Details

analyze1.7s (15.4%)

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)

sample121.0ms (1.1%)

Algorithm

1×

intervals

Results

45.0ms	88×	body	1024	invalid
26.0ms	242×	body	128	valid
12.0ms	35×	body	512	invalid
5.0ms	3×	body	1024	valid
2.0ms	20×	body	128	invalid
2.0ms	10×	body	256	invalid
2.0ms	5×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify65.0ms (0.6%)

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

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

36.2b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.4b	(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)))

rewrite104.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

36.2b

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:

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

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series607.0ms (5.7%)

Error

21.3b

Counts

4 → 50

Calls

4 calls:

253.0ms	(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)))
142.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
76.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5157 to 2598 computations (49.6% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5048	2029

prune147.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Error

21.2b

Counts

108 → 4

Compiler

Compiled 4417 to 1140 computations (74.2% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.1b	(cbrt.f64 (atan2.f64 x.im x.re))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.4b	(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)))

rewrite92.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

21.2b

Rules

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

Counts

4 → 49

Calls

4 calls:

6.0ms	(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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

Compiler

Compiled 2832 to 332 computations (88.3% saved)

series676.0ms (6.3%)

Error

21.2b

Counts

4 → 47

Calls

4 calls:

233.0ms	(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)))
169.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
138.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
75.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 6195 to 2777 computations (55.2% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5100	1885

prune149.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	96	4	100

Error

21.2b

Counts

100 → 4

Compiler

Compiled 5093 to 1136 computations (77.7% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.1b	(cbrt.f64 (atan2.f64 x.im x.re))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.4b	(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)))

rewrite102.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

21.2b

Rules

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

Counts

4 → 49

Calls

4 calls:

6.0ms	(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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

Compiler

Compiled 3469 to 354 computations (89.8% saved)

series730.0ms (6.8%)

Error

21.2b

Counts

4 → 47

Calls

4 calls:

258.0ms	(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)))
163.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
155.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
85.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 7794 to 3032 computations (61.1% saved)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5100	1885

prune158.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Error

21.2b

Counts

100 → 4

Compiler

Compiled 6293 to 1134 computations (82% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.1b	(cbrt.f64 (atan2.f64 x.im x.re))
3.1b	(cbrt.f64 (atan2.f64 x.im x.re))
19.1b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 x.im) y.im)))
32.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite86.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

21.2b

Rules

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

Counts

4 → 45

Calls

4 calls:

5.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 x.im) y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

Compiler

Compiled 2786 to 363 computations (87% saved)

series779.0ms (7.3%)

Error

13.1b

Counts

4 → 38

Calls

4 calls:

298.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 x.im) y.im)))
167.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
156.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
110.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5867 to 2249 computations (61.7% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4927	1317
1	4927	1317

prune115.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	81	6	87

Error

13.1b

Counts

87 → 6

Compiler

Compiled 4725 to 592 computations (87.5% saved)

regimes477.0ms (4.5%)

Accuracy

Total 3.5b remaining (22.8%)

Threshold costs 0b (0%)

Compiler

Compiled 5257 to 2810 computations (46.5% saved)

bsearch234.0ms (2.2%)

Steps

Iters	Range		Point
5	2.6376617726070884e-58	5.424033909004746e-58	3.600263651005658e-58
9	4.348887913636889e-268	1.1024885149971577e-262	1.4292601098046946e-265
8	-2.9365817087543324e-306	4.400622635697252e-307	-5.36951614796057e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	163	287
1	163	287

end0.0ms (0%)

sample4.0s (37.2%)

Algorithm

1×

intervals

Results

1.2s	2379×	body	1024	invalid
826.0ms	7570×	body	128	valid
333.0ms	958×	body	512	invalid
97.0ms	424×	body	256	invalid
88.0ms	170×	body	1024	valid
64.0ms	543×	body	128	invalid
53.0ms	155×	body	512	valid
22.0ms	29×	body	2048	invalid
20.0ms	88×	body	256	valid
14.0ms	17×	body	2048	valid

Compiler

Compiled 1218 to 621 computations (49% saved)

Details

analyze1.7s (15.4%)

sample121.0ms (1.1%)

simplify65.0ms (0.6%)

prune8.0ms (0.1%)

localize22.0ms (0.2%)

rewrite104.0ms (1%)

series607.0ms (5.7%)

simplify81.0ms (0.8%)

prune147.0ms (1.4%)

localize28.0ms (0.3%)

rewrite92.0ms (0.9%)

series676.0ms (6.3%)

simplify72.0ms (0.7%)

prune149.0ms (1.4%)

localize32.0ms (0.3%)

rewrite102.0ms (1%)

series730.0ms (6.8%)

simplify76.0ms (0.7%)

prune158.0ms (1.5%)

localize33.0ms (0.3%)

rewrite86.0ms (0.8%)

series779.0ms (7.3%)

simplify67.0ms (0.6%)

prune115.0ms (1.1%)

regimes477.0ms (4.5%)

bsearch234.0ms (2.2%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample4.0s (37.2%)

Profiling