Details

Time bar (total: 13.8s)

analyze1.2s (8.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
4.7%95.1%0.2%10
12.7%87.1%0.2%11
15.9%83.9%0.2%12
18.4%81.3%0.2%13
29.5%70.3%0.2%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (0.2%)

Algorithm
intervals
Results
9.0ms255×body128valid
1.0ms24×body128invalid
0.0msbody1024valid
Compiler

Compiled 23 to 26 computations (-13% saved)

simplify277.0ms (2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (183.0ms)

IterNodesCost
0478716
1478716

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
9.1b
Counts
2 → 1
Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

9.2b
(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
0.0b
(*.f64 (-.f64 y z) t)
0.0b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0b
(*.f64 (-.f64 y z) t)
9.2b
(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

rewrite31.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64_17150 *-un-lft-identity_binary64_17128
10×add-cbrt-cube_binary64_17164 add-exp-log_binary64_17166
add-cube-cbrt_binary64_17163
pow1_binary64_17189 times-frac_binary64_17134 add-log-exp_binary64_17167 associate-/r*_binary64_17072 associate-*l*_binary64_17069
associate-*l/_binary64_17071
difference-of-squares_binary64_17097 associate-*r*_binary64_17068 flip--_binary64_17103 distribute-lft-out--_binary64_17080 flip3--_binary64_17132
cbrt-undiv_binary64_17162 associate-/r/_binary64_17074 cbrt-unprod_binary64_17161 prod-exp_binary64_17177 associate-/l/_binary64_17075 div-exp_binary64_17179
clear-num_binary64_17127 flip-+_binary64_17102 associate-/l*_binary64_17073 distribute-lft-out_binary64_17079 frac-2neg_binary64_17139 unswap-sqr_binary64_17096 +-commutative_binary64_17058 *-commutative_binary64_17059 sum-log_binary64_17219 pow-prod-down_binary64_17199 flip3-+_binary64_17131 div-inv_binary64_17125
Counts
3 → 63
Calls

6 calls:

10.0ms
(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
9.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
7.0ms
(*.f64 (-.f64 y z) t)
0.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0ms
(*.f64 (-.f64 y z) t)

series826.0ms (6%)

Counts
3 → 80
Calls

3 calls:

466.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
265.0ms
(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
94.0ms
(*.f64 (-.f64 y z) t)
Compiler

Compiled 2144 to 1667 computations (22.2% saved)

simplify92.0ms (0.7%)

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049712501
149712501

prune148.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1367143
Fresh000
Picked101
Done000
Total1377144
Error
0.0b
Counts
144 → 7
Compiler

Compiled 2375 to 493 computations (79.2% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

11.8b
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))
0.0b
(/.f64 (-.f64 a z) t)
0.0b
(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
0.0b
(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
0.0b
(/.f64 (-.f64 a z) t)
11.8b
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))

rewrite75.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
200×times-frac_binary64_17134
173×*-un-lft-identity_binary64_17128
171×add-sqr-sqrt_binary64_17150
87×add-cube-cbrt_binary64_17163
42×difference-of-squares_binary64_17097 distribute-lft-out--_binary64_17080
22×associate-/r*_binary64_17072
10×add-cbrt-cube_binary64_17164 add-exp-log_binary64_17166 associate-/l*_binary64_17073
div-inv_binary64_17125
add-log-exp_binary64_17167
cbrt-undiv_binary64_17162 associate-/l/_binary64_17075 div-exp_binary64_17179
pow1_binary64_17189 div-sub_binary64_17133
clear-num_binary64_17127 flip--_binary64_17103 frac-2neg_binary64_17139 flip3--_binary64_17132
associate-/r/_binary64_17074 flip-+_binary64_17102 distribute-lft-out_binary64_17079 +-commutative_binary64_17058 sum-log_binary64_17219 associate-+r-_binary64_17062 flip3-+_binary64_17131
Counts
3 → 188
Calls

6 calls:

36.0ms
(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
13.0ms
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))
6.0ms
(/.f64 (-.f64 a z) t)
0.0ms
(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
0.0ms
(/.f64 (-.f64 a z) t)

series869.0ms (6.3%)

