Details

Time bar (total: 7.4s)

sample379.0ms

Algorithm
intervals
Results
49.0ms73×body1280valid
23.0ms238×body80valid
17.0ms40×body640valid
6.0ms20×body320valid
3.0ms2×body2560valid
2.0ms8×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.2b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(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:
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)))
9.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(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)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213460
1565419
21299415
32889415
45003415

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(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)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify92.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1731350
21732349
33569349
45002349

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
1.4b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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:
4.0ms
(* (log (hypot x.re x.im)) y.im)
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)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (log (hypot x.re x.im)) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
146.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune365.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.im)
1.4b
(* (atan2 x.im x.re) y.re)
2.3b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
31.4b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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:
1.0ms
(cbrt y.im)
3.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
5.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(cbrt y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
82.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
149.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify99.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0240414
1794352
23477345
35001339

prune354.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

regimes347.0ms

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 3.0b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02822
12822

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2218×body1280valid
728.0ms7950×body80valid
603.0ms1410×body640valid
174.0ms594×body320valid
88.0ms56×body2560valid
51.0ms254×body160valid