Details

analyze1.6s (1.1%)

Algorithm

1×

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

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.4s (1%)

Algorithm

1×

intervals

Results

1.3s	122×	body	8192	exit
74.0ms	256×	body	128	valid
7.0ms	382×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify137.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune16.0ms (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

Error

1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize52.0ms (0%)

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)))

rewrite106.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1783`
23×	`add-log-exp_binary64_1822`
14×	`frac-add_binary64_1791`
13×	`distribute-lft-out_binary64_1734` `sum-log_binary64_1874`
10×	`add-exp-log_binary64_1821`
9×	`add-cbrt-cube_binary64_1819` `pow1_binary64_1844`
7×	`prod-exp_binary64_1832`
6×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
5×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
4×	`associate-r_binary64_1723`
3×	`cbrt-unprod_binary64_1816`
2×	`+-commutative_binary64_1713` `associate-+l+_binary64_1716` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854`
1×	`associate-r/_binary64_1725` `exp-sum_binary64_1829` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `associate-l_binary64_1724` `associate-l/_binary64_1726` `sqrt-prod_binary64_1799` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 74

Calls

4 calls:

52.0ms	(+.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)))
21.0ms	(+.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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series146.0ms (0.1%)

Counts

4 → 10

Calls

4 calls:

99.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
33.0ms	(+.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)))
14.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4912	3345
1	4912	3345

prune481.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Error

0.3b

Counts

86 → 5

Compiler

Compiled 7706 to 5962 computations (22.6% saved)

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

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	(.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)))))

rewrite171.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`associate-*r/_binary64_1725`
68×	`frac-times_binary64_1793`
64×	`frac-add_binary64_1791`
60×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
43×	`flip3--_binary64_1787` `flip--_binary64_1758`
35×	`associate-*l/_binary64_1726`
13×	`add-sqr-sqrt_binary64_1805`
12×	`add-exp-log_binary64_1821`
11×	`add-cbrt-cube_binary64_1819` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
9×	`add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
8×	`prod-exp_binary64_1832`
6×	`distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733` `add-log-exp_binary64_1822`
4×	`cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
3×	`pow-prod-down_binary64_1854`
2×	`associate-+r+_binary64_1715` `associate-+l+_binary64_1716` `*-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `sub-neg_binary64_1776`
1×	`difference-of-squares_binary64_1752` `+-commutative_binary64_1713` `exp-sum_binary64_1829` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `sqrt-prod_binary64_1799` `sum-log_binary64_1874` `unswap-sqr_binary64_1751` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 147

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))
29.0ms	(+.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)))))
21.0ms	(.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))

series176.0ms (0.1%)

Counts

4 → 10

Calls

4 calls:

99.0ms	(.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 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))
36.0ms	(+.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))

simplify191.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5852	16162

prune4.1s (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	157	5	162

Error

0.3b

Counts

162 → 5

Compiler

Compiled 34031 to 27804 computations (18.3% saved)

localize103.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
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))
2.0b	(+.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 -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 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))

rewrite1.1s (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

1456×	`frac-times_binary64_1793`
1197×	`associate-*r/_binary64_1725`
706×	`flip3--_binary64_1787` `flip--_binary64_1758`
703×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
676×	`frac-add_binary64_1791`
417×	`associate-*l/_binary64_1726`
102×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
84×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
72×	`times-frac_binary64_1789`
48×	`add-cube-cbrt_binary64_1818`
24×	`difference-of-squares_binary64_1752`
14×	`add-exp-log_binary64_1821`
12×	`distribute-lft-in_binary64_1732` `distribute-lft-out--_binary64_1735` `distribute-rgt-in_binary64_1733`
10×	`add-cbrt-cube_binary64_1819`
9×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729` `associate-+l+_binary64_1716`
7×	`prod-exp_binary64_1832` `pow-exp_binary64_1851`
6×	`add-log-exp_binary64_1822`
4×	`associate-+r+_binary64_1715` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `sub-neg_binary64_1776` `associate-r_binary64_1723`
3×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `cbrt-unprod_binary64_1816` `pow-unpow_binary64_1860` `unpow3_binary64_1849` `pow-to-exp_binary64_1852`
2×	`sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `cube-div_binary64_1812`
1×	`+-commutative_binary64_1713` `exp-sum_binary64_1829` `rem-cube-cbrt_binary64_1806` `pow-sub_binary64_1859` `pow1/2_binary64_1863` `associate-l_binary64_1724` `sqrt-prod_binary64_1799` `*-commutative_binary64_1714` `sum-log_binary64_1874` `div-exp_binary64_1834` `pow-pow_binary64_1855`

Counts

4 → 860

Calls

4 calls:

80.0ms	(+.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 -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 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))
16.0ms	(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))

series374.0ms (0.2%)

Counts

4 → 10

Calls

4 calls:

238.0ms	(+.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 -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 (+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (-.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 6) (*.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3)))) (+.f64 2 z))))
100.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
17.0ms	(pow.f64 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3) 3)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify3.5s (2.3%)

Algorithm

1×	egg-herbie

Counts

870 → 870

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5244	310084

Details

analyze1.6s (1.1%)

sample1.4s (1%)

simplify137.0ms (0.1%)

prune16.0ms (0%)

localize52.0ms (0%)

rewrite106.0ms (0.1%)

series146.0ms (0.1%)

simplify84.0ms (0.1%)

prune481.0ms (0.3%)

localize80.0ms (0.1%)

rewrite171.0ms (0.1%)

series176.0ms (0.1%)

simplify191.0ms (0.1%)

prune4.1s (2.7%)

localize103.0ms (0.1%)

rewrite1.1s (0.7%)

series374.0ms (0.2%)

simplify3.5s (2.3%)

prune2.3min (90.7%)

Profiling