Counts
3 → 80
Calls

3 calls:

464.0ms
(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
265.0ms
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))
110.0ms
(/.f64 (-.f64 a z) t)
Compiler

Compiled 2148 to 1671 computations (22.2% saved)

simplify109.0ms (0.8%)

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049976430
149976430

prune205.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2653268
Fresh336
Picked011
Done000
Total2687275
Error
0.0b
Counts
275 → 7
Compiler

Compiled 5426 to 860 computations (84.2% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t)))
0.2b
(/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
0.2b
(/.f64 (cbrt.f64 (-.f64 a z)) t)
0.0b
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t))))
0.5b
(cbrt.f64 (-.f64 y z))
0.5b
(cbrt.f64 (-.f64 y z))
0.5b
(cbrt.f64 (-.f64 y z))
4.4b
(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t))

rewrite89.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
440×times-frac_binary64_17134
318×add-sqr-sqrt_binary64_17150 *-un-lft-identity_binary64_17128
295×cbrt-prod_binary64_17159
200×add-cube-cbrt_binary64_17163
59×difference-of-squares_binary64_17097 distribute-lft-out--_binary64_17080
28×associate-/r*_binary64_17072
10×div-inv_binary64_17125
add-exp-log_binary64_17166
associate-/l*_binary64_17073 cbrt-div_binary64_17160
add-cbrt-cube_binary64_17164
flip--_binary64_17103 pow1_binary64_17189 add-log-exp_binary64_17167 flip3--_binary64_17132
pow1/3_binary64_17210 cbrt-undiv_binary64_17162 div-exp_binary64_17179
associate-/l/_binary64_17075
clear-num_binary64_17127 associate-/r/_binary64_17074 frac-2neg_binary64_17139
Counts
4 → 322
Calls

8 calls:

17.0ms
(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t))
3.0ms
(cbrt.f64 (-.f64 y z))
3.0ms
(cbrt.f64 (-.f64 y z))
3.0ms
(cbrt.f64 (-.f64 y z))
0.0ms
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t))))

series961.0ms (7%)

Counts
4 → 48
Calls

4 calls:

730.0ms
(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) t))
78.0ms
(cbrt.f64 (-.f64 y z))
78.0ms
(cbrt.f64 (-.f64 y z))
74.0ms
(cbrt.f64 (-.f64 y z))
Compiler

Compiled 4118 to 2669 computations (35.2% saved)

simplify173.0ms (1.3%)

Algorithm
egg-herbie
Counts
370 → 370
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0498412481
1498412481

prune436.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3700370
Fresh055
Picked011
Done011
Total3707377
Error
0.0b
Counts
377 → 7
Compiler

Compiled 17095 to 2139 computations (87.5% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

2.1b
(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
0.0b
(/.f64 (-.f64 y z) (-.f64 a z))
0.0b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
0.0b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
0.0b
(/.f64 (-.f64 y z) (-.f64 a z))
2.1b
(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite39.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt_binary64_17150
71×*-un-lft-identity_binary64_17128
51×times-frac_binary64_17134
31×associate-*l*_binary64_17069
27×add-cube-cbrt_binary64_17163
22×difference-of-squares_binary64_17097 distribute-lft-out--_binary64_17080
10×add-cbrt-cube_binary64_17164 add-exp-log_binary64_17166
pow1_binary64_17189 associate-/l*_binary64_17073 add-log-exp_binary64_17167 associate-/r*_binary64_17072
associate-/r/_binary64_17074
associate-*r*_binary64_17068 flip--_binary64_17103 flip3--_binary64_17132
cbrt-undiv_binary64_17162 cbrt-unprod_binary64_17161 prod-exp_binary64_17177 unswap-sqr_binary64_17096 associate-/l/_binary64_17075 div-exp_binary64_17179 div-inv_binary64_17125
clear-num_binary64_17127 flip-+_binary64_17102 associate-*l/_binary64_17071 frac-2neg_binary64_17139 div-sub_binary64_17133 +-commutative_binary64_17058 *-commutative_binary64_17059 sum-log_binary64_17219 pow-prod-down_binary64_17199 flip3-+_binary64_17131
Counts
3 → 113
Calls

