Details

Time bar (total: 9.1s)

sample455.0ms

Algorithm
intervals
Results
81.0ms87×body1280valid
47.0ms254×body80valid
31.0ms51×body640valid
9.0ms20×body320valid
6.0ms3×body2560valid
3.0ms9×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.6b

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(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)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms
(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 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune388.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(sin (+ (* (log (* 1 (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)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify111.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune414.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (* 1 (hypot x.re x.im))) y.im)
1.6b
(* (atan2 x.im x.re) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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.im)
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (log (* 1 (hypot x.re x.im))) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
151.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0227443
1694387
22006380
35001378

prune382.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (log (* 1 (hypot x.re x.im))))
1.6b
(* (atan2 x.im x.re) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
5×cbrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×sin-sum pow1/3
Counts
4 → 65
Calls
4 calls:
1.0ms
(cbrt (log (* 1 (hypot x.re x.im))))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
58.0ms
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (log (* 1 (hypot x.re x.im))))
16.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(sin (+ (* (* (cbrt (log (* 1 (hypot x.re x.im)))) (cbrt (log (* 1 (hypot x.re x.im))))) (* (cbrt (log (* 1 (hypot x.re x.im)))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0209568
1552498
21232495
32176492
45001492

prune344.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

regimes290.0ms

Accuracy

0% (0.6b remaining)

Error of 3.6b against oracle of 2.9b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03639
14039
24039

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.0s2299×body1280valid
1.4s7943×body80valid
885.0ms1416×body640valid
264.0ms576×body320valid
96.0ms53×body2560valid
76.0ms237×body160valid