Details

analyze1.5s

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

sample128.0ms

Algorithm

intervals

Results

48.0ms	61×	body	1280	invalid
30.0ms	248×	body	80	valid
13.0ms	25×	body	640	invalid
6.0ms	4×	body	640	valid
4.0ms	11×	body	320	invalid
3.0ms	2×	body	2560	invalid
2.0ms	3×	body	1280	valid
1.0ms	5×	body	160	invalid
1.0ms	9×	body	80	invalid
0.0ms	1×	body	320	valid

simplify484.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune10.0ms

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: 32.8b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

1.9b	(*.f64 (atan2.f64 x.im x.re) y.re)
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.9b	(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.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)))
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)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
12.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
64.0ms	(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	4957	686
1	4957	686

prune73.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 17.2b

Counts

69 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

1.3b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.1b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re))))

rewrite26.0ms

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` `sin-sum_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

4 calls:

7.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 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)))
9.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
52.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 y.re))))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4953	754
1	4953	754

prune62.0ms

Filtered

54 candidates to 69 candidates (-27.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 17.2b

Counts

76 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)) (cbrt.f64 y.re))))

rewrite23.0ms

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)))
9.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)) (cbrt.f64 y.re))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
53.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (.f64 (.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)) (cbrt.f64 y.re))))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4920	686
1	4920	686

prune51.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 17.2b

Counts

75 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

29.4b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.9b	(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)))
33.9b	(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)))
33.9b	(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)))

rewrite28.0ms

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)))
7.0ms	(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)))
7.0ms	(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)))
7.0ms	(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)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
48.0ms	(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)))
50.0ms	(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)))
48.0ms	(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

51 → 51

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4858	842
1	4858	842

prune35.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	49	9	58

Merged error: 17.2b

Counts

58 → 9

regimes305.0ms

Accuracy

77% (3.3b remaining)

Error of 22.7b against oracle of 19.4b and baseline of 33.7b

bsearch46.0ms

Steps

Iters	Range		Point
5	-3.2001959475784966e-301	-1.275923684827059e-301	-1.2955711521312062e-301

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2073×	body	1280	invalid
874.0ms	7552×	body	80	valid
657.0ms	1282×	body	640	invalid
165.0ms	462×	body	320	invalid
93.0ms	54×	body	2560	invalid
93.0ms	123×	body	1280	valid
79.0ms	158×	body	640	valid
49.0ms	398×	body	80	invalid
37.0ms	106×	body	320	valid
37.0ms	158×	body	160	invalid
15.0ms	61×	body	160	valid

Details

analyze1.5s

sample128.0ms

simplify484.0ms

prune10.0ms

localize32.0ms

rewrite25.0ms

series89.0ms

simplify60.0ms

prune73.0ms

localize29.0ms

rewrite26.0ms

series93.0ms

simplify45.0ms

prune62.0ms

localize25.0ms

rewrite23.0ms

series73.0ms

simplify58.0ms

prune51.0ms

localize30.0ms

rewrite28.0ms

series152.0ms

simplify60.0ms

prune35.0ms

regimes305.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling