Details

Time bar (total: 5.5s)

sample312.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
13.0ms149×body80overflowed
4.0ms6×body1280valid
2.0ms3×body640valid
1.0ms3×body320valid
1.0ms3×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.6b

localize35.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
33.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(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:
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
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune378.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
33.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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

series224.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify90.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune382.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.9b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
35.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×pow1
11×associate-*l*
10×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod unswap-sqr
2×log-pow
1×sin-sum
Counts
4 → 72
Calls
4 calls:
7.0ms
(* (log (* 1 (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)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (log (* 1 (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)
153.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0237429
1729375
22088368
35001366

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.9b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
2.2b
(* (atan2 x.im x.re) y.im)
35.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt
9×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×sin-sum pow1/3
Counts
4 → 64
Calls
4 calls:
0.0ms
(cbrt y.re)
10.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
3.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt y.re)
83.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
16.0ms
(* (atan2 x.im x.re) y.im)
176.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify101.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0245484
1824412
23545405
35002399

prune359.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

regimes246.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02816
13216
23216

end0.0ms

sample1.6s

Algorithm
intervals
Results
706.0ms7924×body80valid
358.0ms4095×body80overflowed
85.0ms129×body1280valid
76.0ms175×body640valid
31.0ms107×body320valid
12.0ms60×body160valid