6 calls:

13.0ms
(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
8.0ms
(/.f64 (-.f64 y z) (-.f64 a z))
3.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
0.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
0.0ms
(/.f64 (-.f64 y z) (-.f64 a z))

series893.0ms (6.5%)

Counts
3 → 89
Calls

3 calls:

460.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
272.0ms
(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
161.0ms
(/.f64 (-.f64 y z) (-.f64 a z))
Compiler

Compiled 2522 to 1948 computations (22.8% saved)

simplify86.0ms (0.6%)

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
052194265

prune140.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2020202
Fresh044
Picked011
Done022
Total2027209
Error
0.0b
Counts
209 → 7
Compiler

Compiled 3863 to 737 computations (80.9% saved)

simplify53.0ms (0.4%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
01720844
11720844

regimes483.0ms (3.5%)

Compiler

Compiled 4133 to 3461 computations (16.3% saved)

bsearch0.0ms (0%)

regimes612.0ms (4.4%)

Compiler

Compiled 3902 to 3349 computations (14.2% saved)

bsearch47.0ms (0.3%)

Steps
ItersRangePoint
10
9.51928538275853e-14
0.061168252052219096
9.434183570764376e-09
8
1.5872537044959321e-230
1.7164140116506246e-226
1.266354716065063e-227
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes350.0ms (2.5%)

Compiler

Compiled 1283 to 1519 computations (-18.4% saved)

bsearch39.0ms (0.3%)

Steps
ItersRangePoint
7
5.122040522786301e-83
1.3379253006070545e-81
4.5875175130816466e-82
9
-1.2379723246204271e+26
-1.66817945505843e+17
-2.607906820722103e+20
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes240.0ms (1.7%)

Compiler

Compiled 983 to 1192 computations (-21.3% saved)

bsearch29.0ms (0.2%)

Steps
ItersRangePoint
6
1.5557463632848682e-277
1.5844496101168067e-276
2.121227199050854e-277
6
-2.4084874249390263e-118
-4.0199833702668247e-119
-9.810270338854375e-119
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes475.0ms (3.4%)

Compiler

Compiled 917 to 1132 computations (-23.4% saved)

bsearch85.0ms (0.6%)

Steps
ItersRangePoint
7
3.7559873657563e+50
2.0380177839742203e+52
2.7399348652501344e+51
5
1.6981231603543487e-47
3.646645266143591e-47
1.7171850962601488e-47
6
4.945078059868287e-105
3.023944685530419e-104
2.9658245924063643e-104
7
-4.842542821330507e-49
-1.3382909013199293e-50
-1.8891242327213466e-49
8
-5.070381467750334e+88
-4.2933116102996375e+84
-2.269628994657719e+87
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes438.0ms (3.2%)

Compiler

Compiled 809 to 1024 computations (-26.6% saved)

bsearch82.0ms (0.6%)

Steps
ItersRangePoint
7
3.7559873657563e+50
2.0380177839742203e+52
1.6915671475104914e+52
5
1.6981231603543487e-47
3.646645266143591e-47
1.7171850962601488e-47
6
4.945078059868287e-105
3.023944685530419e-104
2.9658245924063643e-104
7
-4.842542821330507e-49
-1.3382909013199293e-50
-2.993230862827396e-49
8
-5.070381467750334e+88
-4.2933116102996375e+84
-2.3744400148381077e+87
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes390.0ms (2.8%)

Compiler

Compiled 701 to 916 computations (-30.7% saved)

bsearch53.0ms (0.4%)

Steps
ItersRangePoint
7
3.7559873657563e+50
2.0380177839742203e+52
4.005831574744566e+50
7
-4.842542821330507e-49
-1.3382909013199293e-50
-3.0829907836386377e-50
8
-5.070381467750334e+88
-4.2933116102996375e+84
-5.5916010666957924e+87
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes317.0ms (2.3%)

Compiler

Compiled 485 to 700 computations (-44.3% saved)

bsearch79.0ms (0.6%)

