Details

analyze5.0ms (0.2%)

Algorithm

1×

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

Compiler

Compiled 20 to 17 computations (15% saved)

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify300.0ms (10%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	1225	28
1	1225	28

prune3.0ms (0.1%)

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

Compiler

Compiled 38 to 32 computations (15.8% saved)

localize13.0ms (0.4%)

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))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
15.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite43.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`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` `cancel-sign-sub-inv_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_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` `associate-/r/_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 → 95

Calls

4 calls:

16.0ms	(.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 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series222.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
58.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
42.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
39.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify92.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4924	2543
1	4924	2543

prune252.0ms (8.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Merged error: 0.0b

Counts

108 → 4

Compiler

Compiled 4468 to 3648 computations (18.4% saved)

localize14.0ms (0.5%)

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))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.2b	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
15.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite49.0ms (1.6%)

Algorithm

1×	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:

11.0ms	(.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 (/.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 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))

series220.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
58.0ms	(+.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))
43.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
41.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)

simplify87.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4892	2933
1	4892	2933

prune184.0ms (6.1%)

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: 0.0b

Counts

114 → 4

Compiler

Compiled 3404 to 2781 computations (18.3% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.2b	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992)))
15.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite69.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
13×	`pow1_binary64`
10×	`associate-r_binary64` `times-frac_binary64`
7×	`sqrt-prod_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l/_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 103

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992)))
19.0ms	(.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))

series288.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 (sqrt.f64 6369080665019903/9007199254740992) (.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992)))
80.0ms	(.f64 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x) (sqrt.f64 6369080665019903/9007199254740992))
78.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
36.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5104	3206

prune208.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	115	4	119

Merged error: 0.0b

Counts

119 → 4

Compiler

Compiled 3632 to 2987 computations (17.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b

(*.f64 x (+.f64 (*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032) -12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))

0.2b

(*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032)

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
2×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`

Counts

2 → 40

Calls

2 calls:

10.0ms

(*.f64 x (+.f64 (*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032) -12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))

4.0ms

(*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032)

series89.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

66.0ms

(*.f64 x (+.f64 (*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032) -12187874727506178016857224307619355972369422289/5708990770823839524233143877797980545530986496))

22.0ms

(*.f64 x 69091798784915278825083492018586279182693231274342218172050955/51422017416287688817342786954917203280710495801049370729644032)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5166	440

prune37.0ms (1.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	46	4	50

Merged error: 0.0b

Counts

50 → 4

Compiler

Compiled 608 to 476 computations (21.7% saved)

regimes45.0ms (1.5%)

Compiler: Compiled 290 to 248 computations (14.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	28
1	34	28

end0.0ms (0%)

sample580.0ms (19.3%)

Algorithm

1×

intervals

Results

357.0ms

8000×

body

128

valid

Compiler

Compiled 111 to 96 computations (13.5% saved)

Details

analyze5.0ms (0.2%)

sample17.0ms (0.6%)

simplify300.0ms (10%)

prune3.0ms (0.1%)

localize13.0ms (0.4%)

rewrite43.0ms (1.4%)

series222.0ms (7.4%)

simplify92.0ms (3.1%)

prune252.0ms (8.4%)

localize14.0ms (0.5%)

rewrite49.0ms (1.6%)

series220.0ms (7.3%)

simplify87.0ms (2.9%)

prune184.0ms (6.1%)

localize15.0ms (0.5%)

rewrite69.0ms (2.3%)

series288.0ms (9.6%)

simplify82.0ms (2.7%)

prune208.0ms (6.9%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series89.0ms (2.9%)

simplify67.0ms (2.2%)

prune37.0ms (1.2%)

regimes45.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample580.0ms (19.3%)

Profiling