Details

Time bar (total: 9.9s)

analyze448.0ms (4.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.4%)

Algorithm
intervals
Results
10.0ms45×body2048valid
8.0ms160×body128valid
4.0ms14×body4096valid
3.0ms19×body1024valid
2.0ms13×body512valid
1.0ms21×body128nan
0.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify434.0ms (4.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (335.0ms)

IterNodesCost
0183424
1183424

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
36.7b
Counts
2 → 1
Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
0.0b
(*.f64 4 (*.f64 a c))
0.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
0.6b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64_419
20×add-sqr-sqrt_binary64_441
16×associate-*r*_binary64_359
14×add-cube-cbrt_binary64_454
13×times-frac_binary64_425
add-cbrt-cube_binary64_455 add-exp-log_binary64_457
add-log-exp_binary64_458
pow1_binary64_480
distribute-lft-out_binary64_370
associate-*l*_binary64_360 sqrt-prod_binary64_435
sqrt-div_binary64_436 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 flip3--_binary64_423 flip--_binary64_394
flip3-+_binary64_422 pow-prod-down_binary64_490 sub-neg_binary64_412 pow1/2_binary64_499 div-inv_binary64_416 sum-log_binary64_510 associate-*r/_binary64_361 *-commutative_binary64_350 flip-+_binary64_393 diff-log_binary64_511 sqrt-pow1_binary64_437 cancel-sign-sub-inv_binary64_385 rem-sqrt-square_binary64_432 +-commutative_binary64_349 div-exp_binary64_470 cbrt-undiv_binary64_453
Counts
4 → 74
Calls

8 calls:

12.0ms
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 4 (*.f64 a c))

series678.0ms (6.9%)

Counts
4 → 76
Calls

4 calls:

223.0ms
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a))
159.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
151.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
145.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 2172 to 1828 computations (15.8% saved)

simplify85.0ms (0.9%)

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049362958
149362958

prune214.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1437150
Fresh000
Picked101
Done000
Total1447151
Error
6.6b
Counts
151 → 7
Compiler

Compiled 3089 to 1620 computations (47.6% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a))
1.2b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.3b
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
10.2b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite54.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64_425
59×add-sqr-sqrt_binary64_441
44×*-un-lft-identity_binary64_419
30×add-cube-cbrt_binary64_454
27×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
14×difference-of-squares_binary64_388
13×sqrt-prod_binary64_435 associate-/l*_binary64_364
10×associate-/r/_binary64_365 div-exp_binary64_470 cbrt-undiv_binary64_453
associate-/r*_binary64_363
flip3--_binary64_423 distribute-lft-out--_binary64_371 flip--_binary64_394
add-log-exp_binary64_458 div-inv_binary64_416 prod-exp_binary64_468 cbrt-unprod_binary64_452 cancel-sign-sub-inv_binary64_385
pow1_binary64_480
sqrt-div_binary64_436 clear-num_binary64_418 frac-2neg_binary64_430
sub-neg_binary64_412 pow1/2_binary64_499 diff-log_binary64_511 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 associate-/l/_binary64_366
Counts
4 → 136
Calls

8 calls:

14.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
13.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
7.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a))

series1.0s (10.2%)

Counts
4 → 73
Calls

4 calls:

363.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
319.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
164.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
160.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 3049 to 2389 computations (21.6% saved)

simplify107.0ms (1.1%)

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049426184
149426184

prune290.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2063209
Fresh246
Picked101
Done000
Total2097216
Error
6.6b
Counts
216 → 7
Compiler

Compiled 6002 to 3117 computations (48.1% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
0.0b
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))
0.1b
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.2b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64_441
28×*-un-lft-identity_binary64_419
18×times-frac_binary64_425 add-cube-cbrt_binary64_454
11×sqrt-prod_binary64_435
10×difference-of-squares_binary64_388
add-log-exp_binary64_458
cancel-sign-sub-inv_binary64_385
add-cbrt-cube_binary64_455 add-exp-log_binary64_457 associate-/r*_binary64_363
distribute-lft-out--_binary64_371 pow1_binary64_480
flip3--_binary64_423 flip--_binary64_394
associate-/l*_binary64_364
sqrt-div_binary64_436 sub-neg_binary64_412 associate-/r/_binary64_365 diff-log_binary64_511
clear-num_binary64_418 pow1/2_binary64_499 div-inv_binary64_416 frac-2neg_binary64_430 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 div-exp_binary64_470 cbrt-undiv_binary64_453
Counts
4 → 88
Calls

