Details

analyze520.0ms (9.8%)

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)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify173.0ms (3.3%)

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%)

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: 23.4b

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))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
23.1b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_2866` `add-sqr-sqrt_binary64_2853` `*-un-lft-identity_binary64_2831`
9×	`times-frac_binary64_2837`
7×	`add-log-exp_binary64_2870`
5×	`add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
4×	`flip3-+_binary64_2834` `flip-+_binary64_2805`
3×	`pow1_binary64_2892` `associate-/l_binary64_2776` `associate-/r_binary64_2775`
2×	`associate-/l/_binary64_2778` `+-commutative_binary64_2761` `sum-log_binary64_2922` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `div-exp_binary64_2882` `clear-num_binary64_2830`

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))

series306.0ms (5.8%)

Counts

3 → 9

Calls

3 calls:

183.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
82.0ms	(+.f64 (.f64 a c) (.f64 b d))
41.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5006	1420

prune280.0ms (5.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 22.7b

Counts

63 → 9

Compiler

Compiled 6905 to 2802 computations (59.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
15.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2853`
21×	`add-cube-cbrt_binary64_2866` `*-un-lft-identity_binary64_2831`
18×	`times-frac_binary64_2837` `sqrt-prod_binary64_2847`
6×	`pow1_binary64_2892` `sqrt-div_binary64_2848` `add-log-exp_binary64_2870` `add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869` `associate-/r*_binary64_2775`
5×	`flip3-+_binary64_2834` `flip-+_binary64_2805`
3×	`associate-/l*_binary64_2776`
2×	`rem-sqrt-square_binary64_2844` `associate-/l/_binary64_2778` `pow1/2_binary64_2911` `sqrt-pow1_binary64_2849` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `+-commutative_binary64_2761` `div-exp_binary64_2882` `clear-num_binary64_2830` `sum-log_binary64_2922`

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))

series417.0ms (7.9%)

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))))
69.0ms	(+.f64 (.f64 a c) (.f64 b d))
54.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5228	2326

prune183.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 20.2b

Counts

105 → 11

Compiler

Compiled 5178 to 1468 computations (71.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
15.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite74.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2853`
76×	`times-frac_binary64_2837`
53×	`*-un-lft-identity_binary64_2831`
47×	`add-cube-cbrt_binary64_2866` `sqrt-prod_binary64_2847`
28×	`add-exp-log_binary64_2869`
24×	`associate-r_binary64_2771` `associate-l_binary64_2772`
18×	`add-cbrt-cube_binary64_2867`
15×	`unswap-sqr_binary64_2799`
10×	`sqrt-div_binary64_2848`
9×	`div-exp_binary64_2882`
8×	`pow1_binary64_2892` `prod-exp_binary64_2880`
6×	`flip3-+_binary64_2834` `flip-+_binary64_2805` `associate-/r*_binary64_2775` `associate-/r/_binary64_2777`
5×	`cbrt-undiv_binary64_2865`
4×	`add-log-exp_binary64_2870` `cbrt-unprod_binary64_2864`
3×	`div-inv_binary64_2828` `associate-/l*_binary64_2776`
2×	`rem-sqrt-square_binary64_2844` `associate-/l/_binary64_2778` `pow1/2_binary64_2911` `1-exp_binary64_2875` `rec-exp_binary64_2881` `sqrt-pow1_binary64_2849`
1×	`frac-2neg_binary64_2842` `pow-prod-down_binary64_2902` `-commutative_binary64_2762` `associate-l/_binary64_2774` `frac-times_binary64_2841` `clear-num_binary64_2830` `associate-*r/_binary64_2773`

Counts

4 → 160

Calls

4 calls:

32.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
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)))

series599.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
231.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify125.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4956	5405
1	4956	5405

prune216.0ms (4.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	171	12	183

Merged error: 20.2b

Counts

183 → 12

Compiler

Compiled 7141 to 1545 computations (78.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

12.0b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64_2866` `add-sqr-sqrt_binary64_2853` `*-un-lft-identity_binary64_2831`
21×	`cbrt-prod_binary64_2862`
18×	`times-frac_binary64_2837`
8×	`cbrt-div_binary64_2863`
6×	`add-exp-log_binary64_2869` `associate-/r*_binary64_2775`
5×	`flip3-+_binary64_2834` `add-cbrt-cube_binary64_2867` `flip-+_binary64_2805`
4×	`pow1_binary64_2892` `add-log-exp_binary64_2870`
3×	`pow1/3_binary64_2913` `associate-/l*_binary64_2776`
2×	`associate-/l/_binary64_2778` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `div-exp_binary64_2882` `clear-num_binary64_2830`

Counts

4 → 82

Calls

4 calls:

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

series921.0ms (17.4%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
151.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
140.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
124.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5169	2633

prune131.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	7	8
Picked	1	0	1
Done	0	3	3
Total	95	11	106

Merged error: 19.5b

Counts

106 → 11

Compiler

Compiled 4605 to 841 computations (81.7% saved)

regimes131.0ms (2.5%)

Compiler: Compiled 1259 to 797 computations (36.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	119
1	39	119

end0.0ms (0%)

sample856.0ms (16.2%)

Algorithm

1×

intervals

Results

351.0ms	8000×	body	128	valid
20.0ms	481×	body	128	invalid

Compiler

Compiled 365 to 206 computations (43.6% saved)

Details

analyze520.0ms (9.8%)

sample23.0ms (0.4%)

simplify173.0ms (3.3%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite23.0ms (0.4%)

series306.0ms (5.8%)

simplify47.0ms (0.9%)

prune280.0ms (5.3%)

localize12.0ms (0.2%)

rewrite34.0ms (0.6%)

series417.0ms (7.9%)

simplify67.0ms (1.3%)

prune183.0ms (3.5%)

localize15.0ms (0.3%)

rewrite74.0ms (1.4%)

series599.0ms (11.3%)

simplify125.0ms (2.4%)

prune216.0ms (4.1%)

localize18.0ms (0.3%)

rewrite36.0ms (0.7%)

series921.0ms (17.4%)

simplify71.0ms (1.3%)

prune131.0ms (2.5%)

regimes131.0ms (2.5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample856.0ms (16.2%)

Profiling