Steps
ItersRangePoint
8
2.798780619339749e-10
9.138055058492938e-06
3.0339013843065053e-09
9
-3.2391550843528875e-93
-5.205818343439722e-100
-3.196925398238006e-93
9
-40760155445.76627
-29.602837703586957
-220.647905604936
5
-3.4102032452511014e+51
-9.715509115788273e+50
-1.7810524236303283e+51
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes279.0ms (2%)

Compiler

Compiled 275 to 445 computations (-61.8% saved)

bsearch77.0ms (0.6%)

Steps
ItersRangePoint
8
2.798780619339749e-10
9.138055058492938e-06
1.8481797992319505e-09
9
-3.2391550843528875e-93
-5.205818343439722e-100
-3.196925398238006e-93
9
-40760155445.76627
-29.602837703586957
-144.80765736241221
5
-1.181380578889419e+46
-5.0435517195544885e+45
-5.665548523982956e+45
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes257.0ms (1.9%)

Compiler

Compiled 230 to 400 computations (-73.9% saved)

bsearch69.0ms (0.5%)

Steps
ItersRangePoint
7
1.0467816368687045e+33
6.2942860291488525e+34
4.666143669536909e+34
9
-3.2391550843528875e-93
-5.205818343439722e-100
-4.219313419649227e-94
9
-40760155445.76627
-29.602837703586957
-226979239.8244441
5
-1.181380578889419e+46
-5.0435517195544885e+45
-7.205370870232716e+45
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes213.0ms (1.5%)

Compiler

Compiled 185 to 355 computations (-91.9% saved)

bsearch41.0ms (0.3%)

Steps
ItersRangePoint
7
3.7559873657563e+50
2.0380177839742203e+52
3.8392687687523886e+50
10
-1.1589907873097705e-34
-4.842542821330507e-49
-2.539804671575186e-41
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes172.0ms (1.2%)

Compiler

Compiled 115 to 275 computations (-139.1% saved)

bsearch84.0ms (0.6%)

Steps
ItersRangePoint
7
1.0467816368687045e+33
6.2942860291488525e+34
4.082774562727311e+33
9
-3.2391550843528875e-93
-5.205818343439722e-100
-4.640645079994026e-97
9
-40760155445.76627
-29.602837703586957
-7928054331.279097
10
-3.681917648063516e+155
-4.705662517166795e+145
-4.623624693564985e+150
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes126.0ms (0.9%)

Compiler

Compiled 80 to 235 computations (-193.8% saved)

bsearch55.0ms (0.4%)

Steps
ItersRangePoint
8
1.6442990362604346e+168
7.693330474376744e+170
7.609833274098096e+170
8
-5.161507795523016e+69
-1.8782620598342502e+66
-4.471136920446894e+69
8
-1.9214073645560332e+132
-2.1264635682504644e+128
-2.1708911965137315e+128
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes80.0ms (0.6%)

Compiler

Compiled 45 to 195 computations (-333.3% saved)

bsearch22.0ms (0.2%)

Steps
ItersRangePoint
10
-1.3535505799608795e+143
-1.0831264850174934e+133
-8.231696246658259e+140
Compiler

Compiled 1 to 5 computations (-400% saved)

regimes58.0ms (0.4%)

Compiler

Compiled 30 to 165 computations (-450% saved)

bsearch0.0ms (0%)

regimes48.0ms (0.3%)

Compiler

Compiled 25 to 140 computations (-460% saved)

bsearch0.0ms (0%)

regimes41.0ms (0.3%)

Accuracy

Total 1.7b remaining (99.9%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 110 computations (-450% saved)

bsearch21.0ms (0.1%)

Compiler

Compiled 604 to 335 computations (44.5% saved)

simplify30.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0610804
1610804

end0.0ms (0%)

sample1.7s (12.1%)

Algorithm
intervals
Results
307.0ms7998×body128valid
31.0ms761×body128invalid
0.0msbody1024valid
0.0msbody512valid
Compiler

Compiled 1163 to 838 computations (27.9% saved)

Pareto

0.7948505460875652

Profiling

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