Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
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

sample2.3s

Algorithm

intervals

Results

2.2s	104×	body	8192	exit
81.0ms	256×	body	128	valid
6.0ms	361×	pre	128	true
0.0ms	1×	body	128	invalid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4815	115
1	4815	115

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 2

localize52.0ms

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)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
23×	`add-log-exp_binary64`
14×	`frac-add_binary64`
13×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
7×	`prod-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

50.0ms	(+.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)))
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))
25.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series270.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(+.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)))
192.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
28.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify97.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4913	3345
1	4913	3345

prune323.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.3b

Counts

86 → 7

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
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 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

36×	`frac-times_binary64`
35×	`associate-*r/_binary64`
31×	`associate-*l/_binary64`
24×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
19×	`add-exp-log_binary64`
18×	`pow1_binary64` `add-cbrt-cube_binary64`
16×	`frac-add_binary64`
13×	`prod-exp_binary64`
9×	`cbrt-unprod_binary64`
8×	`pow-prod-down_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`associate-r_binary64`
4×	`associate-l_binary64`
2×	`associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `pow-sub_binary64` `exp-sum_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 110

Calls

4 calls:

18.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
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)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
31.0ms	(+.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)))))

series308.0ms

Counts

4 → 10

Calls

4 calls:

53.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
186.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
69.0ms	(+.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)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5799	7789

prune2.0s

Filtered

103 candidates to 120 candidates (-16.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	121	6	127

Merged error: 0.2b

Counts

127 → 6

localize113.0ms

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 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (.f64 z z)))) (.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (/.f64 37594250663499681145595835333358632934967732472689520573060561639594041945026298690821877625/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 (pow.f64 (-.f64 1 z) 3)))) (.f64 (.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (.f64 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))))) (+.f64 2 z))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1456×	`frac-times_binary64`
1197×	`associate-*r/_binary64`
706×	`flip3--_binary64` `flip--_binary64`
703×	`flip3-+_binary64` `flip-+_binary64`
676×	`frac-add_binary64`
417×	`associate-*l/_binary64`
102×	`unpow-prod-down_binary64` `cube-prod_binary64`
84×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
72×	`times-frac_binary64`
48×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
14×	`add-exp-log_binary64`
12×	`distribute-lft-out--_binary64`
10×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64`
7×	`prod-exp_binary64` `pow-exp_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64` `associate-r_binary64` `associate-+l+_binary64` `div-inv_binary64` `associate-+r+_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-prod-down_binary64` `cube-div_binary64` `sqrt-pow1_binary64`
1×	`pow1/2_binary64` `pow-pow_binary64` `associate-l_binary64` `pow-sub_binary64` `rem-cube-cbrt_binary64` `exp-sum_binary64` `div-exp_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 856

Calls

4 calls:

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)))
18.0ms	(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
86.0ms	(+.f64 (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (.f64 z z)))) (.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (/.f64 37594250663499681145595835333358632934967732472689520573060561639594041945026298690821877625/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 (pow.f64 (-.f64 1 z) 3)))) (.f64 (.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (.f64 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))))) (+.f64 2 z))))

series656.0ms

Counts

4 → 10

Calls

4 calls:

169.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
31.0ms	(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
456.0ms	(+.f64 (.f64 (-.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))) (.f64 (+.f64 5678427533549715134633014896091006013944685176209383187104014791596740501419439436594122795778098490726927930959796456992046408203125/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552 (pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)) (-.f64 4 (.f64 z z)))) (.f64 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (/.f64 37594250663499681145595835333358632934967732472689520573060561639594041945026298690821877625/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 (pow.f64 (-.f64 1 z) 3)))) (.f64 (.f64 -5537752839100187/4398046511104 (-.f64 100433627766110534469812883687683627375011214126104286600625/100433627766186892221372630771322662657637687111424552206336 (.f64 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))))) (+.f64 2 z))))

simplify4.0s

Algorithm

egg-herbie

Counts

866 → 866

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5233	302533

prune2.3min

Filtered: 759 candidates to 866 candidates (-14.1%)

Details

analyze1.7s

sample2.3s

simplify36.0ms

prune15.0ms

localize52.0ms

rewrite114.0ms

series270.0ms

simplify97.0ms

prune323.0ms

localize83.0ms

rewrite122.0ms

series308.0ms

simplify118.0ms

prune2.0s

localize113.0ms

rewrite1.1s

series656.0ms

simplify4.0s

prune2.3min

Profiling