Details

analyze1.6s (10.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

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)

sample119.0ms (0.8%)

Algorithm

1×

intervals

Results

41.0ms	78×	body	1024	invalid
28.0ms	243×	body	128	valid
8.0ms	22×	body	512	invalid
8.0ms	9×	body	2048	invalid
3.0ms	15×	body	256	invalid
3.0ms	5×	body	1024	valid
2.0ms	5×	body	512	valid
2.0ms	13×	body	128	invalid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

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

Error

35.0b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(*.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)))
33.2b	(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)))

rewrite106.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

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

Counts

4 → 56

Calls

4 calls:

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

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series806.0ms (5.5%)

Error

21.7b

Counts

4 → 60

Calls

4 calls:

383.0ms	(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)))
143.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
126.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 6412 to 3276 computations (48.9% saved)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4972	2439
1	4972	2439

prune172.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	9	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

21.7b

Counts

117 → 9

Compiler

Compiled 5116 to 1437 computations (71.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
1.1b	(*.f64 y.re (atan2.f64 x.im x.re))
18.1b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

21.7b

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series451.0ms (3.1%)

Error

11.6b

Counts

4 → 46

Calls

4 calls:

136.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
130.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
72.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
70.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3366 to 1763 computations (47.6% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5078	1484

prune122.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Error

11.6b

Counts

113 → 11

Compiler

Compiled 3352 to 892 computations (73.4% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
33.2b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
33.2b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite165.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_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×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 39

Calls

4 calls:

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

Compiler

Compiled 3576 to 1765 computations (50.6% saved)

series1.6s (11.3%)

Error

11.6b

Counts

4 → 70

Calls

4 calls:

434.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
426.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
410.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
161.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 15837 to 9278 computations (41.4% saved)

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4981	3713
1	4981	3713

prune423.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	109	11	120

Error

11.6b

Counts

120 → 11

Compiler

Compiled 9440 to 4674 computations (50.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

11.8b	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))) 3))
31.1b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
31.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite153.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cube-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `distribute-lft-out_binary64`
1×	`sin-sum_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64`

Counts

4 → 61

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
7.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
5.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3307 to 1470 computations (55.5% saved)

series1.0s (6.9%)

Error

11.6b

Counts

4 → 66

Calls

4 calls:

353.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2))))))) 3))
292.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
136.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
130.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 7553 to 4464 computations (40.9% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4950	3645
1	4950	3645

prune211.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	126	12	138

Error

11.6b

Counts

138 → 12

Compiler

Compiled 5577 to 2296 computations (58.8% saved)

regimes1.3s (9%)

Accuracy

Total 10.1b remaining (47.8%)

Threshold costs 0b (0%)

Compiler

Compiled 11972 to 7395 computations (38.2% saved)

bsearch446.0ms (3.1%)

Steps

Iters	Range		Point
5	5.54418997658011e+147	1.427354550575465e+148	8.974528308302968e+147
8	0.00022369283073073282	0.35470339786757005	0.0003698274412800461
10	3.333217658678562e-162	1.8616075096432164e-151	8.427778181788499e-157
11	-7.896658659264402e-275	-1.6417461347809156e-307	-4.9159159806039255e-295
6	-1.0688001393611278e-16	-1.6209351392353e-17	-9.372599816172701e-17
9	-2.0349158131471108e+71	-9.579415448801595e+65	-2.1308440972502256e+67

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	442
1	112	442

end0.0ms (0%)

sample5.2s (36%)

Algorithm

1×

intervals

Results

1.3s	2552×	body	1024	invalid
859.0ms	7563×	body	128	valid
322.0ms	918×	body	512	invalid
167.0ms	185×	body	2048	invalid
93.0ms	178×	body	1024	valid
77.0ms	325×	body	256	invalid
57.0ms	496×	body	128	invalid
53.0ms	145×	body	512	valid
23.0ms	99×	body	256	valid
12.0ms	15×	body	2048	valid

Compiler

Compiled 2640 to 1546 computations (41.4% saved)

Details

analyze1.6s (10.7%)

sample119.0ms (0.8%)

simplify68.0ms (0.5%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite106.0ms (0.7%)

series806.0ms (5.5%)

simplify81.0ms (0.6%)

prune172.0ms (1.2%)

localize18.0ms (0.1%)

rewrite80.0ms (0.6%)

series451.0ms (3.1%)

simplify65.0ms (0.4%)

prune122.0ms (0.8%)

localize39.0ms (0.3%)

rewrite165.0ms (1.1%)

series1.6s (11.3%)

simplify73.0ms (0.5%)

prune423.0ms (2.9%)

localize30.0ms (0.2%)

rewrite153.0ms (1%)

series1.0s (6.9%)

simplify126.0ms (0.9%)

prune211.0ms (1.4%)

regimes1.3s (9%)

bsearch446.0ms (3.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample5.2s (36%)

Profiling