Details

Time bar (total: 1.3min)

analyze1.8s (2.4%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04804115
14804115
011
111
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
0%74.9%25.1%2
18.7%56.2%25.1%3
37.5%37.5%25.1%4
42.1%32.8%25.1%5
46.8%28.1%25.1%6
48%26.9%25.1%7
49.2%25.8%25.1%8
49.5%25.5%25.1%9
49.8%25.2%25.1%10
49.8%25.2%25.1%11
49.8%25.1%25.1%12
49.9%25%25.1%13
49.9%25%25.1%14
Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.3s (1.7%)

Algorithm
intervals
Results
1.2s107×body8192exit
80.0ms256×body128valid
7.0ms372×pre128true
3.0msbody128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify51.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
04804115
14804115

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
1.8b
Counts
2 → 2
Compiler

Compiled 271 to 232 computations (14.4% saved)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b
(-.f64 (-.f64 1 z) 1)
6.1b
(-.f64 (-.f64 1 z) 1)
6.1b
(-.f64 (-.f64 1 z) 1)
6.1b
(-.f64 (-.f64 1 z) 1)

rewrite1.1s (1.5%)

Algorithm
rewrite-expression-head
Error
1.8b
Rules
36×*-un-lft-identity_binary64_2465
28×add-sqr-sqrt_binary64_2487
24×add-log-exp_binary64_2504 cancel-sign-sub-inv_binary64_2431
16×associate--l+_binary64_2402
12×diff-log_binary64_2557 add-cube-cbrt_binary64_2500 distribute-lft-out--_binary64_2417
sub-neg_binary64_2458 difference-of-squares_binary64_2434
pow1_binary64_2526 add-exp-log_binary64_2503 add-cbrt-cube_binary64_2501 flip3--_binary64_2469 flip--_binary64_2440 difference-of-sqr-1_binary64_2435 associate--l-_binary64_2403
Counts
4 → 100
Calls

4 calls:

9.0ms
(-.f64 (-.f64 1 z) 1)
8.0ms
(-.f64 (-.f64 1 z) 1)
8.0ms
(-.f64 (-.f64 1 z) 1)
8.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series218.0ms (0.3%)

Error
1.8b
Counts
4 → 12
Calls

4 calls:

40.0ms
(-.f64 (-.f64 1 z) 1)
40.0ms
(-.f64 (-.f64 1 z) 1)
39.0ms
(-.f64 (-.f64 1 z) 1)
38.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify79.0ms (0.1%)

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05392704

prune1.1s (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done000
Total1122114
Error
1.8b
Counts
114 → 2
Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.6b
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite544.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
24×*-un-lft-identity_binary64_2465
23×add-log-exp_binary64_2504
14×frac-add_binary64_2473
13×sum-log_binary64_2556 distribute-lft-out_binary64_2416
10×add-exp-log_binary64_2503
pow1_binary64_2526 add-cbrt-cube_binary64_2501
prod-exp_binary64_2514
flip3-+_binary64_2468 flip-+_binary64_2439
add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487
associate-*r*_binary64_2405
cbrt-unprod_binary64_2498
associate-+l+_binary64_2398 +-commutative_binary64_2395 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
pow1/2_binary64_2545 sqrt-prod_binary64_2481 pow-to-exp_binary64_2534 pow-exp_binary64_2533 pow-sub_binary64_2541 associate-*r/_binary64_2407 associate-*l/_binary64_2408 associate-*l*_binary64_2406 exp-sum_binary64_2511 *-commutative_binary64_2396
Counts
4 → 74
Calls

4 calls:

47.0ms
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
25.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
16.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 6884 to 5351 computations (22.3% saved)

series347.0ms (0.5%)

Error
1.1b
Counts
4 → 18
Calls

4 calls:

197.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
40.0ms
(+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
36.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 3328 to 2676 computations (19.6% saved)

simplify104.0ms (0.1%)

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049253537
149253537

prune568.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New86692
Fresh000
Picked101
Done011
Total87794
Error
0.3b
Counts
94 → 7
Compiler

Compiled 8416 to 6519 computations (22.5% saved)

