Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample16.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4564	19
1	4564	19

prune2.0ms

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
17.9b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 89

Calls

4 calls:

3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
17.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
9.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
7.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4819	1588
1	4819	1588

prune94.0ms

Filtered

74 candidates to 101 candidates (-36.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Merged error: 0b

Counts

102 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992) (*.f64 x -6369080665019903/9007199254740992))
0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.1b	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
17.9b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`associate-l_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

10.0ms	(+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992) (*.f64 x -6369080665019903/9007199254740992))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
10.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
10.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992) (*.f64 x -6369080665019903/9007199254740992))
7.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
6.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
6.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5539	1962

prune114.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0b

Counts

114 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)))
0.6b	(.f64 (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))) (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x))))
17.9b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
17.9b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

63×	`pow1_binary64`
38×	`pow-prod-down_binary64`
37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`times-frac_binary64`
18×	`pow1/2_binary64` `sqrt-pow1_binary64`
16×	`associate-*r/_binary64`
14×	`sqrt-div_binary64`
13×	`sqrt-prod_binary64`
10×	`associate-r_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`pow-prod-up_binary64`
7×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
6×	`associate-/r_binary64` `sqrt-unprod_binary64` `associate-/l_binary64` `pow-sqr_binary64`
4×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
2×	`cbrt-undiv_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`swap-sqr_binary64` `rem-square-sqrt_binary64` `distribute-lft-out--_binary64` `pow2_binary64`

Counts

4 → 149

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)))
33.0ms	(.f64 (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))) (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x))))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)))
14.0ms	(.f64 (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))) (.f64 (sqrt.f64 6369080665019903/9007199254740992) (sqrt.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x))))
5.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4901	3510
1	4901	3510

prune242.0ms

Filtered

103 candidates to 161 candidates (-56.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	161	4	165

Merged error: 0b

Counts

165 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.1b	(.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3))
17.9b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
21.7b	(cbrt.f64 (.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`associate-r_binary64`
18×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
11×	`times-frac_binary64`
10×	`add-cbrt-cube_binary64`
7×	`unpow-prod-down_binary64` `cube-prod_binary64`
6×	`pow1_binary64` `associate-r/_binary64` `associate-l*_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `cube-div_binary64` `prod-exp_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`cbrt-div_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `cbrt-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 103

Calls

4 calls:

6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
17.0ms	(.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
14.0ms	(cbrt.f64 (.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
10.0ms	(.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3))
5.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
9.0ms	(cbrt.f64 (.f64 258362957859890061108688731537891632215118627327/730750818665451459101842416358141509827966271488 (pow.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) 3)))

simplify78.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5645	2192

prune113.0ms

Filtered

82 candidates to 115 candidates (-40.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	115	4	119

Merged error: 0b

Counts

119 → 4

regimes64.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample448.0ms

Algorithm

intervals

Results

354.0ms

8000×

body

valid

Details

analyze4.0ms

sample16.0ms

simplify104.0ms

prune2.0ms

localize11.0ms

rewrite37.0ms

series25.0ms

simplify75.0ms

prune94.0ms

localize13.0ms

rewrite40.0ms

series27.0ms

simplify71.0ms

prune114.0ms

localize15.0ms

rewrite73.0ms

series40.0ms

simplify91.0ms

prune242.0ms

localize17.0ms

rewrite48.0ms

series34.0ms

simplify78.0ms

prune113.0ms

regimes64.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample448.0ms

Profiling