Details

Time bar (total: 2.5min)

analyze1.9s (1.2%)

Algorithm
1×search
2×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)

sample1.6s (1.1%)

Algorithm
1×intervals
Results
1.5s134×body8192exit
74.0ms256×body128valid
10.0ms394×pre128true
1.0ms4×body128invalid
Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify50.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
04804115
14804115

prune16.0ms (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)

localize54.0ms (0%)

Local error

Found 4 expressions with local error:

4.8b
(-.f64 (-.f64 1 z) 1)
4.8b
(-.f64 (-.f64 1 z) 1)
4.8b
(-.f64 (-.f64 1 z) 1)
4.8b
(-.f64 (-.f64 1 z) 1)

rewrite998.0ms (0.7%)

Algorithm
1×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
8×sub-neg_binary64_2458 difference-of-squares_binary64_2434
4×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:

11.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
9.0ms
(-.f64 (-.f64 1 z) 1)
Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series216.0ms (0.1%)

Error
1.8b
Counts
4 → 12
Calls

4 calls:

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

Compiled 4356 to 3833 computations (12% saved)

simplify81.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05392704

prune1.4s (0.9%)

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)

localize55.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 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)))

rewrite469.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Error
1.1b
Rules
19×*-un-lft-identity_binary64_2465
18×add-log-exp_binary64_2504
10×add-exp-log_binary64_2503
9×sum-log_binary64_2556 pow1_binary64_2526 add-cbrt-cube_binary64_2501 distribute-lft-out_binary64_2416
8×frac-add_binary64_2473
7×prod-exp_binary64_2514
5×add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 flip3-+_binary64_2468 flip-+_binary64_2439
4×associate-*r*_binary64_2405
3×cbrt-unprod_binary64_2498
2×associate-+l+_binary64_2398 +-commutative_binary64_2395 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
1×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 → 70
Calls

4 calls:

40.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
23.0ms
(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
17.0ms
(*.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 6200 to 4800 computations (22.6% saved)

series449.0ms (0.3%)

Error
1.2b
Counts
4 → 30
Calls

4 calls:

204.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
69.0ms
(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
62.0ms
(+.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 4904 to 3924 computations (20% saved)

simplify67.0ms (0%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
057602977

prune493.0ms (0.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New946100
Fresh000
Picked101
Done101
Total966102
Error
1.1b
Counts
102 → 6
Compiler

Compiled 8617 to 6615 computations (23.2% saved)

localize67.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (/.f64 848079078717083/1099511627776 (-.f64 3 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 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (*.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))

rewrite1.1s (0.7%)

Algorithm
1×rewrite-expression-head
Error
0.3b
Rules
21×associate-*r/_binary64_2407
17×frac-add_binary64_2473
16×flip3-+_binary64_2468 flip-+_binary64_2439
10×add-exp-log_binary64_2503
9×pow1_binary64_2526 add-cbrt-cube_binary64_2501
8×add-log-exp_binary64_2504 frac-times_binary64_2475
7×*-un-lft-identity_binary64_2465 prod-exp_binary64_2514
6×flip3--_binary64_2469 flip--_binary64_2440
5×add-cube-cbrt_binary64_2500 add-sqr-sqrt_binary64_2487 associate-*l/_binary64_2408
4×associate-*r*_binary64_2405
3×cbrt-unprod_binary64_2498
2×sum-log_binary64_2556 distribute-rgt-in_binary64_2415 associate-+l+_binary64_2398 distribute-lft-in_binary64_2414 associate-+r+_binary64_2397 +-commutative_binary64_2395 pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483
1×pow1/2_binary64_2545 sqrt-prod_binary64_2481 pow-to-exp_binary64_2534 pow-exp_binary64_2533 pow-sub_binary64_2541 associate-*l*_binary64_2406 exp-sum_binary64_2511 *-commutative_binary64_2396 distribute-lft-out_binary64_2416
Counts
4 → 76
Calls

4 calls:

