Details

Time bar (total: 6.9s)

sample416.0ms

Algorithm
intervals
Results
40.0ms254×body80valid
30.0ms51×body1280valid
18.0ms46×body640valid
5.0ms19×body320valid
4.0ms13×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
139.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205456
1546415
21264411
32748411
45001411

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
29.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

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 cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
131.0ms
(cos (+ (* (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
0253386
1722346
21719345
33543345
45002345

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
0.5b
(* (atan2 x.im x.re) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
33.0b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

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×cos-sum log-pow
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (log (hypot x.re x.im)) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
134.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0228396
1717347
21656345
33133345
45001345

prune327.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
0.5b
(* (atan2 x.im x.re) y.im)
1.0b
(* (atan2 x.im x.re) y.re)
33.0b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log1p-udef log1p-expm1
Counts
4 → 61
Calls
4 calls:
0.0ms
(log1p (cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
9.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(log1p (cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re))))
15.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (atan2 x.im x.re) y.re)
131.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify162.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0182419
1502365
21132365
31907365
44796365
55001365

prune289.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

regimes245.0ms

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 2.9b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02619
12619

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s1988×body1280valid
653.0ms7999×body80valid
532.0ms1390×body640valid
180.0ms690×body320valid
52.0ms299×body160valid