Details

analyze1.4s

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample167.0ms

Algorithm

intervals

Results

74.0ms	95×	body	1280	invalid
34.0ms	241×	body	80	valid
19.0ms	37×	body	640	invalid
7.0ms	18×	body	320	invalid
4.0ms	8×	body	640	valid
3.0ms	4×	body	1280	valid
3.0ms	11×	body	160	invalid
1.0ms	10×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify501.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune25.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 32.5b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(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)))

rewrite25.0ms

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_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)))
10.0ms	(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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
77.0ms	(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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4938	686
1	4938	686

prune110.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 21.1b

Counts

70 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(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)))
31.7b	(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)))
31.7b	(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)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_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×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
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)))
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)))
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)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
56.0ms	(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)))
58.0ms	(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)))
59.0ms	(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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4858	842
1	4858	842

prune91.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	50	8	58

Merged error: 21.1b

Counts

58 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite21.0ms

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_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)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
59.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4938	686
1	4938	686

prune93.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 21.1b

Counts

76 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

12.1b	(cbrt.f64 (pow.f64 (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))) 3))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.7b	(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)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-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×	`unpow-prod-down_binary64` `cube-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `sin-sum_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 59

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (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))) 3))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
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)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt.f64 (pow.f64 (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))) 3))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
60.0ms	(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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5332	1128

prune73.0ms

Filtered

55 candidates to 71 candidates (-29.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 21.1b

Counts

79 → 9

regimes409.0ms

Accuracy

77.1% (3.1b remaining)

Error of 23.2b against oracle of 20.0b and baseline of 33.7b

bsearch87.0ms

Steps

Iters	Range		Point
8	-2.750531836398237e-307	1.4213517346234429e-306	-3.1791748587786e-310

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2082×	body	1280	invalid
866.0ms	7554×	body	80	valid
620.0ms	1240×	body	640	invalid
172.0ms	483×	body	320	invalid
107.0ms	144×	body	1280	valid
84.0ms	168×	body	640	valid
60.0ms	35×	body	2560	invalid
46.0ms	390×	body	80	invalid
39.0ms	169×	body	160	invalid
29.0ms	85×	body	320	valid
12.0ms	49×	body	160	valid

Details

analyze1.4s

sample167.0ms

simplify501.0ms

prune25.0ms

localize25.0ms

rewrite25.0ms

series100.0ms

simplify60.0ms

prune110.0ms

localize29.0ms

rewrite29.0ms

series182.0ms

simplify58.0ms

prune91.0ms

localize24.0ms

rewrite21.0ms

series82.0ms

simplify58.0ms

prune93.0ms

localize26.0ms

rewrite25.0ms

series134.0ms

simplify46.0ms

prune73.0ms

regimes409.0ms

bsearch87.0ms

simplify3.0ms

end0.0ms

sample4.0s

Profiling