Details

Time bar (total: 7.2s)

sample359.0ms

Algorithm
intervals
Results
46.0ms75×body1280valid
25.0ms258×body80valid
19.0ms47×body640valid
6.0ms20×body320valid
3.0ms14×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (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)))
30.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

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×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)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms
(cos (+ (* (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
0207456
1556415
21286411
32863411
45002411

prune431.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
95.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (* 1 (hypot x.re x.im))) y.re)
1.9b
(* (atan2 x.im x.re) y.im)

rewrite28.0ms

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:
11.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (* 1 (hypot x.re x.im))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series366.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
140.0ms
(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
103.0ms
(* (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

prune359.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (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)))
30.8b
(cos (+ (* (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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
6.0ms
(* (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)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207454
1556413
21286411
32863411
45002411

prune447.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.5b

regimes196.0ms

Accuracy

0% (0.6b remaining)

Error of 4.4b against oracle of 3.8b and baseline of 4.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0208
1248
2248

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2105×body1280valid
718.0ms7913×body80valid
617.0ms1477×body640valid
194.0ms686×body320valid
67.0ms323×body160valid