Details

Time bar (total: 7.2s)

sample431.0ms

Algorithm
intervals
Results
44.0ms73×body1280valid
39.0ms49×body640valid
23.0ms247×body80valid
6.0ms22×body320valid
2.0ms12×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(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)))

simplify79.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune393.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

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)
2.9b
(* (atan2 x.im x.re) y.im)
27.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite51.0ms

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:
20.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
96.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune363.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (exp (log (hypot x.re x.im)))) y.re)
2.9b
(* (atan2 x.im x.re) y.im)
5.6b
(exp (log (hypot x.re x.im)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1 exp-prod associate-*l*
8×add-exp-log add-cbrt-cube
7×log-pow add-log-exp
6×associate-*r* exp-sum
4×expm1-log1p-u log1p-expm1-u
3×log-prod rem-exp-log
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg exp-diff diff-log prod-diff
Counts
4 → 80
Calls
4 calls:
24.0ms
(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
18.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(exp (log (hypot x.re x.im)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
103.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)
48.0ms
(exp (log (hypot x.re x.im)))

simplify55.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0258497
1699434
22091412
35001406

prune361.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
0.3b
(* (log (exp (log (hypot x.re x.im)))) y.re)
2.9b
(* (atan2 x.im x.re) y.im)
5.6b
(exp (log (hypot x.re x.im)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1 add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log exp-prod add-cbrt-cube
7×log-pow
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×expm1-log1p rem-exp-log expm1-udef
Counts
4 → 73
Calls
4 calls:
0.0ms
(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
17.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(exp (log (hypot x.re x.im)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
106.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
47.0ms
(exp (log (hypot x.re x.im)))

simplify121.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0237464
1625392
21740381
34715370
45001370

prune335.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

regimes240.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02211
12411
22411

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s2046×body1280valid
708.0ms7961×body80valid
596.0ms1466×body640valid
180.0ms648×body320valid
59.0ms322×body160valid