Details

analyze520.0ms (11%)

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify169.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune4.0ms (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)

localize14.0ms (0.3%)

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)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_2805` `add-sqr-sqrt_binary64_2794` `*-un-lft-identity_binary64_2773`
9×	`times-frac_binary64_2779`
7×	`add-log-exp_binary64_2809`
5×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
4×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
3×	`pow1_binary64_2831` `associate-/r_binary64_2719` `associate-/l_binary64_2720`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `sum-log_binary64_2861` `+-commutative_binary64_2705`
1×	`cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `div-inv_binary64_2770` `div-exp_binary64_2821` `clear-num_binary64_2772`

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

series304.0ms (6.4%)

Counts

3 → 9

Calls

3 calls:

182.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
82.0ms	(+.f64 (.f64 a c) (.f64 b d))
40.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5263	1420

prune77.0ms (1.6%)

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 1621 to 304 computations (81.2% 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 (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2794`
21×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
18×	`times-frac_binary64_2779` `sqrt-prod_binary64_2788`
6×	`sqrt-div_binary64_2789` `add-exp-log_binary64_2808` `pow1_binary64_2831` `associate-/r*_binary64_2719` `add-cbrt-cube_binary64_2806` `add-log-exp_binary64_2809`
5×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
3×	`associate-/l*_binary64_2720`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `sqrt-pow1_binary64_2790` `pow1/2_binary64_2850` `rem-sqrt-square_binary64_2786`
1×	`cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `div-inv_binary64_2770` `div-exp_binary64_2821` `sum-log_binary64_2861` `clear-num_binary64_2772` `+-commutative_binary64_2705`

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

series410.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
77.0ms	(+.f64 (.f64 a c) (.f64 b d))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
44.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4991	2326
1	4991	2326

prune102.0ms (2.2%)

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 3352 to 477 computations (85.8% 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)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2794`
21×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
18×	`times-frac_binary64_2779` `sqrt-prod_binary64_2788`
6×	`sqrt-div_binary64_2789` `add-exp-log_binary64_2808` `pow1_binary64_2831` `associate-/r*_binary64_2719` `add-cbrt-cube_binary64_2806` `add-log-exp_binary64_2809`
5×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
3×	`associate-/l*_binary64_2720`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `sqrt-pow1_binary64_2790` `pow1/2_binary64_2850` `rem-sqrt-square_binary64_2786`
1×	`cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `div-inv_binary64_2770` `div-exp_binary64_2821` `sum-log_binary64_2861` `clear-num_binary64_2772` `+-commutative_binary64_2705`

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))))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series408.0ms (8.6%)

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))))
72.0ms	(+.f64 (.f64 a c) (.f64 b d))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
42.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4991	2326
1	4991	2326

prune107.0ms (2.3%)

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 3519 to 668 computations (81% saved)

localize12.0ms (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))))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2794`
21×	`*-un-lft-identity_binary64_2773`
20×	`times-frac_binary64_2779` `add-cube-cbrt_binary64_2805`
17×	`add-exp-log_binary64_2808`
15×	`associate-r_binary64_2715`
11×	`add-cbrt-cube_binary64_2806`
8×	`add-log-exp_binary64_2809`
7×	`pow1_binary64_2831`
6×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
4×	`associate-/r/_binary64_2721` `div-exp_binary64_2821` `prod-exp_binary64_2819`
3×	`unswap-sqr_binary64_2741` `associate-l_binary64_2716` `associate-/r_binary64_2719` `associate-/l_binary64_2720`
2×	`cbrt-unprod_binary64_2803` `cbrt-undiv_binary64_2804` `div-inv_binary64_2770` `1-exp_binary64_2814` `sum-log_binary64_2861` `+-commutative_binary64_2705` `frac-times_binary64_2783` `rec-exp_binary64_2820` `associate-*l/_binary64_2718`
1×	`frac-2neg_binary64_2784` `pow-prod-down_binary64_2841` `pow-flip_binary64_2844` `-commutative_binary64_2706` `clear-num_binary64_2772` `associate-r/_binary64_2717` `un-div-inv_binary64_2771` `inv-pow_binary64_2855`

Counts

4 → 97

Calls

4 calls:

14.0ms	(.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))

series353.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
80.0ms	(+.f64 (.f64 a c) (.f64 b d))
49.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4953	2169
1	4953	2169

prune85.0ms (1.8%)

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 2551 to 524 computations (79.5% saved)

regimes335.0ms (7.1%)

Compiler: Compiled 4265 to 2378 computations (44.2% saved)

bsearch3.0ms (0.1%)

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	82
1	39	82

end0.0ms (0%)

sample1.3s (28.3%)

Algorithm

1×

intervals

Results

531.0ms	8000×	body	128	valid
20.0ms	472×	body	128	invalid

Compiler

Compiled 922 to 504 computations (45.3% saved)

Details

analyze520.0ms (11%)

sample22.0ms (0.5%)

simplify169.0ms (3.6%)

prune4.0ms (0.1%)

localize14.0ms (0.3%)

rewrite23.0ms (0.5%)

series304.0ms (6.4%)

simplify60.0ms (1.3%)

prune77.0ms (1.6%)

localize12.0ms (0.3%)

rewrite33.0ms (0.7%)

series410.0ms (8.7%)

simplify67.0ms (1.4%)

prune102.0ms (2.2%)

localize14.0ms (0.3%)

rewrite37.0ms (0.8%)

series408.0ms (8.6%)

simplify68.0ms (1.4%)

prune107.0ms (2.3%)

localize12.0ms (0.2%)

rewrite42.0ms (0.9%)

series353.0ms (7.5%)

simplify99.0ms (2.1%)

prune85.0ms (1.8%)

regimes335.0ms (7.1%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (28.3%)

Profiling