Details

analyze1.3s

Algorithm

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

sample132.0ms

Algorithm

intervals

Results

49.0ms	63×	body	1280	invalid
28.0ms	244×	body	80	valid
22.0ms	45×	body	640	invalid
4.0ms	6×	body	1280	valid
3.0ms	23×	body	80	invalid
2.0ms	7×	body	320	invalid
2.0ms	9×	body	160	invalid
2.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid

simplify591.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4950	72
1	4950	72

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.9b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(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)))

rewrite24.0ms

Algorithm

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:

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

series287.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
206.0ms	(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)))

simplify126.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4808	1251
1	4808	1251

prune100.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 18.4b

Counts

69 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 65

Calls

4 calls:

7.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
5.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
79.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
30.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4971	1650
1	4971	1650

prune86.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 3.2b

Counts

82 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(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)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series332.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
27.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
188.0ms	(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)))

simplify103.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4990	1364
1	4990	1364

prune102.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	68	9	77

Merged error: 3.2b

Counts

77 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt.f64 (atan2.f64 x.im x.re))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(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)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_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×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `cos-sum_binary64`

Counts

4 → 49

Calls

4 calls:

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

series278.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
27.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
24.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
180.0ms	(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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5021	1143

prune97.0ms

Filtered

53 candidates to 61 candidates (-15.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	61	9	70

Merged error: 3.2b

Counts

70 → 9

regimes174.0ms

Accuracy

64.6% (5.8b remaining)

Error of 9.2b against oracle of 3.3b and baseline of 19.8b

bsearch213.0ms

Steps

Iters	Range	Point
8	-5.75132543572778e-308	7.579527332822757e-307	2.00717256179774e-310
6	-3.38718536736432e-281	-5.749858459227235e-282	-3.1117626072306344e-281
6	-5.647500856219568e-106	-5.503420474491162e-107	-5.535585097585727e-106

Iters

Range

Point

-5.75132543572778e-308

7.579527332822757e-307

2.00717256179774e-310

-3.38718536736432e-281

-5.749858459227235e-282

-3.1117626072306344e-281

-5.647500856219568e-106

-5.503420474491162e-107

-5.535585097585727e-106

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	84	127
1	84	127

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1917×	body	1280	invalid
812.0ms	7580×	body	80	valid
588.0ms	1255×	body	640	invalid
166.0ms	504×	body	320	invalid
93.0ms	133×	body	1280	valid
72.0ms	155×	body	640	valid
55.0ms	244×	body	160	invalid
45.0ms	403×	body	80	invalid
32.0ms	88×	body	320	valid
10.0ms	44×	body	160	valid

Details

analyze1.3s

sample132.0ms

simplify591.0ms

prune8.0ms

localize32.0ms

rewrite24.0ms

series287.0ms

simplify126.0ms

prune100.0ms

localize15.0ms

rewrite21.0ms

series261.0ms

simplify98.0ms

prune86.0ms

localize26.0ms

rewrite24.0ms

series332.0ms

simplify103.0ms

prune102.0ms

localize31.0ms

rewrite17.0ms

series278.0ms

simplify76.0ms

prune97.0ms

regimes174.0ms

bsearch213.0ms

simplify5.0ms

end0.0ms

sample3.6s

Profiling