Details

analyze1.5s (14.5%)

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)

sample106.0ms (1%)

Algorithm

1×

intervals

Results

37.0ms	69×	body	1024	invalid
32.0ms	243×	body	128	valid
9.0ms	25×	body	512	invalid
3.0ms	5×	body	1024	valid
3.0ms	11×	body	256	invalid
2.0ms	19×	body	128	invalid
2.0ms	5×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify160.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

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

Error

30.8b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(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)))

rewrite28.0ms (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)))
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.im)

series616.0ms (6%)

Counts

4 → 57

Calls

4 calls:

251.0ms	(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)))
147.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
144.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
73.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3740 to 2473 computations (33.9% saved)

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4945	2175
1	4945	2175

prune172.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Error

17.4b

Counts

115 → 6

Compiler

Compiled 4796 to 1288 computations (73.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.2b	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite18.0ms (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` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_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 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
1.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series413.0ms (4%)

Counts

4 → 50

Calls

4 calls:

140.0ms	(cos.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
70.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
69.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 2214 to 1566 computations (29.3% saved)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5105	1673

prune119.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Error

3.4b

Counts

114 → 9

Compiler

Compiled 3415 to 909 computations (73.4% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.6b	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(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)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

7.0ms	(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)))
2.0ms	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))

series843.0ms (8.3%)

Counts

4 → 57

Calls

4 calls:

307.0ms	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))
237.0ms	(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)))
151.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
147.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5140 to 2817 computations (45.2% saved)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4947	2090
1	4947	2090

prune169.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Error

3.4b

Counts

113 → 9

Compiler

Compiled 6041 to 1315 computations (78.2% saved)

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

4.6b	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))
27.4b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
27.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.3b	(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)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `cos-sum_binary64` `cbrt-prod_binary64`

Counts

4 → 49

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
2.0ms	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))

series881.0ms (8.6%)

Counts

4 → 57

Calls

4 calls:

322.0ms	(cbrt.f64 (*.f64 y.im (atan2.f64 x.im x.re)))
248.0ms	(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)))
157.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
153.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 5410 to 3261 computations (39.7% saved)

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4947	2120
1	4947	2120

prune197.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Error

3.4b

Counts

115 → 8

Compiler

Compiled 6168 to 2034 computations (67% saved)

regimes440.0ms (4.3%)

Accuracy

Total 6.6b remaining (65.4%)

Threshold costs 0b (0%)

Compiler

Compiled 4612 to 2990 computations (35.2% saved)

bsearch150.0ms (1.5%)

Steps

Iters	Range		Point
8	3.9460097874426614e-126	2.3665549662820997e-123	6.322417595566576e-124
8	-4137.314810416361	-5.699185527645271	-5.774070607658753

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	82	138
1	82	138

end0.0ms (0%)

sample3.9s (37.8%)

Algorithm

1×

intervals

Results

1.2s	2355×	body	1024	invalid
839.0ms	7571×	body	128	valid
326.0ms	960×	body	512	invalid
100.0ms	420×	body	256	invalid
90.0ms	181×	body	1024	valid
62.0ms	536×	body	128	invalid
50.0ms	148×	body	512	valid
30.0ms	39×	body	2048	invalid
19.0ms	84×	body	256	valid
13.0ms	16×	body	2048	valid

Compiler

Compiled 1014 to 642 computations (36.7% saved)

Details

analyze1.5s (14.5%)

sample106.0ms (1%)

simplify160.0ms (1.6%)

prune8.0ms (0.1%)

localize30.0ms (0.3%)

rewrite28.0ms (0.3%)

series616.0ms (6%)

simplify105.0ms (1%)

prune172.0ms (1.7%)

localize20.0ms (0.2%)

rewrite18.0ms (0.2%)

series413.0ms (4%)

simplify71.0ms (0.7%)

prune119.0ms (1.2%)

localize28.0ms (0.3%)

rewrite23.0ms (0.2%)

series843.0ms (8.3%)

simplify102.0ms (1%)

prune169.0ms (1.7%)

localize38.0ms (0.4%)

rewrite29.0ms (0.3%)

series881.0ms (8.6%)

simplify105.0ms (1%)

prune197.0ms (1.9%)

regimes440.0ms (4.3%)

bsearch150.0ms (1.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.9s (37.8%)

Profiling