Details

analyze513.0ms (11.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify169.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (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: 26.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.5b	(+.f64 (.f64 a c) (.f64 b d))
26.0b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `add-sqr-sqrt_binary64_2509`
9×	`times-frac_binary64_2493`
7×	`add-log-exp_binary64_2526`
5×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
4×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
3×	`associate-/r_binary64_2431` `associate-/l_binary64_2432` `pow1_binary64_2548`
2×	`associate-/r/_binary64_2433` `+-commutative_binary64_2417` `sum-log_binary64_2578` `associate-/l/_binary64_2434`
1×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`

Counts

3 → 53

Calls

3 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))

series299.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

186.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
75.0ms	(+.f64 (.f64 a c) (.f64 b d))
38.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5006	1420

prune267.0ms (6.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 25.7b

Counts

63 → 8

Compiler

Compiled 6768 to 2623 computations (61.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 a c) (.f64 b d))
16.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
32.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
32.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2509`
21×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522`
18×	`sqrt-prod_binary64_2503` `times-frac_binary64_2493`
6×	`add-exp-log_binary64_2525` `associate-/r*_binary64_2431` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548` `add-log-exp_binary64_2526` `sqrt-div_binary64_2504`
5×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
3×	`associate-/l*_binary64_2432`
2×	`associate-/r/_binary64_2433` `sqrt-pow1_binary64_2505` `associate-/l/_binary64_2434` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567`
1×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series413.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
71.0ms	(+.f64 (.f64 a c) (.f64 b d))
48.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5228	2326

prune167.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 24.4b

Counts

104 → 10

Compiler

Compiled 4838 to 1348 computations (72.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 a c) (.f64 b d))
16.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
32.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
32.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2509`
21×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522`
18×	`sqrt-prod_binary64_2503` `times-frac_binary64_2493`
6×	`add-exp-log_binary64_2525` `associate-/r*_binary64_2431` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548` `add-log-exp_binary64_2526` `sqrt-div_binary64_2504`
5×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
3×	`associate-/l*_binary64_2432`
2×	`associate-/r/_binary64_2433` `sqrt-pow1_binary64_2505` `associate-/l/_binary64_2434` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567`
1×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series411.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
80.0ms	(+.f64 (.f64 a c) (.f64 b d))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5228	2326

prune116.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Merged error: 24.4b

Counts

106 → 10

Compiler

Compiled 3739 to 806 computations (78.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.4b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
0.5b	(+.f64 (.f64 a c) (.f64 b d))
25.8b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2509`
21×	`*-un-lft-identity_binary64_2487`
20×	`times-frac_binary64_2493` `add-cube-cbrt_binary64_2522`
17×	`add-exp-log_binary64_2525`
15×	`associate-r_binary64_2427`
11×	`add-cbrt-cube_binary64_2523`
8×	`add-log-exp_binary64_2526`
7×	`pow1_binary64_2548`
6×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
4×	`associate-/r/_binary64_2433` `prod-exp_binary64_2536` `div-exp_binary64_2538`
3×	`unswap-sqr_binary64_2455` `associate-/r_binary64_2431` `associate-/l_binary64_2432` `associate-l_binary64_2428`
2×	`associate-*l/_binary64_2430` `frac-times_binary64_2497` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `cbrt-unprod_binary64_2520` `rec-exp_binary64_2537` `1-exp_binary64_2531` `cbrt-undiv_binary64_2521`
1×	`un-div-inv_binary64_2485` `-commutative_binary64_2418` `frac-2neg_binary64_2498` `pow-flip_binary64_2561` `clear-num_binary64_2486` `pow-prod-down_binary64_2558` `inv-pow_binary64_2572` `associate-r/_binary64_2429`

Counts

4 → 97

Calls

4 calls:

16.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series531.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
74.0ms	(+.f64 (.f64 a c) (.f64 b d))
47.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
40.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5495	2169

prune110.0ms (2.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	109	10	119

Merged error: 24.4b

Counts

119 → 10

Compiler

Compiled 3020 to 816 computations (73% saved)

regimes84.0ms (1.9%)

Compiler: Compiled 848 to 548 computations (35.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	38
1	18	38

end0.0ms (0%)

sample804.0ms (18.5%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	128	valid
20.0ms	472×	body	128	invalid

Compiler

Compiled 287 to 178 computations (38% saved)

Details

analyze513.0ms (11.8%)

sample20.0ms (0.5%)

simplify169.0ms (3.9%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite24.0ms (0.6%)

series299.0ms (6.9%)

simplify45.0ms (1%)

prune267.0ms (6.2%)

localize12.0ms (0.3%)

rewrite33.0ms (0.8%)

series413.0ms (9.5%)

simplify66.0ms (1.5%)

prune167.0ms (3.9%)

localize14.0ms (0.3%)

rewrite34.0ms (0.8%)

series411.0ms (9.5%)

simplify65.0ms (1.5%)

prune116.0ms (2.7%)

localize11.0ms (0.2%)

rewrite40.0ms (0.9%)

series531.0ms (12.3%)

simplify72.0ms (1.7%)

prune110.0ms (2.5%)

regimes84.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample804.0ms (18.5%)

Profiling