Details

analyze524.0ms (18.3%)

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

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

simplify192.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (190.0ms)

Iter	Nodes	Cost
0	4821	15
1	4821	15

prune7.0ms (0.2%)

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: 28.0b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
27.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series56.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
12.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
7.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify51.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5785	976

prune113.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 27.1b

Counts

64 → 9

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
18.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
30.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite28.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series72.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
13.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
8.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5760	1553

prune124.0ms (4.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 23.9b

Counts

106 → 10

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
16.0b	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
18.5b	(/.f64 (.f64 x.re y.im) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 68

Calls

4 calls:

8.0ms	(/.f64 (.f64 x.re y.im) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
7.0ms	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

series52.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 (.f64 x.re y.im) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
18.0ms	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
8.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
7.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify50.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4962	880
1	4962	880

prune113.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	80	10	90

Merged error: 22.0b

Counts

90 → 10

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.0b	(.f64 (/.f64 x.re (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 y.im (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
16.0b	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
30.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite47.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64` `sqrt-div_binary64`
6×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
5×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

25.0ms	(.f64 (/.f64 x.re (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 y.im (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
7.0ms	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series51.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(.f64 (/.f64 x.re (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 y.im (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
18.0ms	(/.f64 (.f64 x.im y.re) (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4967	2105
1	4967	2105

prune135.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Merged error: 21.8b

Counts

152 → 8

regimes404.0ms (14.1%)

Accuracy

Total 0.7b remaining (2.8%)

Threshold costs 0.7b (2.8%)

bsearch35.0ms (1.2%)

Steps

Iters	Range		Point
9	3.578591583768455e-199	1.9224846528789776e-190	7.741980536026424e-194
7	-0.0025133320054770117	-1.8132444495535047e-05	-2.024796178527634e-05

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	75
1	93	75

end0.0ms (0%)

sample569.0ms (19.9%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	80	valid
21.0ms	515×	body	80	invalid

Details

analyze524.0ms (18.3%)

sample22.0ms (0.8%)

simplify192.0ms (6.7%)

prune7.0ms (0.2%)

localize9.0ms (0.3%)

rewrite19.0ms (0.7%)

series56.0ms (1.9%)

simplify51.0ms (1.8%)

prune113.0ms (4%)

localize12.0ms (0.4%)

rewrite28.0ms (1%)

series72.0ms (2.5%)

simplify56.0ms (1.9%)

prune124.0ms (4.3%)

localize10.0ms (0.4%)

rewrite25.0ms (0.9%)

series52.0ms (1.8%)

simplify50.0ms (1.7%)

prune113.0ms (3.9%)

localize13.0ms (0.4%)

rewrite47.0ms (1.7%)

series51.0ms (1.8%)

simplify69.0ms (2.4%)

prune135.0ms (4.7%)

regimes404.0ms (14.1%)

bsearch35.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample569.0ms (19.9%)

Profiling