Details

Time bar (total: 7.2s)

sample428.0ms

Algorithm
intervals
Results
42.0ms253×body80valid
38.0ms57×body1280valid
19.0ms47×body640valid
4.0ms15×body320valid
4.0ms9×body160valid
3.0ms2×body2560valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0211458
1555417
21277415
32762415
45002415

prune384.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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:
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify91.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune391.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
33.2b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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:
8.0ms
(* (log (hypot x.re x.im)) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (log (hypot x.re x.im)) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
144.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0233400
1725351
21668349
33156349
45001349

prune342.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize24.0ms

Local error

Found 4 expressions with local error:

7.1b
(cbrt (* (atan2 x.im x.re) y.im))
7.1b
(cbrt (* (atan2 x.im x.re) y.im))
7.1b
(cbrt (* (atan2 x.im x.re) y.im))
33.2b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
17.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(cbrt (* (atan2 x.im x.re) y.im))
57.0ms
(cbrt (* (atan2 x.im x.re) y.im))
58.0ms
(cbrt (* (atan2 x.im x.re) y.im))
142.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify117.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (24.0ms)

IterNodesCost
0122349
1194310
2336292
3770286
42708283
55001283

prune258.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

regimes266.0ms

Accuracy

0% (0.1b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02624
12624

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2185×body1280valid
703.0ms7965×body80valid
557.0ms1363×body640valid
162.0ms579×body320valid
70.0ms46×body2560valid
44.0ms228×body160valid