Details

analyze522.0ms (9.6%)

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)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify415.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	5127	30

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: 26.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

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))
25.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
9×	`times-frac_binary64_757`
7×	`add-log-exp_binary64_787`
5×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`associate-/r_binary64_697` `pow1_binary64_809` `associate-/l_binary64_698`
2×	`flip3-+_binary64_754` `associate-/l/_binary64_700` `flip--_binary64_726` `associate-/r/_binary64_699` `flip3--_binary64_755` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `div-sub_binary64_756` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `div-exp_binary64_799`

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))

series318.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

198.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
83.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
37.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5716	1814

prune100.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	11	64

Merged error: 25.1b

Counts

64 → 11

Compiler

Compiled 1717 to 743 computations (56.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_751`
28×	`sqrt-prod_binary64_766`
25×	`add-sqr-sqrt_binary64_772`
24×	`times-frac_binary64_757`
23×	`add-cube-cbrt_binary64_783`
10×	`distribute-lft-out_binary64_704` `unpow-prod-down_binary64_827`
8×	`associate-/r*_binary64_697`
6×	`pow1_binary64_809` `add-log-exp_binary64_787` `sqrt-div_binary64_767` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`flip3-+_binary64_754` `associate-/l*_binary64_698` `flip-+_binary64_725`
2×	`associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `associate-/r/_binary64_699` `sqrt-pow1_binary64_768` `flip3--_binary64_755`
1×	`div-sub_binary64_756` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `div-exp_binary64_799`

Counts

4 → 95

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
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))

series426.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
79.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
48.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5185	3239

prune154.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 23.6b

Counts

118 → 10

Compiler

Compiled 3722 to 1579 computations (57.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite60.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary64_767` `*-un-lft-identity_binary64_751`
10×	`sqrt-prod_binary64_766` `add-sqr-sqrt_binary64_772`
9×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`flip3-+_binary64_754` `add-cube-cbrt_binary64_783` `associate-/r/_binary64_699` `flip-+_binary64_725`
6×	`pow1_binary64_809` `add-log-exp_binary64_787`
4×	`frac-times_binary64_761` `distribute-lft-out_binary64_704` `unpow-prod-down_binary64_827`
3×	`times-frac_binary64_757` `associate-/l*_binary64_698`
2×	`associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `associate-r/_binary64_695` `cbrt-undiv_binary64_782` `associate-l/_binary64_696` `sqrt-pow1_binary64_768` `flip3--_binary64_755` `div-exp_binary64_799`
1×	`prod-exp_binary64_797` `div-sub_binary64_756` `associate-/r*_binary64_697` `div-inv_binary64_748` `diff-log_binary64_840` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `sub-neg_binary64_744`

Counts

4 → 77

Calls

4 calls:

30.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series349.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
75.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4955	2122
1	4955	2122

prune132.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 23.6b

Counts

99 → 10

Compiler

Compiled 2760 to 1615 computations (41.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_751`
30×	`sqrt-prod_binary64_766`
25×	`add-sqr-sqrt_binary64_772`
24×	`times-frac_binary64_757`
23×	`add-cube-cbrt_binary64_783`
12×	`distribute-lft-out_binary64_704` `unpow-prod-down_binary64_827`
8×	`associate-/r*_binary64_697`
6×	`pow1_binary64_809` `add-log-exp_binary64_787` `sqrt-div_binary64_767` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`flip3-+_binary64_754` `associate-/l*_binary64_698` `flip-+_binary64_725`
2×	`associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `associate-/r/_binary64_699` `sqrt-pow1_binary64_768` `flip3--_binary64_755`
1×	`div-sub_binary64_756` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `div-exp_binary64_799`

Counts

4 → 97

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series421.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
78.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
49.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4916	3269
1	4916	3269

prune178.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	109	10	119

Merged error: 23.6b

Counts

119 → 10

Compiler

Compiled 3792 to 2224 computations (41.4% saved)

regimes399.0ms (7.4%)

Compiler: Compiled 4604 to 3432 computations (25.5% saved)

bsearch5.0ms (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	70	105
1	70	105

end0.0ms (0%)

sample1.4s (26.7%)

Algorithm

1×

intervals

Results

351.0ms	8000×	body	128	valid
20.0ms	470×	body	128	invalid

Compiler

Compiled 974 to 709 computations (27.2% saved)

Details

analyze522.0ms (9.6%)

sample21.0ms (0.4%)

simplify415.0ms (7.7%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite22.0ms (0.4%)

series318.0ms (5.9%)

simplify74.0ms (1.4%)

prune100.0ms (1.8%)

localize17.0ms (0.3%)

rewrite44.0ms (0.8%)

series426.0ms (7.9%)

simplify63.0ms (1.2%)

prune154.0ms (2.8%)

localize13.0ms (0.2%)

rewrite60.0ms (1.1%)

series349.0ms (6.4%)

simplify78.0ms (1.4%)

prune132.0ms (2.4%)

localize15.0ms (0.3%)

rewrite47.0ms (0.9%)

series421.0ms (7.8%)

simplify83.0ms (1.5%)

prune178.0ms (3.3%)

regimes399.0ms (7.4%)

bsearch5.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (26.7%)

Profiling