Details

analyze9.0ms (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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify338.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	4600	28
1	4600	28

prune5.0ms (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)

localize23.0ms (0.3%)

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)))
12.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2828`
20×	`*-un-lft-identity_binary64_2806`
18×	`add-cube-cbrt_binary64_2841`
10×	`add-exp-log_binary64_2844` `times-frac_binary64_2812` `add-cbrt-cube_binary64_2842`
9×	`associate-r_binary64_2746`
8×	`pow1_binary64_2867`
6×	`associate-l_binary64_2747` `cancel-sign-sub-inv_binary64_2772` `add-log-exp_binary64_2845`
5×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756`
4×	`flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-*r/_binary64_2748`
3×	`associate-/r_binary64_2750` `associate-/l_binary64_2751`
2×	`associate-/l/_binary64_2753` `*-commutative_binary64_2737` `prod-exp_binary64_2855` `sub-neg_binary64_2799` `cbrt-unprod_binary64_2839` `difference-of-squares_binary64_2775` `associate-/r/_binary64_2752` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`
1×	`div-inv_binary64_2803` `div-exp_binary64_2857` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `distribute-lft-out--_binary64_2758` `sum-log_binary64_2897` `flip--_binary64_2781` `clear-num_binary64_2805` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 95

Calls

4 calls:

29.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
13.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
11.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
6.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series191.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
59.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
36.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
32.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

simplify145.0ms (2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4809	2543
1	4809	2543

prune277.0ms (3.9%)

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 3023 to 2422 computations (19.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
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)
12.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_2828`
22×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
19×	`times-frac_binary64_2812`
18×	`associate-l_binary64_2747`
13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `associate-r_binary64_2746`
5×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
4×	`associate-/r/_binary64_2752`
3×	`associate-/r_binary64_2750` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `associate-/l_binary64_2751` `unswap-sqr_binary64_2774`
2×	`associate-/l/_binary64_2753` `div-inv_binary64_2803` `div-exp_binary64_2857` `-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `associate-r/_binary64_2748` `pow-prod-down_binary64_2877`
1×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `sum-log_binary64_2897` `clear-num_binary64_2805` `associate-*l/_binary64_2749` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 98

Calls

4 calls:

20.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
13.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
12.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series171.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
39.0ms	(.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 6369080665019903/9007199254740992)
37.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
33.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

simplify229.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (170.0ms)

Iter	Nodes	Cost
0	4856	2543
1	4856	2543

prune360.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	110	4	114

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 3378 to 2768 computations (18.1% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
1.9b	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
4.7b	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

rewrite150.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_2812`
166×	`add-sqr-sqrt_binary64_2828`
163×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
153×	`sqrt-prod_binary64_2822`
30×	`associate-/r*_binary64_2750`
20×	`sqrt-div_binary64_2823`
17×	`associate-/r/_binary64_2752`
13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
12×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
9×	`div-inv_binary64_2803` `associate-/l*_binary64_2751`
7×	`pow1_binary64_2867`
4×	`associate-/l/_binary64_2753` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `add-log-exp_binary64_2845`
3×	`associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`clear-num_binary64_2805` `associate-*r/_binary64_2748` `frac-2neg_binary64_2817`
1×	`pow1/2_binary64_2886` `*-commutative_binary64_2737` `distribute-lft-in_binary64_2755` `sqrt-pow1_binary64_2824` `distribute-rgt-in_binary64_2756` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `rem-sqrt-square_binary64_2819` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`

Counts

4 → 271

Calls

4 calls:

32.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))
16.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
11.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

series204.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
61.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
46.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))
29.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

simplify398.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4902	13440
1	4902	13440

prune1.8s (25%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	283	4	287

Merged error: 0b

Counts

287 → 4

Compiler

Compiled 11981 to 9924 computations (17.2% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.2b	(pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3)
12.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
19.3b	(cbrt.f64 (pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3))

rewrite77.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_2828`
16×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
11×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
9×	`times-frac_binary64_2812` `pow1_binary64_2867`
8×	`cbrt-prod_binary64_2837`
6×	`associate-*r/_binary64_2748`
4×	`add-log-exp_binary64_2845` `cube-div_binary64_2835`
3×	`associate-l_binary64_2747` `associate-/r_binary64_2750` `pow-unpow_binary64_2883` `flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-r_binary64_2746` `associate-/l_binary64_2751`
2×	`associate-/l/_binary64_2753` `pow-exp_binary64_2874` `cbrt-div_binary64_2838` `flip3--_binary64_2810` `cube-prod_binary64_2834` `unpow3_binary64_2872` `pow-pow_binary64_2878` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unpow-prod-down_binary64_2885` `flip--_binary64_2781` `sqr-pow_binary64_2778` `cube-mult_binary64_2836` `associate-/r/_binary64_2752` `pow-prod-down_binary64_2877` `rem-cube-cbrt_binary64_2829`
1×	`div-inv_binary64_2803` `pow1/3_binary64_2888` `div-exp_binary64_2857` `*-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `pow-to-exp_binary64_2875` `clear-num_binary64_2805` `rem-cbrt-cube_binary64_2830` `unswap-sqr_binary64_2774` `frac-2neg_binary64_2817`

Counts

4 → 96

Calls

4 calls:

28.0ms	(pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3)
14.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
12.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(cbrt.f64 (pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3))

series244.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
67.0ms	(pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3)
60.0ms	(cbrt.f64 (pow.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x)) 3))
43.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5022	3093

prune324.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Merged error: 0b

Counts

112 → 4

Compiler

Compiled 3353 to 2735 computations (18.4% saved)

regimes272.0ms (3.8%)

Compiler: Compiled 1514 to 1268 computations (16.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	31
1	29	31

end0.0ms (0%)

sample1.5s (21.1%)

Algorithm

1×

intervals

Results

666.0ms

8000×

body

128

valid

Compiler

Compiled 401 to 338 computations (15.7% saved)

Details

analyze9.0ms (0.1%)

sample31.0ms (0.4%)

simplify338.0ms (4.7%)

prune5.0ms (0.1%)

localize23.0ms (0.3%)

rewrite76.0ms (1.1%)

series191.0ms (2.7%)

simplify145.0ms (2%)

prune277.0ms (3.9%)

localize27.0ms (0.4%)

rewrite74.0ms (1%)

series171.0ms (2.4%)

simplify229.0ms (3.2%)

prune360.0ms (5.1%)

localize35.0ms (0.5%)

rewrite150.0ms (2.1%)

series204.0ms (2.9%)

simplify398.0ms (5.6%)

prune1.8s (25%)

localize30.0ms (0.4%)

rewrite77.0ms (1.1%)

series244.0ms (3.4%)

simplify138.0ms (1.9%)

prune324.0ms (4.5%)

regimes272.0ms (3.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (21.1%)

Profiling