "-2.04783749770362 - 1.18231953055579*I"
+    ],
+    [
+      "-2.04783749770362 + 1.18231953055579*I"
+    ],
+    [
+      "-1.81141861274661 - 1.51996068986334*I"
+    ],
+    [
+      "-1.81141861274661 + 1.51996068986334*I"
+    ],
+    [
+      "-1.51996068986334 - 1.81141861274661*I"
+    ],
+    [
+      "-1.51996068986334 + 1.81141861274661*I"
+    ],
+    [
+      "-1.18231953055579 - 2.04783749770362*I"
+    ],
+    [
+      "-1.18231953055579 + 2.04783749770362*I"
+    ],
+    [
+      "-0.808754190594859 - 2.22203387654867*I"
+    ],
+    [
+      "-0.808754190594859 + 2.22203387654867*I"
+    ],
+    [
+      "-0.410615263802068 - 2.32871488045820*I"
+    ],
+    [
+      "-0.410615263802068 + 2.32871488045820*I"
+    ],
+    [
+      "-2.36463906111158*I"
+    ],
+    [
+      "2.36463906111158*I"
+    ],
+    [
+      "0.410615263802068 - 2.32871488045820*I"
+    ],
+    [
+      "0.410615263802068 + 2.32871488045820*I"
+    ],
+    [
+      "0.808754190594859 - 2.22203387654867*I"
+    ],
+    [
+      "0.808754190594859 + 2.22203387654867*I"
+    ],
+    [
+      "1.18231953055579 - 2.04783749770362*I"
+    ],
+    [
+      "1.18231953055579 + 2.04783749770362*I"
+    ],
+    [
+      "1.51996068986334 - 1.81141861274661*I"
+    ],
+    [
+      "1.51996068986334 + 1.81141861274661*I"
+    ],
+    [
+      "1.81141861274661 - 1.51996068986334*I"
+    ],
+    [
+      "1.81141861274661 + 1.51996068986334*I"
+    ],
+    [
+      "2.04783749770362 - 1.18231953055579*I"
+    ],
+    [
+      "2.04783749770362 + 1.18231953055579*I"
+    ],
+    [
+      "2.22203387654867 - 0.808754190594859*I"
+    ],
+    [
+      "2.22203387654867 + 0.808754190594859*I"
+    ],
+    [
+      "2.32871488045820 - 0.410615263802068*I"
+    ],
+    [
+      "2.32871488045820 + 0.410615263802068*I"
+    ]
+  ]
+}
\ No newline at end of file
diff --git a/tests/track.rs b/tests/track.rs
index 80431ef..5cf5ff0 100644
--- a/tests/track.rs
+++ b/tests/track.rs
@@ -42,7 +42,6 @@ macro_rules! nasty_examples {
     $(
         #[test]
         fn $name() {
-            println!("{}", $e);
             let path = PathBuf::from($e);
             let mut conf = algpath::cli::Configuration {
                 path: Some(path),
@@ -66,7 +65,7 @@ macro_rules! nasty_examples {
                     .unwrap();
 
                 let _tr = parametric_system
-                    .track(mbox, &path[1].clone().into())
+                    .track_path(mbox, &path)
                     .unwrap();
             }
         }
@@ -75,12 +74,14 @@ macro_rules! nasty_examples {
 }
 
 // Nasty examples description :
-//     nasty_1: linear homotopy with a single degree 9 polynomial that has 4 close roots
+//     nasty_1: linear homotopy with a single degree 9 polynomial that has 4 close roots (hc.jl is not able to solve correctly)
 //     nasty_2: bivariate polynomial (degree (12, 12)), with very unbalanced coefficients (10^12 ratio between min and max coeff) and very sensitive to big values for the parameter (parameter degree is 12).
-//     nasty_3: start system of nasty_2 setting the parameter to -37 (the ratio between min and max coeff is now 10^42).
+//     nasty_3: start system of nasty_2 setting the parameter to -37 (with rescaling).
+//     nasty_4: linear homotopy with a single degree 36 polynomial with unbalanced coefficients
 
 nasty_examples! {
-    nasty_1: "data/eric_1.json",
+    nasty_1: "data/eric_1_start.json",
     nasty_2: "data/eric_2_whole.json",
     nasty_3: "data/eric_2_start.json",
+    nasty_4: "data/eric_3_start.json",
 }
\ No newline at end of file
-- 
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