Details

analyze4.0ms (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 18 to 15 computations (16.7% saved)

sample16.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 35 to 30 computations (14.3% saved)

simplify35.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	489	25
1	489	25

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 34 to 28 computations (17.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(-.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)))
4.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series199.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
52.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
44.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
36.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

simplify109.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4840	2141
1	4840	2141

prune177.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	4	94

Merged error: 0b

Counts

94 → 4

Compiler

Compiled 3171 to 2523 computations (20.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.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)
15.5b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
18.3b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3))

rewrite55.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`cbrt-prod_binary64`
30×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `*-commutative_binary64`

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

series199.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
47.0ms	(pow.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) 3)
43.0ms	(/.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))

simplify113.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5213	5038

prune301.0ms (9.6%)

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 4792 to 3888 computations (18.9% 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 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
15.5b	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

rewrite49.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/r/_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`div-exp_binary64`
4×	`cbrt-undiv_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 146

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
10.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series184.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
38.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
37.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
34.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

simplify135.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4894	4804
1	4894	4804

prune263.0ms (8.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	158	4	162

Merged error: 0b

Counts

162 → 4

Compiler

Compiled 4706 to 3810 computations (19% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 x 371319058228565835421295263225/5070602400912917605986812821504)
0.2b	(pow.f64 (*.f64 x 609359547581365/2251799813685248) 3)
0.2b	(.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672))
21.3b	(/.f64 (+.f64 (pow.f64 162377988252285/70368744177664 3) (pow.f64 (.f64 x 609359547581365/2251799813685248) 3)) (.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 26366611068859205468807721225/4951760157141521099596496896 (.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672)))))

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sum-cubes_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/r*_binary64` `flip3--_binary64` `sqr-pow_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `cube-prod_binary64` `div-inv_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 103

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (pow.f64 162377988252285/70368744177664 3) (pow.f64 (.f64 x 609359547581365/2251799813685248) 3)) (.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 26366611068859205468807721225/4951760157141521099596496896 (.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672)))))
8.0ms	(.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672))
4.0ms	(*.f64 x 371319058228565835421295263225/5070602400912917605986812821504)
4.0ms	(pow.f64 (*.f64 x 609359547581365/2251799813685248) 3)

series204.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672))
66.0ms	(/.f64 (+.f64 (pow.f64 162377988252285/70368744177664 3) (pow.f64 (.f64 x 609359547581365/2251799813685248) 3)) (.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (+.f64 26366611068859205468807721225/4951760157141521099596496896 (.f64 x (-.f64 (.f64 x 371319058228565835421295263225/5070602400912917605986812821504) 98946577458584588455184669025/158456325028528675187087900672)))))
46.0ms	(pow.f64 (*.f64 x 609359547581365/2251799813685248) 3)
21.0ms	(*.f64 x 371319058228565835421295263225/5070602400912917605986812821504)

simplify105.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4883	2326
1	4883	2326

prune242.0ms (7.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	115	4	119

Merged error: 0b

Counts

119 → 4

Compiler

Compiled 4272 to 3437 computations (19.5% saved)

regimes30.0ms (1%)

Compiler: Compiled 210 to 176 computations (16.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	25
1	31	25

end0.0ms (0%)

sample562.0ms (17.9%)

Algorithm

1×

intervals

Results

323.0ms

8000×

body

128

valid

Compiler

Compiled 122 to 103 computations (15.6% saved)

Details

analyze4.0ms (0.1%)

sample16.0ms (0.5%)

simplify35.0ms (1.1%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite37.0ms (1.2%)

series199.0ms (6.4%)

simplify109.0ms (3.5%)

prune177.0ms (5.6%)

localize15.0ms (0.5%)

rewrite55.0ms (1.8%)

series199.0ms (6.3%)

simplify113.0ms (3.6%)

prune301.0ms (9.6%)

localize13.0ms (0.4%)

rewrite49.0ms (1.6%)

series184.0ms (5.9%)

simplify135.0ms (4.3%)

prune263.0ms (8.4%)

localize25.0ms (0.8%)

rewrite48.0ms (1.5%)

series204.0ms (6.5%)

simplify105.0ms (3.3%)

prune242.0ms (7.7%)

regimes30.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample562.0ms (17.9%)

Profiling