Details

analyze1.3s (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
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample129.0ms (1.8%)

Algorithm

1×

intervals

Results

46.0ms	60×	body	1280	invalid
27.0ms	246×	body	80	valid
24.0ms	49×	body	640	invalid
6.0ms	14×	body	320	invalid
3.0ms	6×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	5×	body	160	invalid
1.0ms	8×	body	80	invalid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify476.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune12.0ms (0.2%)

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: 33.5b

Counts

2 → 1

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.2b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series95.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4939	677
1	4939	677

prune101.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 20.7b

Counts

69 → 5

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `exp-sum_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
5.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series81.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
25.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4936	840
1	4936	840

prune118.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 3.2b

Counts

85 → 9

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series30.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4949	624
1	4949	624

prune107.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 3.2b

Counts

84 → 9

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.7b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
40×	`unpow-prod-down_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`associate-/l*_binary64`
12×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`neg-mul-1_binary64` `sqr-pow_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `exp-to-pow_binary64` `pow-exp_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

3 → 101

Calls

3 calls:

8.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))

series52.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
11.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
10.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4939	1676
1	4939	1676

prune103.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	109	10	119

Merged error: 3.2b

Counts

119 → 10

regimes410.0ms (5.8%)

Accuracy

Total 5.2b remaining (57.8%)

Threshold costs 0b (0%)

bsearch99.0ms (1.4%)

Steps

Iters	Range		Point
11	-5.432686138407363e-292	1.981960550474511e-300	3.42306661262197e-310

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms (0%)

sample3.6s (50.7%)

Algorithm

1×

intervals

Results

1.3s	1878×	body	1280	invalid
827.0ms	7539×	body	80	valid
607.0ms	1314×	body	640	invalid
171.0ms	516×	body	320	invalid
91.0ms	131×	body	1280	valid
86.0ms	176×	body	640	valid
50.0ms	229×	body	160	invalid
44.0ms	397×	body	80	invalid
32.0ms	98×	body	320	valid
13.0ms	56×	body	160	valid

Details

analyze1.3s (18.3%)

sample129.0ms (1.8%)

simplify476.0ms (6.7%)

prune12.0ms (0.2%)

localize23.0ms (0.3%)

rewrite25.0ms (0.3%)

series95.0ms (1.3%)

simplify60.0ms (0.8%)

prune101.0ms (1.4%)

localize15.0ms (0.2%)

rewrite21.0ms (0.3%)

series81.0ms (1.1%)

simplify54.0ms (0.8%)

prune118.0ms (1.7%)

localize23.0ms (0.3%)

rewrite19.0ms (0.3%)

series30.0ms (0.4%)

simplify55.0ms (0.8%)

prune107.0ms (1.5%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series52.0ms (0.7%)

simplify65.0ms (0.9%)

prune103.0ms (1.4%)

regimes410.0ms (5.8%)

bsearch99.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (50.7%)

Profiling