Details

analyze544.0ms (22.7%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	40×	body	80	invalid

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

prune6.0ms (0.3%)

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: 0.0b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 11

Calls

1 calls:

4.0ms

(+.f64 (*.f64 x.re y.im) (*.f64 x.im y.re))

series15.0ms (0.6%)

Counts

1 → 3

Calls

1 calls:

15.0ms

(+.f64 (*.f64 x.re y.im) (*.f64 x.im y.re))

simplify79.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4869	141
1	4869	141

prune19.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.0b

Counts

15 → 2

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) (sqrt.f64 (+.f64 (.f64 x.re y.im) (*.f64 x.im y.re))))
1.5b	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
1.5b	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) (sqrt.f64 (+.f64 (.f64 x.re y.im) (*.f64 x.im y.re))))
4.0ms	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))

series77.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
12.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) (sqrt.f64 (+.f64 (.f64 x.re y.im) (*.f64 x.im y.re))))
12.0ms	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))

simplify35.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5537	1320

prune106.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	109	3	112

Merged error: 0.0b

Counts

112 → 3

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3)
1.5b	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
1.5b	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
8.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3))

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`pow1_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cube-div_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqrt-pow1_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))

series132.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3)
27.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 3))
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))

simplify59.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5017	1328

prune105.0ms (4.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Merged error: 0.0b

Counts

108 → 3

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))
0.3b	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4)
1.5b	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
10.9b	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`unpow-prod-down_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `rem-sqrt-square_binary64`
4×	`add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4))
5.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4)
4.0ms	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))

series120.0ms (5%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4)
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re)))
13.0ms	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))
12.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x.re y.im) (.f64 x.im y.re))) 4))

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5041	854

prune80.0ms (3.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0.0b

Counts

87 → 3

regimes363.0ms (15.2%)

Accuracy

Total 0.0b remaining (11.2%)

Threshold costs 0.0b (11.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms (0%)

sample490.0ms (20.4%)

Algorithm

1×

intervals

Results

218.0ms	8000×	body	80	valid
35.0ms	1339×	body	80	invalid

Details

analyze544.0ms (22.7%)

sample19.0ms (0.8%)

simplify5.0ms (0.2%)

prune6.0ms (0.3%)

localize5.0ms (0.2%)

rewrite5.0ms (0.2%)

series15.0ms (0.6%)

simplify79.0ms (3.3%)

prune19.0ms (0.8%)

localize7.0ms (0.3%)

rewrite27.0ms (1.1%)

series77.0ms (3.2%)

simplify35.0ms (1.5%)

prune106.0ms (4.4%)

localize10.0ms (0.4%)

rewrite22.0ms (0.9%)

series132.0ms (5.5%)

simplify59.0ms (2.5%)

prune105.0ms (4.4%)

localize9.0ms (0.4%)

rewrite21.0ms (0.9%)

series120.0ms (5%)

simplify33.0ms (1.4%)

prune80.0ms (3.4%)

regimes363.0ms (15.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample490.0ms (20.4%)

Profiling