Details

Time bar (total: 7.5s)

sample372.0ms

Algorithm
intervals
Results
45.0ms68×body1280valid
26.0ms249×body80valid
19.0ms43×body640valid
7.0ms23×body320valid
2.0ms12×body160valid
2.0ms1×body2560valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
4.0ms
(* (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
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune394.0ms

Filtered
78 candidates to 66 candidates (84.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify94.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune389.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
0.8b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow
Counts
4 → 71
Calls
4 calls:
3.0ms
(* (log (hypot x.re x.im)) y.re)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (log (hypot x.re x.im)) y.re)
17.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
158.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify85.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0233400
1725351
21668349
33156349
45001349

prune339.0ms

Filtered
83 candidates to 61 candidates (73.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y.re)
0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
1.7b
(* (atan2 x.im x.re) y.im)
33.5b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
11×add-sqr-sqrt
10×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
6×cbrt-prod
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×*-commutative
1×sin-sum pow1/3 unswap-sqr
Counts
4 → 69
Calls
4 calls:
1.0ms
(cbrt y.re)
35.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
3.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt y.re)
39.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
17.0ms
(* (atan2 x.im x.re) y.im)
182.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify142.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0275568
11150460
24969434
35001434

prune327.0ms

Filtered
81 candidates to 59 candidates (72.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes271.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03049
13049

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2156×body1280valid
743.0ms7910×body80valid
656.0ms1475×body640valid
171.0ms549×body320valid
66.0ms41×body2560valid
49.0ms242×body160valid