Details

Time bar (total: 7.6s)

sample384.0ms

Algorithm
intervals
Results
54.0ms88×body1280valid
23.0ms247×body80valid
17.0ms43×body640valid
6.0ms21×body320valid
3.0ms2×body2560valid
1.0ms6×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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)
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(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)))
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0213458
1565417
21299415
32889415
45003415

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
31.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

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:
4.0ms
(* (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)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
163.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify92.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0259390
1727350
21728349
33565349
45002349

prune425.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.im)
0.4b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
31.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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)
4.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(* (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)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (log (hypot x.re x.im)) y.im)
16.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
162.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0223400
1696351
21619349
32891349
45001349

prune421.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y.im)
1.0b
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
1.0b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
31.0b
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
11×add-cbrt-cube
9×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×cbrt-prod
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×*-commutative
1×sin-sum pow1/3 unswap-sqr
Counts
4 → 70
Calls
4 calls:
1.0ms
(cbrt y.im)
11.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
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)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(cbrt y.im)
44.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
87.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
158.0ms
(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify37.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0264579
1994452
25002417

prune425.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.9b

regimes431.0ms

Accuracy

0% (0.4b remaining)

Error of 3.5b against oracle of 3.1b and baseline of 3.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03423
13823
23823

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2232×body1280valid
692.0ms7957×body80valid
564.0ms1379×body640valid
154.0ms559×body320valid
75.0ms48×body2560valid
41.0ms227×body160valid