8 calls:

8.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
7.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
0.0ms
(*.f64 -1/2 (*.f64 4 (*.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))))

series733.0ms (7.4%)

Counts
4 → 73
Calls

4 calls:

267.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
159.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
156.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
151.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 2690 to 2305 computations (14.3% saved)

simplify79.0ms (0.8%)

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049833577
149833577

prune192.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1610161
Fresh066
Picked011
Done000
Total1617168
Error
6.6b
Counts
168 → 7
Compiler

Compiled 4145 to 2465 computations (40.5% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 4 (*.f64 a c))
0.0b
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))) a))
9.8b
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
10.7b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
26.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_441 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
add-log-exp_binary64_458 sqrt-prod_binary64_435 pow1_binary64_480
sqrt-div_binary64_436 times-frac_binary64_425 flip3--_binary64_423 flip--_binary64_394 associate-/r*_binary64_363
difference-of-squares_binary64_388 prod-exp_binary64_468 cbrt-unprod_binary64_452 div-exp_binary64_470 cbrt-undiv_binary64_453
pow1/2_binary64_499 associate-/r/_binary64_365 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432
clear-num_binary64_418 sub-neg_binary64_412 div-inv_binary64_416 frac-2neg_binary64_430 diff-log_binary64_511 cancel-sign-sub-inv_binary64_385 associate-/l*_binary64_364
Counts
4 → 70
Calls

8 calls:

8.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
3.0ms
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
0.0ms
(*.f64 -1/2 (/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))) a))

series868.0ms (8.8%)

Counts
4 → 75
Calls

4 calls:

376.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
173.0ms
(-.f64 b (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
160.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
159.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Compiler

Compiled 3906 to 2901 computations (25.7% saved)

simplify59.0ms (0.6%)

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
052363195

prune194.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh055
Picked011
Done011
Total1457152
Error
6.6b
Counts
152 → 7
Compiler

Compiled 4833 to 2486 computations (48.6% saved)

simplify27.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (8.0ms)

IterNodesCost
05271626
15271626

regimes662.0ms (6.7%)

Compiler

Compiled 3207 to 2457 computations (23.4% saved)

bsearch98.0ms (1%)

Steps
ItersRangePoint
9
1.1935307154283341e+95
4.0136306422491975e+100
5.513576328640909e+99
5
2.3280598367501807e-277
6.026491473597822e-277
3.201370751245736e-277
9
-1.0451269989421558e+143
-1.1049780562537373e+138
-1.303984552860991e+140
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes271.0ms (2.7%)

Compiler

Compiled 555 to 528 computations (4.9% saved)

bsearch49.0ms (0.5%)

Steps
ItersRangePoint
9
1.1935307154283341e+95
4.0136306422491975e+100
3.0794489170197573e+97
6
-5.781806328546769e-124
-8.565900891222301e-125
-3.935594578192137e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes180.0ms (1.8%)

Compiler

Compiled 306 to 321 computations (-4.9% saved)

bsearch48.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
1.192658630200912e-59
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.7015362524443945e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes178.0ms (1.8%)

Compiler

Compiled 270 to 288 computations (-6.7% saved)

bsearch50.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
2.0197238409036384e-59
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.380455948034893e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes161.0ms (1.6%)

Compiler

Compiled 234 to 252 computations (-7.7% saved)

bsearch48.0ms (0.5%)

Steps
ItersRangePoint
8
1.4915430749632438e-60
8.191130340726901e-58
4.156489435550409e-59
6
-5.781806328546769e-124
-8.565900891222301e-125
-5.7015362524443945e-124
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes113.0ms (1.1%)

Compiler

Compiled 204 to 222 computations (-8.8% saved)

bsearch7.0ms (0.1%)

Steps
ItersRangePoint
2
-3.4555292518757554e-207
-3.087791938118972e-207
-3.1124603004849597e-207
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0.3%)

Compiler

Compiled 27 to 69 computations (-155.6% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

Accuracy

Total 1.1b remaining (16.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 201 to 146 computations (27.4% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0151298
1151298

end0.0ms (0%)

sample2.3s (23%)

Algorithm
intervals
Results
283.0ms1159×body2048valid
263.0ms5195×body128valid
128.0ms680×body1024valid
126.0ms419×body4096valid
50.0ms362×body512valid
32.0ms680×body128nan
19.0ms396×body128invalid
17.0ms185×body256valid
Compiler

Compiled 1328 to 1004 computations (24.4% saved)

Pareto

0.5490694829455598

Profiling

Loading profile data...