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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample130.0ms

Algorithm

intervals

Results

39.0ms	54×	body	1280	invalid
28.0ms	241×	body	80	valid
23.0ms	46×	body	640	invalid
8.0ms	6×	body	1280	valid
4.0ms	10×	body	320	invalid
2.0ms	4×	body	640	valid
2.0ms	9×	body	160	invalid
1.0ms	9×	body	80	invalid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify467.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune24.0ms

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: 34.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`cos-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)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify42.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5029	677

prune128.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

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: 18.6b

Counts

69 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `exp-sum` `flip-+`

Counts

4 → 68

Calls

4 calls:

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

series77.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4925	844
1	4925	844

prune134.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 4.2b

Counts

85 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (neg x.re)) y.re)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r`
3×	`exp-prod`
2×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`flip3--` `exp-diff` `exp-sum` `log-pow` `flip--`

Counts

4 → 62

Calls

4 calls:

4.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(exp (- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms	(* (log (neg x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series64.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
23.0ms	(exp (- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms	(* (log (neg x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify59.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4979	693
1	4979	693

prune108.0ms

Filtered

52 candidates to 74 candidates (-42.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 4.2b

Counts

82 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify97.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5349	723

prune93.0ms

Filtered

56 candidates to 69 candidates (-23.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	69	8	77

Merged error: 4.2b

Counts

77 → 8

regimes485.0ms

Accuracy

82.6% (5.6b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 36.1b

bsearch94.0ms

Steps

Iters	Range		Point
10	-6.928164999109624e-293	2.440688741743257e-305	2.25401773596525e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1933×	body	1280	invalid
844.0ms	7540×	body	80	valid
645.0ms	1308×	body	640	invalid
181.0ms	516×	body	320	invalid
102.0ms	140×	body	1280	valid
83.0ms	156×	body	640	valid
63.0ms	251×	body	160	invalid
47.0ms	404×	body	80	invalid
35.0ms	102×	body	320	valid
14.0ms	62×	body	160	valid

Details

analyze1.5s

sample130.0ms

simplify467.0ms

prune24.0ms

localize24.0ms

rewrite22.0ms

series89.0ms

simplify42.0ms

prune128.0ms

localize16.0ms

rewrite19.0ms

series77.0ms

simplify38.0ms

prune134.0ms

localize14.0ms

rewrite17.0ms

series64.0ms

simplify59.0ms

prune108.0ms

localize30.0ms

rewrite22.0ms

series92.0ms

simplify97.0ms

prune93.0ms

regimes485.0ms

bsearch94.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling