Details

Time bar (total: 6.8s)

sample355.0ms

Algorithm
intervals
Results
35.0ms61×body1280valid
21.0ms239×body80valid
17.0ms46×body640valid
7.0ms26×body320valid
2.0ms9×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.2b

localize26.0ms

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)))
31.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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:
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
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207454
1556413
21286411
32863411
45002411

prune388.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log prod-diff flip-+ hypot-def
Counts
4 → 79
Calls
4 calls:
7.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune348.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.0b
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum pow-prod-down
2×sub-neg diff-log prod-diff prod-exp log-pow *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff fma-neg flip--
Counts
4 → 76
Calls
4 calls:
5.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)

series360.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
102.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
102.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)

simplify103.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0269584
1861528
23384509
35001508

prune332.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.0b
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (* 1 (hypot x.re x.im))) y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum pow-prod-down
2×sub-neg diff-log prod-diff prod-exp log-pow *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff fma-neg flip--
Counts
4 → 76
Calls
4 calls:
5.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
4.0ms
(* (atan2 x.im x.re) y.im)

series355.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
108.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
100.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify101.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0269584
1861528
23384509
35001508

prune314.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.8b

regimes216.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0228
1248
2248

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2064×body1280valid
661.0ms7974×body80valid
572.0ms1459×body640valid
177.0ms668×body320valid
56.0ms317×body160valid