Details

Time bar (total: 7.5s)

sample451.0ms

Algorithm
intervals
Results
47.0ms74×body1280valid
44.0ms255×body80valid
19.0ms47×body640valid
6.0ms22×body320valid
1.0ms7×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
30.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite77.0ms

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:
13.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
159.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune383.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
30.6b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite40.0ms

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

series241.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
166.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify97.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1727350
21728349
33565349
45002349

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
0.7b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
30.6b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

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)
9.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (log (hypot x.re x.im)) y.re)
22.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
166.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0233400
1725351
21668349
33156349
45001349

prune350.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (* (atan2 x.im x.re) y.im))
5.2b
(cbrt (* (atan2 x.im x.re) y.im))
5.2b
(cbrt (* (atan2 x.im x.re) y.im))
30.6b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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

series366.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(cbrt (* (atan2 x.im x.re) y.im))
67.0ms
(cbrt (* (atan2 x.im x.re) y.im))
63.0ms
(cbrt (* (atan2 x.im x.re) y.im))
169.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify118.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (25.0ms)

IterNodesCost
0122349
1194310
2336292
3770286
42708283
55001283

prune264.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

regimes286.0ms

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
02826
12826

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2201×body1280valid
691.0ms7935×body80valid
613.0ms1513×body640valid
163.0ms584×body320valid
63.0ms42×body2560valid
51.0ms253×body160valid