Details

Time bar (total: 7.6s)

sample381.0ms

Algorithm
intervals
Results
56.0ms84×body1280valid
22.0ms258×body80valid
21.0ms51×body640valid
6.0ms21×body320valid
2.0ms1×body2560valid
1.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b
(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)
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)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms
(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
0213460
1565419
21299415
32889415
45003415

prune392.0ms

Filtered
78 candidates to 66 candidates (84.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (atan2 x.im x.re) y.re)
0.8b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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

series226.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify110.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0263404
1755360
21828359
34355359
45001359

prune397.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (* 1 (hypot x.re x.im))) y.im)
0.7b
(* (atan2 x.im x.re) y.re)
0.8b
(* (atan2 x.im x.re) y.im)
31.1b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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:
9.0ms
(* (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)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (log (* 1 (hypot x.re x.im))) y.im)
19.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0227443
1694387
22006380
35001378

prune389.0ms

Filtered
84 candidates to 64 candidates (76.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt y.re)
0.7b
(cbrt y.re)
0.8b
(* (atan2 x.im x.re) y.im)
31.4b
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log cbrt-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×pow1/3
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
0.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt y.re)
176.0ms
(cbrt y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
183.0ms
(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify95.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
0171380
1461337
21101333
33036331
45001331

prune350.0ms

Filtered
68 candidates to 56 candidates (82.4%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.1b

regimes324.0ms

Accuracy

0% (0.6b remaining)

Error of 3.6b against oracle of 3.0b and baseline of 3.6b

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03221
13621
23621

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2210×body1280valid
712.0ms7976×body80valid
608.0ms1456×body640valid
169.0ms595×body320valid
91.0ms56×body2560valid
48.0ms242×body160valid