Details

analyze5.0ms (0.1%)

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)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify285.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

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)

localize15.0ms (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))
0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
15.3b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite44.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2853`
20×	`*-un-lft-identity_binary64_2831`
18×	`add-cube-cbrt_binary64_2866`
10×	`add-cbrt-cube_binary64_2867` `times-frac_binary64_2837` `add-exp-log_binary64_2869`
9×	`associate-r_binary64_2771`
8×	`pow1_binary64_2892`
6×	`add-log-exp_binary64_2870` `cancel-sign-sub-inv_binary64_2797` `associate-l_binary64_2772`
5×	`distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`
4×	`flip3-+_binary64_2834` `flip-+_binary64_2805` `associate-*r/_binary64_2773`
3×	`associate-/l_binary64_2776` `associate-/r_binary64_2775`
2×	`pow-prod-down_binary64_2902` `associate-/l/_binary64_2778` `cbrt-unprod_binary64_2864` `*-commutative_binary64_2762` `sub-neg_binary64_2824` `unswap-sqr_binary64_2799` `prod-exp_binary64_2880` `difference-of-squares_binary64_2800` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `flip3--_binary64_2835` `distribute-lft-out--_binary64_2783` `+-commutative_binary64_2761` `div-exp_binary64_2882` `flip--_binary64_2806` `clear-num_binary64_2830` `sum-log_binary64_2922`

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))
8.0ms	(/.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))

series215.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
61.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
41.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
38.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4910	2543
1	4910	2543

prune261.0ms (7.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Merged error: 0b

Counts

108 → 4

Compiler

Compiled 4611 to 3767 computations (18.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))) x))
0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
15.3b	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

rewrite81.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64_2837`
80×	`add-sqr-sqrt_binary64_2853`
67×	`*-un-lft-identity_binary64_2831`
62×	`add-cube-cbrt_binary64_2866`
21×	`add-exp-log_binary64_2869`
18×	`associate-/r*_binary64_2775`
15×	`add-cbrt-cube_binary64_2867`
13×	`associate-r_binary64_2771`
11×	`associate-/r/_binary64_2777`
9×	`pow1_binary64_2892`
8×	`div-exp_binary64_2882`
7×	`flip3-+_binary64_2834` `div-inv_binary64_2828` `flip-+_binary64_2805`
6×	`cancel-sign-sub-inv_binary64_2797` `associate-l_binary64_2772` `associate-/l*_binary64_2776`
5×	`difference-of-squares_binary64_2800` `distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`
4×	`add-log-exp_binary64_2870` `cbrt-undiv_binary64_2865` `associate-*r/_binary64_2773`
2×	`frac-2neg_binary64_2842` `pow-prod-down_binary64_2902` `associate-/l/_binary64_2778` `1-exp_binary64_2875` `cbrt-unprod_binary64_2864` `*-commutative_binary64_2762` `rec-exp_binary64_2881` `distribute-lft-out--_binary64_2783` `sub-neg_binary64_2824` `unswap-sqr_binary64_2799` `prod-exp_binary64_2880` `clear-num_binary64_2830`
1×	`inv-pow_binary64_2916` `pow-flip_binary64_2905` `flip3--_binary64_2835` `flip--_binary64_2806`

Counts

4 → 172

Calls

4 calls:

33.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))) x))
10.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
9.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
7.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))

series210.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
61.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))) x))
39.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
36.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

simplify131.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4899	5825
1	4899	5825

prune397.0ms (10.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	184	4	188

Merged error: 0b

Counts

188 → 4

Compiler

Compiled 6010 to 4915 computations (18.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.1b	(pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3)
15.3b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
20.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3))

