Details

analyze1.9s (15.6%)

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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample181.0ms (1.5%)

Algorithm

1×

intervals

Results

65.0ms	87×	body	1024	invalid
38.0ms	240×	body	128	valid
24.0ms	38×	body	512	invalid
5.0ms	6×	body	1024	valid
5.0ms	26×	body	128	invalid
3.0ms	11×	body	256	invalid
3.0ms	6×	body	512	valid
2.0ms	2×	body	2048	invalid
2.0ms	4×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune10.0ms (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

36.0b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
36.0b	(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)))

rewrite121.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

36.0b

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×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

13.0ms	(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)))
7.0ms	(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)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series747.0ms (6.1%)

Error

20.8b

Counts

4 → 53

Calls

4 calls:

287.0ms	(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)))
165.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
92.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5485 to 2785 computations (49.2% saved)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5151	2077

prune225.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Error

20.8b

Counts

110 → 7

Compiler

Compiled 4585 to 1222 computations (73.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
20.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite100.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

20.8b

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:

6.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
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)
1.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series521.0ms (4.3%)

Error

4.3b

Counts

4 → 46

Calls

4 calls:

159.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
145.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
84.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
77.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3346 to 1765 computations (47.3% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5125	1469

prune115.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	103	8	111

Error

4.3b

Counts

111 → 8

Compiler

Compiled 3142 to 776 computations (75.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (log.f64 x.re) y.re)
1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
20.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite104.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

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

Counts

4 → 62

Calls

4 calls:

8.0ms	(*.f64 (log.f64 x.re) y.re)
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
3.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1468 to 322 computations (78.1% saved)

series517.0ms (4.2%)

Error

4.3b

Counts

4 → 33

Calls

4 calls:

193.0ms	(*.f64 (log.f64 x.re) y.re)
144.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
85.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
77.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1806 to 924 computations (48.8% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4967	1102
1	4967	1102

prune100.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	95	8	103

Error

4.3b

Counts

103 → 8

Compiler

Compiled 2208 to 436 computations (80.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
20.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
20.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
20.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 39

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1616 to 207 computations (87.2% saved)

series591.0ms (4.8%)

Error

4.3b

Counts

4 → 36

Calls

4 calls:

161.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
158.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
154.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
82.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3771 to 1222 computations (67.6% saved)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5028	958

prune89.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	75	8	83

Error

4.3b

Counts

83 → 8

Compiler

Compiled 2802 to 214 computations (92.4% saved)

regimes807.0ms (6.6%)

Accuracy

Total 5.6b remaining (61.2%)

Threshold costs 0b (0%)

Compiler

Compiled 4957 to 3180 computations (35.8% saved)

bsearch524.0ms (4.3%)

Steps

Iters	Range		Point
7	0.0006378605605385915	0.0338249057669876	0.020903545878702613
7	9.4554428379052e-192	1.6287549076290145e-190	3.0726427254929475e-191
9	-1.8400108148144397e-304	1.790964503970258e-307	2.76765119975385e-310
8	-1.4400710557275133e-236	-3.4633224462706004e-241	-4.449935006270931e-241
10	-4.777569920403634e-155	-9.996578869885557e-167	-2.5341068578095944e-163
10	-32548.403154743562	-1.430601335525306e-09	-0.1567682849090526

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	269
1	130	269

end0.0ms (0%)

sample5.0s (40.6%)

Algorithm

1×

intervals

Results

1.5s	2422×	body	1024	invalid
1.0s	7562×	body	128	valid
423.0ms	1009×	body	512	invalid
115.0ms	418×	body	256	invalid
113.0ms	166×	body	1024	valid
81.0ms	592×	body	128	invalid
64.0ms	153×	body	512	valid
31.0ms	32×	body	2048	invalid
28.0ms	106×	body	256	valid
15.0ms	13×	body	2048	valid

Compiler

Compiled 1151 to 700 computations (39.2% saved)

Details

analyze1.9s (15.6%)

sample181.0ms (1.5%)

simplify79.0ms (0.6%)

prune10.0ms (0.1%)

localize29.0ms (0.2%)

rewrite121.0ms (1%)

series747.0ms (6.1%)

simplify105.0ms (0.9%)

prune225.0ms (1.8%)

localize29.0ms (0.2%)

rewrite100.0ms (0.8%)

series521.0ms (4.3%)

simplify76.0ms (0.6%)

prune115.0ms (0.9%)

localize25.0ms (0.2%)

rewrite104.0ms (0.9%)

series517.0ms (4.2%)

simplify82.0ms (0.7%)

prune100.0ms (0.8%)

localize18.0ms (0.1%)

rewrite70.0ms (0.6%)

series591.0ms (4.8%)

simplify74.0ms (0.6%)

prune89.0ms (0.7%)

regimes807.0ms (6.6%)

bsearch524.0ms (4.3%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample5.0s (40.6%)

Profiling