Details

analyze1.5s (14.9%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample131.0ms (1.3%)

Algorithm

1×

intervals

Results

51.0ms	72×	body	1024	invalid
31.0ms	247×	body	128	valid
14.0ms	33×	body	512	invalid
8.0ms	6×	body	2048	invalid
3.0ms	11×	body	256	invalid
2.0ms	3×	body	1024	valid
1.0ms	11×	body	128	invalid
1.0ms	5×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify232.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune12.0ms (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: 34.1b

Counts

2 → 1

Compiler

Compiled 146 to 76 computations (47.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(sin.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)))

rewrite31.0ms (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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(sin.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)))
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.re)

series531.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(sin.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)))
54.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4874	1270
1	4874	1270

prune222.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Merged error: 20.4b

Counts

69 → 6

Compiler

Compiled 5325 to 2310 computations (56.6% saved)

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(sin.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)))
33.1b	(sin.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)))
33.1b	(sin.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)))

rewrite35.0ms (0.3%)

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×	`sin-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	(sin.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)))
7.0ms	(sin.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)))
7.0ms	(sin.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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series1.1s (10.5%)

Counts

4 → 12

Calls

4 calls:

352.0ms	(sin.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)))
350.0ms	(sin.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)))
341.0ms	(sin.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)))
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5056	1579

prune190.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	51	6	57

Merged error: 20.4b

Counts

57 → 6

Compiler

Compiled 4742 to 2476 computations (47.8% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
1.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
19.8b	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) 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	(*.f64 (atan2.f64 x.im x.re) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series401.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
53.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
44.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5022	1147

prune136.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	70	7	77

Merged error: 11.6b

Counts

77 → 7

Compiler

Compiled 3620 to 1175 computations (67.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
0.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
1.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
19.8b	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
9×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`log-pow_binary64` `sin-sum_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
5.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series448.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
81.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
55.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
43.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4967	1125
1	4967	1125

prune205.0ms (2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	72	10	82

Merged error: 11.5b

Counts

82 → 10

Compiler

Compiled 5127 to 2048 computations (60.1% saved)

regimes400.0ms (3.9%)

Compiler: Compiled 2192 to 1300 computations (40.7% saved)

bsearch174.0ms (1.7%)

Steps

Iters	Range		Point
9	-3.3717620368255286e-301	1.3885635823988996e-307	-2.9795338187053e-310
8	-302704043381297.7	-272981380342.46088	-374000418249.14233

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	186
1	85	186

end0.0ms (0%)

sample4.1s (39.4%)

Algorithm

1×

intervals

Results

1.5s	2393×	body	1024	invalid
922.0ms	7589×	body	128	valid
330.0ms	827×	body	512	invalid
213.0ms	170×	body	2048	invalid
99.0ms	162×	body	1024	valid
88.0ms	334×	body	256	invalid
63.0ms	499×	body	128	invalid
56.0ms	138×	body	512	valid
26.0ms	101×	body	256	valid
10.0ms	10×	body	2048	valid

Compiler

Compiled 554 to 306 computations (44.8% saved)

Details

analyze1.5s (14.9%)

sample131.0ms (1.3%)

simplify232.0ms (2.2%)

prune12.0ms (0.1%)

localize24.0ms (0.2%)

rewrite31.0ms (0.3%)

series531.0ms (5.1%)

simplify105.0ms (1%)

prune222.0ms (2.2%)

localize38.0ms (0.4%)

rewrite35.0ms (0.3%)

series1.1s (10.5%)

simplify75.0ms (0.7%)

prune190.0ms (1.8%)

localize27.0ms (0.3%)

rewrite24.0ms (0.2%)

series401.0ms (3.9%)

simplify80.0ms (0.8%)

prune136.0ms (1.3%)

localize18.0ms (0.2%)

rewrite25.0ms (0.2%)

series448.0ms (4.3%)

simplify76.0ms (0.7%)

prune205.0ms (2%)

regimes400.0ms (3.9%)

bsearch174.0ms (1.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.1s (39.4%)

Profiling