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)

simplify272.0ms (8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

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)

localize12.0ms (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)))
14.6b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite45.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_3131`
18×	`*-un-lft-identity_binary64_3110`
16×	`add-cube-cbrt_binary64_3142`
10×	`times-frac_binary64_3116` `add-exp-log_binary64_3145` `add-cbrt-cube_binary64_3143`
9×	`associate-r_binary64_3052`
8×	`pow1_binary64_3168`
6×	`add-log-exp_binary64_3146` `associate-l_binary64_3053`
4×	`associate-*r/_binary64_3054` `flip3-+_binary64_3113` `flip-+_binary64_3084`
3×	`associate-/r_binary64_3056` `associate-/l_binary64_3057`
2×	`sub-neg_binary64_3103` `prod-exp_binary64_3156` `pow-prod-down_binary64_3178` `cbrt-unprod_binary64_3140` `associate-/l/_binary64_3059` `associate-/r/_binary64_3058` `difference-of-squares_binary64_3079` `*-commutative_binary64_3043` `unswap-sqr_binary64_3078` `distribute-lft-in_binary64_3061` `distribute-rgt-in_binary64_3062`
1×	`+-commutative_binary64_3042` `cbrt-undiv_binary64_3141` `div-exp_binary64_3158` `clear-num_binary64_3109` `sum-log_binary64_3198` `distribute-lft-out--_binary64_3064` `frac-2neg_binary64_3121` `flip3--_binary64_3114` `div-inv_binary64_3107` `flip--_binary64_3085`

Counts

4 → 89

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))

series212.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
57.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
39.0ms	(+.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)))))

simplify96.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4959	2363
1	4959	2363

prune165.0ms (4.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	2	102

Merged error: 0b

Counts

102 → 2

Compiler

Compiled 2878 to 2302 computations (20% saved)

localize13.0ms (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 x 3881060112545747418883236907595/20282409603651670423947251286016)
14.6b	(/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3131`
16×	`add-cube-cbrt_binary64_3142` `*-un-lft-identity_binary64_3110`
10×	`add-exp-log_binary64_3145` `add-cbrt-cube_binary64_3143`
9×	`times-frac_binary64_3116`
8×	`pow1_binary64_3168`
6×	`add-log-exp_binary64_3146` `associate-l_binary64_3053` `associate-r_binary64_3052`
4×	`flip3-+_binary64_3113` `flip-+_binary64_3084`
3×	`associate-/r_binary64_3056` `associate-/l_binary64_3057`
2×	`prod-exp_binary64_3156` `pow-prod-down_binary64_3178` `cbrt-unprod_binary64_3140` `associate-/l/_binary64_3059` `associate-/r/_binary64_3058` `associate-r/_binary64_3054` `-commutative_binary64_3043` `unswap-sqr_binary64_3078`
1×	`+-commutative_binary64_3042` `cbrt-undiv_binary64_3141` `div-exp_binary64_3158` `clear-num_binary64_3109` `sum-log_binary64_3198` `frac-2neg_binary64_3121` `distribute-lft-in_binary64_3061` `distribute-rgt-in_binary64_3062` `div-inv_binary64_3107`

Counts

4 → 82

Calls

4 calls:

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)
3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series180.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
40.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
39.0ms	(/.f64 (+.f64 1034198505402457344669710228355/633825300114114700748351602688 (.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
22.0ms	(*.f64 x 3881060112545747418883236907595/20282409603651670423947251286016)

simplify87.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5364	1660

prune134.0ms (4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	94	2	96

Merged error: 0b

Counts

96 → 2

Compiler

Compiled 2496 to 1998 computations (20% saved)

localize27.0ms (0.8%)

Local error

Found 4 expressions with local error:

14.6b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
14.6b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
14.6b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
20.1b	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 3) (pow.f64 x 3))) (+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (+.f64 (.f64 x x) (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))))

rewrite111.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64_3116` `add-cube-cbrt_binary64_3142` `*-un-lft-identity_binary64_3110` `add-sqr-sqrt_binary64_3131`
15×	`add-exp-log_binary64_3145` `add-cbrt-cube_binary64_3143`
14×	`associate-/r/_binary64_3058`
12×	`associate-/r*_binary64_3056`
10×	`flip3-+_binary64_3113` `flip-+_binary64_3084` `associate-/l*_binary64_3057`
8×	`associate-/l/_binary64_3059`
6×	`frac-add_binary64_3118`
5×	`cbrt-undiv_binary64_3141` `div-exp_binary64_3158`
4×	`clear-num_binary64_3109` `pow1_binary64_3168` `associate-*r/_binary64_3054` `add-log-exp_binary64_3146` `frac-2neg_binary64_3121` `div-inv_binary64_3107`
2×	`frac-times_binary64_3120` `associate-*l/_binary64_3055`
1×	`prod-exp_binary64_3156` `cbrt-unprod_binary64_3140` `flip3--_binary64_3114` `flip--_binary64_3085`

Counts

4 → 124

Calls

4 calls:

59.0ms	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 3) (pow.f64 x 3))) (+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (+.f64 (.f64 x x) (.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)))))
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.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)))))

series330.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) 3) (pow.f64 x 3))) (+.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (+.f64 (.f64 x x) (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))))
37.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
35.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
35.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify100.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5107	6842

prune950.0ms (28%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	136	2	138

Merged error: 0b

Counts

138 → 2

Compiler

Compiled 12418 to 9714 computations (21.8% saved)

regimes14.0ms (0.4%)

Compiler: Compiled 98 to 80 computations (18.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	28
1	26	28

end0.0ms (0%)

sample592.0ms (17.4%)

Algorithm

1×

intervals

Results

372.0ms

8000×

body

128

valid

Compiler

Compiled 135 to 112 computations (17% saved)

Details

analyze5.0ms (0.1%)

sample17.0ms (0.5%)

simplify272.0ms (8%)

prune3.0ms (0.1%)

localize12.0ms (0.4%)

rewrite45.0ms (1.3%)

series212.0ms (6.2%)

simplify96.0ms (2.8%)

prune165.0ms (4.9%)

localize13.0ms (0.4%)

rewrite28.0ms (0.8%)

series180.0ms (5.3%)

simplify87.0ms (2.6%)

prune134.0ms (4%)

localize27.0ms (0.8%)

rewrite111.0ms (3.3%)

series330.0ms (9.7%)

simplify100.0ms (2.9%)

prune950.0ms (28%)

regimes14.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample592.0ms (17.4%)

Profiling