Details

Time bar (total: 6.0s)

sample345.0ms

Algorithm
intervals
Results
38.0ms62×body1280valid
24.0ms258×body80valid
15.0ms37×body640valid
5.0ms18×body320valid
1.0ms3×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune29.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.0b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×hypot-def
9×*-commutative
4×sqrt-div
3×+-commutative
2×flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 19
Calls
4 calls:
2.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify132.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0122130
1264128
2585124
31404124
44462124
55001124

prune148.0ms

Filtered
31 candidates to 22 candidates (71.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New26531
Fresh011
Picked101
Done000
Total27633

Merged error: 22.6b

Counts
33 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×*-commutative
5×hypot-def
2×+-commutative sin-sum sqrt-div
1×flip3-+ pow1/2 flip-+
Counts
4 → 12
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify135.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
011993
126192
258390
3140290
4446090
5500190

prune106.0ms

Filtered
24 candidates to 16 candidates (66.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New21324
Fresh415
Picked101
Done000
Total26430

Merged error: 3.2b

Counts
30 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.3b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
3×*-commutative
2×sin-sum
1×+-commutative
Counts
4 → 5
Calls
4 calls:
2.0ms
(* (log (hypot x.re x.im)) y.re)
2.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (log (hypot x.re x.im)) y.re)
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
151.0ms
(sin (+ (* (log (hypot x.im x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify348.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
07772
112972
222370
372670
4305370
5500170

prune77.0ms

Filtered
17 candidates to 12 candidates (70.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New15217
Fresh123
Picked011
Done000
Total16521

Merged error: 2.9b

Counts
21 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.3b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
16.7b
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.im)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
7×*-commutative
6×sin-sum
4×prod-diff
3×sin-diff
2×log-prod div-inv associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in
Counts
4 → 12
Calls
4 calls:
2.0ms
(* (log (hypot x.re x.im)) y.re)
2.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.im)))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (log (hypot x.re x.im)) y.re)
16.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
126.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.im)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
0161269
1253265
2428262
31155262
45001262

prune63.0ms

Filtered
24 candidates to 12 candidates (50.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New23124
Fresh033
Picked011
Done011
Total23629

Merged error: 2.8b

Counts
29 → 6

regimes174.0ms

Accuracy

0% (0.2b remaining)

Error of 3.4b against oracle of 3.2b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02415
12415

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2118×body1280valid
695.0ms7925×body80valid
568.0ms1387×body640valid
153.0ms533×body320valid
67.0ms43×body2560valid
45.0ms246×body160valid