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)

sample17.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify274.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

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)

localize11.0ms (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))
0.0b	(.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)))))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2457`
18×	`*-un-lft-identity_binary64_2436`
16×	`add-cube-cbrt_binary64_2468`
10×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `times-frac_binary64_2442`
9×	`associate-r_binary64_2378`
8×	`pow1_binary64_2494`
6×	`add-log-exp_binary64_2472` `associate-l_binary64_2379`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-*r/_binary64_2380`
3×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
2×	`prod-exp_binary64_2482` `distribute-rgt-in_binary64_2388` `*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `associate-/r/_binary64_2384` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `associate-/l/_binary64_2385` `distribute-lft-in_binary64_2387` `sub-neg_binary64_2429` `difference-of-squares_binary64_2405`
1×	`cbrt-undiv_binary64_2467` `distribute-lft-out--_binary64_2390` `div-inv_binary64_2433` `div-exp_binary64_2484` `flip3--_binary64_2440` `sum-log_binary64_2524` `clear-num_binary64_2435` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `flip--_binary64_2411`

Counts

4 → 89

Calls

4 calls:

15.0ms	(.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)))))
7.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
4.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series221.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(.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))
43.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
40.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

simplify97.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4959	2363
1	4959	2363

prune166.0ms (4.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Merged error: 0b

Counts

102 → 3

Compiler

Compiled 2846 to 2279 computations (19.9% saved)

localize15.0ms (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))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_2457`
45×	`times-frac_binary64_2442`
44×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
36×	`cbrt-prod_binary64_2464`
30×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461`
11×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
10×	`associate-/r/_binary64_2384`
7×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `pow1_binary64_2494`
5×	`div-inv_binary64_2433`
4×	`add-log-exp_binary64_2472`
3×	`associate-/l_binary64_2383` `pow-unpow_binary64_2510` `associate-/r_binary64_2382` `associate-r_binary64_2378` `associate-l_binary64_2379`
2×	`cbrt-undiv_binary64_2467` `rem-cube-cbrt_binary64_2458` `div-exp_binary64_2484` `associate-*r/_binary64_2380` `cube-mult_binary64_2463` `pow-exp_binary64_2501` `unpow3_binary64_2499` `sqr-pow_binary64_2408` `associate-/l/_binary64_2385` `cube-div_binary64_2462`
1×	`pow1/3_binary64_2515` `prod-exp_binary64_2482` `distribute-rgt-in_binary64_2388` `*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `rem-cbrt-cube_binary64_2459` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-pow_binary64_2505` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387` `cbrt-div_binary64_2465`

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)
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)))

series200.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
46.0ms	(pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3)
43.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3))
38.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify91.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5705	5038

prune348.0ms (9.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Merged error: 0b

Counts

164 → 3

Compiler

Compiled 5106 to 4204 computations (17.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (.f64 x -6369080665019903/9007199254740992))
0.0b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.2b	(*.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)
15.3b	(/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2457`
16×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
10×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
9×	`times-frac_binary64_2442`
8×	`pow1_binary64_2494`
6×	`add-log-exp_binary64_2472` `associate-r_binary64_2378` `associate-l_binary64_2379`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
3×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
2×	`prod-exp_binary64_2482` `-commutative_binary64_2369` `pow-prod-down_binary64_2504` `associate-/r/_binary64_2384` `associate-r/_binary64_2380` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `associate-/l/_binary64_2385`
1×	`cbrt-undiv_binary64_2467` `distribute-rgt-in_binary64_2388` `div-inv_binary64_2433` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387`

Counts

4 → 82

Calls

4 calls:

11.0ms	(+.f64 (/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (.f64 x -6369080665019903/9007199254740992))
7.0ms	(/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
4.0ms	(*.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)

series204.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
58.0ms	(+.f64 (/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (.f64 x -6369080665019903/9007199254740992))
40.0ms	(/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
20.0ms	(*.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)

simplify99.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5337	2017

prune138.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	3	97

Merged error: 0b

Counts

97 → 3

Compiler

Compiled 2526 to 2018 computations (20.1% 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	(.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))
0.2b	(.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)))
15.3b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite61.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2457`
21×	`*-un-lft-identity_binary64_2436`
19×	`add-cube-cbrt_binary64_2468`
15×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `associate-l_binary64_2379`
13×	`pow1_binary64_2494`
10×	`associate-r_binary64_2378` `times-frac_binary64_2442`
7×	`sqrt-prod_binary64_2451`
5×	`prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466`
4×	`add-log-exp_binary64_2472` `associate-r/_binary64_2380` `associate-l/_binary64_2381`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `-commutative_binary64_2369` `associate-/l_binary64_2383` `associate-/r*_binary64_2382` `unswap-sqr_binary64_2404`
2×	`associate-/r/_binary64_2384` `flip3--_binary64_2440` `associate-/l/_binary64_2385` `flip--_binary64_2411` `difference-of-squares_binary64_2405`
1×	`cbrt-undiv_binary64_2467` `distribute-lft-out--_binary64_2390` `distribute-rgt-in_binary64_2388` `div-inv_binary64_2433` `div-exp_binary64_2484` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387`

Counts

4 → 103

Calls

4 calls:

19.0ms	(.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)))
17.0ms	(.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)))

series293.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(.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)))
77.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
73.0ms	(.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))
40.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5197	3206

prune213.0ms (5.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	115	3	118

Merged error: 0b

Counts

118 → 3

Compiler

Compiled 3623 to 2979 computations (17.8% saved)

regimes157.0ms (4.2%)

Compiler: Compiled 1767 to 1487 computations (15.8% 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%)

sample912.0ms (24.2%)

Algorithm

1×

intervals

Results

358.0ms

8000×

body

128

valid

Compiler

Compiled 505 to 427 computations (15.4% saved)

Details

analyze5.0ms (0.1%)

sample17.0ms (0.5%)

simplify274.0ms (7.3%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite41.0ms (1.1%)

series221.0ms (5.9%)

simplify97.0ms (2.6%)

prune166.0ms (4.4%)

localize15.0ms (0.4%)

rewrite50.0ms (1.3%)

series200.0ms (5.3%)

simplify91.0ms (2.4%)

prune348.0ms (9.2%)

localize14.0ms (0.4%)

rewrite36.0ms (0.9%)

series204.0ms (5.4%)

simplify99.0ms (2.6%)

prune138.0ms (3.7%)

localize16.0ms (0.4%)

rewrite61.0ms (1.6%)

series293.0ms (7.8%)

simplify88.0ms (2.3%)

prune213.0ms (5.6%)

regimes157.0ms (4.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample912.0ms (24.2%)

Profiling