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.6b
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite4.1s (5.4%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
83×associate-*r/_binary64_2407
68×frac-times_binary64_2475
64×frac-add_binary64_2473
60×flip3-+_binary64_2468 flip-+_binary64_2439
43×flip3--_binary64_2469 flip--_binary64_2440
35×associate-*l/_binary64_2408
13×add-sqr-sqrt_binary64_2487
12×add-exp-log_binary64_2503
11×pow1_binary64_2526 add-cbrt-cube_binary64_2501 *-un-lft-identity_binary64_2465
add-cube-cbrt_binary64_2500 associate-*r*_binary64_2405
prod-exp_binary64_2514
add-log-exp_binary64_2504 distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414 cancel-sign-sub-inv_binary64_2431
cbrt-unprod_binary64_2498 associate-*l*_binary64_2406
pow-prod-down_binary64_2536
associate-+l+_binary64_2398 associate-+r+_binary64_2397 sqrt-pow1_binary64_2483 sub-neg_binary64_2458 *-commutative_binary64_2396
sum-log_binary64_2556 +-commutative_binary64_2395 pow1/2_binary64_2545 sqrt-prod_binary64_2481 unswap-sqr_binary64_2433 difference-of-squares_binary64_2434 distribute-lft-out--_binary64_2417 pow-to-exp_binary64_2534 pow-exp_binary64_2533 pow-sub_binary64_2541 exp-sum_binary64_2511
Counts
4 → 147
Calls

4 calls:

37.0ms
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
34.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
16.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 34356 to 28188 computations (18% saved)

series535.0ms (0.7%)

Error
0.3b
Counts
4 → 18
Calls

4 calls:

217.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
80.0ms
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
77.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 6742 to 5534 computations (17.9% saved)

simplify200.0ms (0.3%)

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0573916319

prune4.2s (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1641165
Fresh055
Picked011
Done011
Total1648172
Error
0.3b
Counts
172 → 8
Compiler

Compiled 35262 to 28787 computations (18.4% saved)

localize84.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b
(sqrt.f64 PI.f64)
2.6b
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite4.5s (5.8%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
83×associate-*r/_binary64_2407
68×frac-times_binary64_2475
64×frac-add_binary64_2473
60×flip3-+_binary64_2468 flip-+_binary64_2439
43×flip3--_binary64_2469 flip--_binary64_2440
35×associate-*l/_binary64_2408
20×add-exp-log_binary64_2503
17×prod-exp_binary64_2514
15×add-cbrt-cube_binary64_2501 add-sqr-sqrt_binary64_2487
12×*-un-lft-identity_binary64_2465
10×add-cube-cbrt_binary64_2500
pow1_binary64_2526 associate-*r*_binary64_2405
cbrt-unprod_binary64_2498
add-log-exp_binary64_2504 distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414 cancel-sign-sub-inv_binary64_2431
associate-*l*_binary64_2406
sqrt-prod_binary64_2481
associate-+l+_binary64_2398 associate-+r+_binary64_2397 pow-prod-down_binary64_2536 sub-neg_binary64_2458 *-commutative_binary64_2396 pow-to-exp_binary64_2534 pow-exp_binary64_2533
sum-log_binary64_2556 +-commutative_binary64_2395 pow1/2_binary64_2545 sqrt-pow1_binary64_2483 rem-sqrt-square_binary64_2478 unswap-sqr_binary64_2433 difference-of-squares_binary64_2434 distribute-lft-out--_binary64_2417 pow-sub_binary64_2541 exp-sum_binary64_2511
Counts
4 → 153
Calls

4 calls:

38.0ms
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
35.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
19.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 35553 to 29003 computations (18.4% saved)

series523.0ms (0.7%)

Error
0.3b
Counts
4 → 18
Calls

4 calls:

225.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
79.0ms
(*.f64 (+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
79.0ms
(+.f64 (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 6770 to 5550 computations (18% saved)

simplify202.0ms (0.3%)

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0578916484

prune4.4s (5.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1692171
Fresh235
Picked101
Done112
Total1736179
Error
0.3b
Counts
179 → 6
Compiler

Compiled 35867 to 29116 computations (18.8% saved)

regimes704.0ms (0.9%)

Accuracy

Total 0.2b remaining (44.8%)

Threshold costs 0.2b (44.8%)

Compiler

Compiled 10370 to 8694 computations (16.2% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0138257
1138257

end0.0ms (0%)

sample50.1s (65.1%)

Algorithm
intervals
Results
43.0s3893×body8192exit
2.4s8000×body128valid
223.0ms11993×pre128true
32.0ms100×body128invalid
Compiler

Compiled 5355 to 4490 computations (16.2% saved)

Profiling

Loading profile data...