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_2853`
45×	`times-frac_binary64_2837`
44×	`add-cube-cbrt_binary64_2866` `*-un-lft-identity_binary64_2831`
36×	`cbrt-prod_binary64_2862`
30×	`unpow-prod-down_binary64_2910` `cube-prod_binary64_2859`
11×	`add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
10×	`associate-/r/_binary64_2777`
7×	`pow1_binary64_2892` `flip3-+_binary64_2834` `flip-+_binary64_2805`
5×	`div-inv_binary64_2828`
4×	`add-log-exp_binary64_2870`
3×	`pow-unpow_binary64_2908` `associate-r_binary64_2771` `associate-l_binary64_2772` `associate-/l_binary64_2776` `associate-/r_binary64_2775`
2×	`associate-/l/_binary64_2778` `pow-exp_binary64_2899` `sqr-pow_binary64_2803` `cbrt-undiv_binary64_2865` `cube-mult_binary64_2861` `rem-cube-cbrt_binary64_2854` `cube-div_binary64_2860` `div-exp_binary64_2882` `unpow3_binary64_2897` `associate-*r/_binary64_2773`
1×	`frac-2neg_binary64_2842` `pow-prod-down_binary64_2902` `pow-pow_binary64_2903` `cbrt-unprod_binary64_2864` `pow1/3_binary64_2913` `*-commutative_binary64_2762` `rem-cbrt-cube_binary64_2855` `unswap-sqr_binary64_2799` `prod-exp_binary64_2880` `pow-to-exp_binary64_2900` `clear-num_binary64_2830` `distribute-lft-in_binary64_2780` `cbrt-div_binary64_2863` `distribute-rgt-in_binary64_2781`

Counts

4 → 149

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3))
9.0ms	(pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3)
8.0ms	(/.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)))

series197.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
43.0ms	(pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3)
42.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
40.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3))

simplify115.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5214	5038

prune329.0ms (9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Merged error: 0b

Counts

165 → 4

Compiler

Compiled 5116 to 4212 computations (17.7% saved)

localize14.0ms (0.4%)

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)
15.3b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_2853`
22×	`add-cube-cbrt_binary64_2866` `*-un-lft-identity_binary64_2831`
19×	`times-frac_binary64_2837`
18×	`associate-l_binary64_2772`
13×	`add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
8×	`pow1_binary64_2892`
6×	`add-log-exp_binary64_2870` `associate-r_binary64_2771`
5×	`flip3-+_binary64_2834` `flip-+_binary64_2805`
4×	`associate-/r/_binary64_2777`
3×	`cbrt-unprod_binary64_2864` `unswap-sqr_binary64_2799` `prod-exp_binary64_2880` `associate-/l_binary64_2776` `associate-/r_binary64_2775`
2×	`pow-prod-down_binary64_2902` `associate-/l/_binary64_2778` `-commutative_binary64_2762` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `div-exp_binary64_2882` `associate-r/_binary64_2773`
1×	`frac-2neg_binary64_2842` `associate-*l/_binary64_2774` `+-commutative_binary64_2761` `clear-num_binary64_2830` `sum-log_binary64_2922` `distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`

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))
10.0ms	(/.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 (6%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
60.0ms	(+.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))
41.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
38.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify88.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4891	2933
1	4891	2933

prune203.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 3590 to 2939 computations (18.1% saved)

regimes15.0ms (0.4%)

Compiler: Compiled 97 to 83 computations (14.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	31
1	35	31

end0.0ms (0%)

sample579.0ms (15.8%)

Algorithm

1×

intervals

Results

348.0ms

8000×

body

128

valid

Compiler

Compiled 136 to 117 computations (14% saved)

Details

analyze5.0ms (0.1%)

sample21.0ms (0.6%)

simplify285.0ms (7.8%)

prune3.0ms (0.1%)

localize15.0ms (0.4%)

rewrite44.0ms (1.2%)

series215.0ms (5.9%)

simplify93.0ms (2.5%)

prune261.0ms (7.1%)

localize15.0ms (0.4%)

rewrite81.0ms (2.2%)

series210.0ms (5.7%)

simplify131.0ms (3.6%)

prune397.0ms (10.9%)

localize16.0ms (0.4%)

rewrite52.0ms (1.4%)

series197.0ms (5.4%)

simplify115.0ms (3.2%)

prune329.0ms (9%)

localize14.0ms (0.4%)

rewrite50.0ms (1.4%)

series220.0ms (6%)

simplify88.0ms (2.4%)

prune203.0ms (5.6%)

regimes15.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample579.0ms (15.8%)

Profiling