82.0ms
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
30.0ms
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
17.0ms
(*.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 11231 to 9048 computations (19.4% saved)

series540.0ms (0.4%)

Error
1.1b
Counts
4 → 24
Calls

4 calls:

203.0ms
(*.f64 (*.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
173.0ms
(+.f64 (/.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (*.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z))))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
64.0ms
(+.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 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))
0.0ms
(sqrt.f64 (*.f64 PI.f64 2))
Compiler

Compiled 4862 to 3928 computations (19.2% saved)

simplify103.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
051086361

prune1.1s (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New964100
Fresh325
Picked011
Done000
Total997106
Error
0.3b
Counts
106 → 7
Compiler

Compiled 13259 to 10577 computations (20.2% saved)

localize97.0ms (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
(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
1.0b
(sqrt.f64 (*.f64 PI.f64 2))
2.0b
(+.f64 (*.f64 (*.f64 (-.f64 8 (pow.f64 z 3)) (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))) (*.f64 (*.f64 (+.f64 4 (*.f64 z (+.f64 z 2))) (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (/.f64 37594250663499681145595835333358632934967732472689520573060561639594041945026298690821877625/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 (pow.f64 (-.f64 1 z) 3))))) (*.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (*.f64 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))))

rewrite2.3min (92.8%)

Algorithm
1×rewrite-expression-head
Rules
1456×frac-times_binary64_2475
885×associate-*r/_binary64_2407
729×associate-*l/_binary64_2408
708×flip3--_binary64_2469 flip--_binary64_2440
703×flip3-+_binary64_2468 flip-+_binary64_2439
676×frac-add_binary64_2473
154×*-un-lft-identity_binary64_2465
130×add-sqr-sqrt_binary64_2487
120×times-frac_binary64_2471
102×unpow-prod-down_binary64_2544 cube-prod_binary64_2493
70×add-cube-cbrt_binary64_2500
64×cancel-sign-sub-inv_binary64_2431
62×associate-+l+_binary64_2398
40×difference-of-squares_binary64_2434
39×distribute-rgt-in_binary64_2415 distribute-lft-in_binary64_2414
20×distribute-lft-out--_binary64_2417
14×add-exp-log_binary64_2503
12×distribute-lft-out_binary64_2416 associate-/r/_binary64_2411
10×add-cbrt-cube_binary64_2501
9×pow1_binary64_2526
8×associate-+r+_binary64_2397
7×pow-exp_binary64_2533 prod-exp_binary64_2514
6×add-log-exp_binary64_2504 sub-neg_binary64_2458 div-inv_binary64_2462
4×associate-*r*_binary64_2405
3×unpow3_binary64_2531 cube-mult_binary64_2495 sqr-pow_binary64_2437 pow-unpow_binary64_2542 pow-to-exp_binary64_2534 cbrt-unprod_binary64_2498
2×pow-prod-down_binary64_2536 sqrt-pow1_binary64_2483 cube-div_binary64_2494
1×sum-log_binary64_2556 +-commutative_binary64_2395 pow1/2_binary64_2545 sqrt-prod_binary64_2481 pow-pow_binary64_2537 div-exp_binary64_2516 rem-cube-cbrt_binary64_2488 pow-sub_binary64_2541 associate-*l*_binary64_2406 exp-sum_binary64_2511 *-commutative_binary64_2396
Counts
4 → 918
Calls

4 calls:

128.0ms
(+.f64 (*.f64 (*.f64 (-.f64 8 (pow.f64 z 3)) (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3))) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))) (*.f64 (*.f64 (+.f64 4 (*.f64 z (+.f64 z 2))) (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (/.f64 37594250663499681145595835333358632934967732472689520573060561639594041945026298690821877625/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 (pow.f64 (-.f64 1 z) 3))))) (*.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (*.f64 (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)) (/.f64 (+.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) -3349966604360028729823972713705/4951760157141521099596496896) (-.f64 1 z)))))))
17.0ms
(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
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))

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