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

sample163.0ms

Algorithm

intervals

Results

66.0ms	85×	body	1280	invalid
30.0ms	247×	body	80	valid
28.0ms	52×	body	640	invalid
8.0ms	2×	body	2560	invalid
3.0ms	9×	body	320	invalid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
2.0ms	8×	body	160	invalid
2.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify623.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4950	72
1	4950	72

prune9.0ms

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: 33.7b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.5b	(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)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
22.0ms	(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)))
223.0ms	(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)))

simplify130.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4838	1270
1	4838	1270

prune117.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

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: 19.3b

Counts

69 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
30.8b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
30.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.5b	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`sqrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`sin-sum_binary64`

Counts

4 → 57

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
36.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
24.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
25.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
200.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify90.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5028	1297

prune144.0ms

Filtered

54 candidates to 69 candidates (-27.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Merged error: 19.2b

Counts

76 → 8

localize38.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.5b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) 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:

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 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
189.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
188.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
185.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify88.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5044	1579

prune172.0ms

Filtered

49 candidates to 51 candidates (-4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	51	8	59

Merged error: 19.2b

Counts

59 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.8b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.2b	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
30.8b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
29.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
156.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
27.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4839	1147
1	4839	1147

prune68.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	68	11	79

Merged error: 11.6b

Counts

79 → 11

regimes292.0ms

Accuracy

76.2% (4.9b remaining)

Error of 17.7b against oracle of 12.9b and baseline of 33.4b

bsearch336.0ms

Steps

Iters	Range		Point
8	-5.418256131246544e-307	1.4670708365425242e-307	2.7747355521088e-310
5	-4.5667240563801356e-257	-1.6183037814701356e-257	-2.054387041127435e-257
10	-5.153748302180885e-188	-9.993350302135847e-201	-9.305949498214368e-199
6	-1.6690360359972105e-22	-1.7187940215324266e-23	-1.5876991366774867e-22

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	312
1	91	312

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2055×	body	1280	invalid
887.0ms	7569×	body	80	valid
638.0ms	1232×	body	640	invalid
161.0ms	447×	body	320	invalid
97.0ms	131×	body	1280	valid
88.0ms	50×	body	2560	invalid
82.0ms	160×	body	640	valid
45.0ms	364×	body	80	invalid
45.0ms	188×	body	160	invalid
30.0ms	83×	body	320	valid
14.0ms	57×	body	160	valid

Details

analyze1.3s

sample163.0ms

simplify623.0ms

prune9.0ms

localize33.0ms

rewrite25.0ms

series297.0ms

simplify130.0ms

prune117.0ms

localize35.0ms

rewrite60.0ms

series273.0ms

simplify90.0ms

prune144.0ms

localize38.0ms

rewrite29.0ms

series583.0ms

simplify88.0ms

prune172.0ms

localize25.0ms

rewrite19.0ms

series241.0ms

simplify130.0ms

prune68.0ms

regimes292.0ms

bsearch336.0ms

simplify7.0ms

end0.0ms

sample4.1s

Profiling