Details

analyze1.4s (17.5%)

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

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample114.0ms (1.4%)

Algorithm

1×

intervals

Results

45.0ms	79×	body	1024	invalid
27.0ms	240×	body	128	valid
10.0ms	29×	body	512	invalid
2.0ms	11×	body	256	invalid
2.0ms	3×	body	2048	invalid
2.0ms	9×	body	256	valid
2.0ms	17×	body	128	invalid
2.0ms	3×	body	1024	valid
1.0ms	4×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify156.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

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: 32.4b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.5b	(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)))

rewrite27.0ms (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:

8.0ms	(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)))
4.0ms	(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)))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series288.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(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)))
26.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4863	1251
1	4863	1251

prune101.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Merged error: 17.6b

Counts

69 → 4

Compiler

Compiled 2942 to 797 computations (72.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.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)
1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 66

Calls

4 calls:

5.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(-.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))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series257.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(-.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))
84.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
26.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4958	1662
1	4958	1662

prune93.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	75	7	82

Merged error: 3.6b

Counts

82 → 7

Compiler

Compiled 2110 to 1023 computations (51.5% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

28.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.5b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.5b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.5b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cos-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

7.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series572.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
179.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
178.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4990	1522
1	4990	1522

prune163.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	51	7	58

Merged error: 3.6b

Counts

58 → 7

Compiler

Compiled 4319 to 2237 computations (48.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.2b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
7×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
6×	`associate-r_binary64`
5×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `log-pow_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`

Counts

3 → 49

Calls

3 calls:

6.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))

series151.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

85.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
39.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5488	989

prune41.0ms (0.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	58	7	65

Merged error: 3.6b

Counts

65 → 7

Compiler

Compiled 1086 to 316 computations (70.9% saved)

regimes268.0ms (3.4%)

Compiler: Compiled 2382 to 1630 computations (31.6% saved)

bsearch315.0ms (4%)

Steps

Iters	Range		Point
6	9.353538533214603e-45	6.10448516542931e-44	3.5492325277206613e-44
6	3.802382081096709e-165	2.762138674541015e-164	9.97621392264661e-165
6	-4.179053529427529e-308	1.1602034729424457e-308	3.39539490050286e-310
8	-9.064501477833234e-204	-2.2718525260766316e-208	-1.6071323931041203e-204
9	-2.503884142365357e-97	-3.1144040188293025e-103	-1.848237701150158e-101

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	203
1	101	203

end0.0ms (0%)

sample3.5s (44.1%)

Algorithm

1×

intervals

Results

1.2s	2384×	body	1024	invalid
810.0ms	7600×	body	128	valid
357.0ms	1055×	body	512	invalid
94.0ms	424×	body	256	invalid
72.0ms	148×	body	1024	valid
58.0ms	516×	body	128	invalid
47.0ms	142×	body	512	valid
27.0ms	38×	body	2048	invalid
22.0ms	101×	body	256	valid
7.0ms	9×	body	2048	valid

Compiler

Compiled 602 to 380 computations (36.9% saved)

Details

analyze1.4s (17.5%)

sample114.0ms (1.4%)

simplify156.0ms (2%)

prune8.0ms (0.1%)

localize29.0ms (0.4%)

rewrite27.0ms (0.3%)

series288.0ms (3.6%)

simplify115.0ms (1.5%)

prune101.0ms (1.3%)

localize15.0ms (0.2%)

rewrite25.0ms (0.3%)

series257.0ms (3.2%)

simplify60.0ms (0.8%)

prune93.0ms (1.2%)

localize33.0ms (0.4%)

rewrite31.0ms (0.4%)

series572.0ms (7.2%)

simplify72.0ms (0.9%)

prune163.0ms (2.1%)

localize11.0ms (0.1%)

rewrite16.0ms (0.2%)

series151.0ms (1.9%)

simplify72.0ms (0.9%)

prune41.0ms (0.5%)

regimes268.0ms (3.4%)

bsearch315.0ms (4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.5s (44.1%)

Profiling