Details

analyze1.8s

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

sample188.0ms

Algorithm

intervals

Results

70.0ms	75×	body	1280	invalid
44.0ms	242×	body	80	valid
27.0ms	38×	body	640	invalid
7.0ms	13×	body	320	invalid
4.0ms	5×	body	1280	valid
3.0ms	5×	body	320	valid
2.0ms	1×	body	2560	invalid
2.0ms	7×	body	160	invalid
2.0ms	3×	body	640	valid
2.0ms	11×	body	80	invalid
0.0ms	1×	body	160	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4937	72
1	4937	72

prune20.0ms

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: 31.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
112.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5130	1275

prune272.0ms

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: 20.7b

Counts

69 → 7

localize59.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (pow x.re 2) (pow x.im 2)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-sum`
2×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 41

Calls

4 calls:

8.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
8.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
9.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
98.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
96.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
91.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify93.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5027	1624

prune509.0ms

Filtered

48 candidates to 53 candidates (-10.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	51	9	60

Merged error: 20.7b

Counts

60 → 9

localize84.0ms

Local error

Found 4 expressions with local error:

31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
31.6b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

7.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
91.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
59.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))
73.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify89.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4808	1740
1	4808	1740

prune633.0ms

Filtered

44 candidates to 44 candidates (0.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 20.7b

Counts

53 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.5b	(cbrt (pow (* y.im (atan2 x.im x.re)) 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`cbrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `unpow-prod-down` `sin-sum` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
2.0ms	(cbrt (pow (* y.im (atan2 x.im x.re)) 3))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cbrt (pow (* y.im (atan2 x.im x.re)) 3))

simplify88.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5284	1350

prune211.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	67	9	76

Merged error: 20.7b

Counts

76 → 9

regimes608.0ms

Accuracy

79.8% (2.9b remaining)

Error of 21.7b against oracle of 18.8b and baseline of 33.2b

bsearch72.0ms

Steps

Iters	Range		Point
7	-3.549524535819085e-307	1.57175523787345e-308	3.5816343427214e-310

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	129
1	73	129

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	2118×	body	1280	invalid
1.2s	7569×	body	80	valid
894.0ms	1268×	body	640	invalid
227.0ms	464×	body	320	invalid
115.0ms	114×	body	1280	valid
104.0ms	150×	body	640	valid
70.0ms	42×	body	2560	invalid
63.0ms	341×	body	80	invalid
59.0ms	181×	body	160	invalid
51.0ms	101×	body	320	valid
22.0ms	66×	body	160	valid

Details

analyze1.8s

sample188.0ms

simplify91.0ms

prune20.0ms

localize22.0ms

rewrite31.0ms

series145.0ms

simplify79.0ms

prune272.0ms

localize59.0ms

rewrite33.0ms

series291.0ms

simplify93.0ms

prune509.0ms

localize84.0ms

rewrite40.0ms

series329.0ms

simplify89.0ms

prune633.0ms

localize33.0ms

rewrite18.0ms

series91.0ms

simplify88.0ms

prune211.0ms

regimes608.0ms

bsearch72.0ms

simplify4.0ms

end0.0ms

sample5.4s

Profiling