Details

analyze326.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	202×	body	128	valid
5.0ms	21×	body	2048	valid
3.0ms	12×	body	4096	valid
2.0ms	13×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify172.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 37.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.9b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2548` `add-log-exp_binary64_2526`
7×	`*-un-lft-identity_binary64_2487`
6×	`add-sqr-sqrt_binary64_2509`
5×	`add-cube-cbrt_binary64_2522`
4×	`sqrt-prod_binary64_2503` `add-exp-log_binary64_2525` `flip-+_binary64_2461` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523` `sqrt-div_binary64_2504`
3×	`sqrt-pow1_binary64_2505`
2×	`+-commutative_binary64_2417` `sum-log_binary64_2578` `pow1/2_binary64_2567` `associate-*r/_binary64_2429`
1×	`distribute-lft-out_binary64_2438` `pow-prod-down_binary64_2558` `rem-sqrt-square_binary64_2500`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series357.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
51.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	1040

prune211.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 15.3b

Counts

64 → 7

Compiler

Compiled 3633 to 2244 computations (38.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
21.4b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2509`
14×	`*-un-lft-identity_binary64_2487`
9×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
8×	`add-cube-cbrt_binary64_2522` `pow1_binary64_2548`
7×	`sqrt-prod_binary64_2503`
6×	`times-frac_binary64_2493` `difference-of-squares_binary64_2456` `associate-/r*_binary64_2431` `add-log-exp_binary64_2526`
3×	`cancel-sign-sub-inv_binary64_2453` `sqrt-pow1_binary64_2505` `distribute-lft-out--_binary64_2439` `sqrt-div_binary64_2504`
2×	`flip--_binary64_2462` `associate-/r/_binary64_2433` `div-exp_binary64_2538` `pow1/2_binary64_2567` `flip3--_binary64_2491` `cbrt-undiv_binary64_2521`
1×	`sub-neg_binary64_2480` `diff-log_binary64_2579` `prod-exp_binary64_2536` `frac-2neg_binary64_2498` `associate-/l_binary64_2432` `flip-+_binary64_2461` `clear-num_binary64_2486` `div-inv_binary64_2484` `flip3-+_binary64_2490` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `rem-sqrt-square_binary64_2500` `associate-r/_binary64_2429`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
12.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series383.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
105.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
53.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4916	1730
1	4916	1730

prune190.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 11.6b

Counts

92 → 9

Compiler

Compiled 4134 to 1988 computations (51.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.4b	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2509`
25×	`*-un-lft-identity_binary64_2487`
24×	`associate-r_binary64_2427`
19×	`times-frac_binary64_2493`
17×	`add-cube-cbrt_binary64_2522`
13×	`pow1_binary64_2548`
9×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
8×	`sqrt-prod_binary64_2503` `difference-of-squares_binary64_2456`
6×	`add-log-exp_binary64_2526`
4×	`sqrt-pow1_binary64_2505` `distribute-lft-out--_binary64_2439` `pow-prod-down_binary64_2558`
3×	`cancel-sign-sub-inv_binary64_2453` `sqrt-div_binary64_2504` `associate-l_binary64_2428` `associate-*r/_binary64_2429`
2×	`unswap-sqr_binary64_2455` `flip--_binary64_2462` `associate-/r/_binary64_2433` `prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow1/2_binary64_2567` `flip3--_binary64_2491`
1×	`sub-neg_binary64_2480` `*-commutative_binary64_2418` `diff-log_binary64_2579` `flip-+_binary64_2461` `div-inv_binary64_2484` `flip3-+_binary64_2490` `div-exp_binary64_2538` `rem-sqrt-square_binary64_2500` `cbrt-undiv_binary64_2521`

Counts

4 → 88

Calls

4 calls:

20.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
13.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series360.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(sqrt.f64 (.f64 2 (.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))))
91.0ms	(.f64 im (/.f64 im (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
51.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5470	1951

prune165.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 10.7b

Counts

109 → 8

Compiler

Compiled 3712 to 1712 computations (53.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (.f64 (.f64 im im) 2))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2509`
50×	`sqrt-prod_binary64_2503`
38×	`*-un-lft-identity_binary64_2487`
36×	`times-frac_binary64_2493`
26×	`add-cube-cbrt_binary64_2522`
12×	`difference-of-squares_binary64_2456`
11×	`pow1_binary64_2548`
9×	`associate-/r*_binary64_2431`
6×	`add-exp-log_binary64_2525` `distribute-lft-out--_binary64_2439` `add-cbrt-cube_binary64_2523` `add-log-exp_binary64_2526`
4×	`associate-/l*_binary64_2432` `sqrt-pow1_binary64_2505` `sqrt-div_binary64_2504`
3×	`cancel-sign-sub-inv_binary64_2453` `pow-prod-down_binary64_2558`
2×	`flip--_binary64_2462` `associate-/r/_binary64_2433` `pow1/2_binary64_2567` `flip3--_binary64_2491`
1×	`sub-neg_binary64_2480` `sqrt-undiv_binary64_2508` `diff-log_binary64_2579` `frac-2neg_binary64_2498` `flip-+_binary64_2461` `clear-num_binary64_2486` `div-inv_binary64_2484` `flip3-+_binary64_2490` `div-exp_binary64_2538` `rem-sqrt-square_binary64_2500` `cbrt-undiv_binary64_2521`

Counts

4 → 108

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

series319.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
54.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5246	3621

prune235.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	118	10	128

Merged error: 7.7b

Counts

128 → 10

Compiler

Compiled 5426 to 2521 computations (53.5% saved)

regimes1.1s (17.5%)

Compiler: Compiled 7192 to 4861 computations (32.4% saved)

bsearch76.0ms (1.3%)

Steps

Iters	Range	Point
7	1.0783879871995089e+121	6.321203557273547e+122	5.6392861707035385e+122
7	-9.089728099399469e-302	-5.2137122067099377e-303	-5.2611073750173795e-303
9	-7.879764341688507e+170	-2.5496100832393085e+162	-2.5991937408382053e+162

Iters

Range

Point

1.0783879871995089e+121

6.321203557273547e+122

5.6392861707035385e+122

-9.089728099399469e-302

-5.2137122067099377e-303

-5.2611073750173795e-303

-7.879764341688507e+170

-2.5496100832393085e+162

-2.5991937408382053e+162

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	103
1	62	103

end0.0ms (0%)

sample1.7s (27.5%)

Algorithm

1×

intervals

Results

301.0ms	6143×	body	128	valid
148.0ms	495×	body	4096	valid
145.0ms	623×	body	2048	valid
67.0ms	368×	body	1024	valid
33.0ms	247×	body	512	valid
11.0ms	124×	body	256	valid

Compiler

Compiled 1038 to 692 computations (33.3% saved)

Details

analyze326.0ms (5.4%)

sample28.0ms (0.5%)

simplify172.0ms (2.8%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite30.0ms (0.5%)

series357.0ms (5.9%)

simplify59.0ms (1%)

prune211.0ms (3.5%)

localize15.0ms (0.2%)

rewrite44.0ms (0.7%)

series383.0ms (6.3%)

simplify55.0ms (0.9%)

prune190.0ms (3.1%)

localize13.0ms (0.2%)

rewrite56.0ms (0.9%)

series360.0ms (5.9%)

simplify73.0ms (1.2%)

prune165.0ms (2.7%)

localize13.0ms (0.2%)

rewrite48.0ms (0.8%)

series319.0ms (5.3%)

simplify84.0ms (1.4%)

prune235.0ms (3.9%)

regimes1.1s (17.5%)

bsearch76.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (27.5%)

Profiling