Details

Time bar (total: 6.6s)

sample358.0ms

Algorithm
intervals
Results
45.0ms79×body1280valid
21.0ms248×body80valid
18.0ms41×body640valid
4.0ms16×body320valid
1.0ms6×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune379.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)
1.9b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:
8.0ms
(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)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(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)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune346.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re)
0.5b
(* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))
1.9b
(* (atan2 x.im x.re) y.im)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
20×add-exp-log
18×unpow-prod-down associate-*l*
17×add-cube-cbrt *-un-lft-identity
13×associate-*r*
11×prod-exp unswap-sqr
10×add-cbrt-cube sqr-pow
9×pow1
7×swap-sqr add-log-exp
6×pow-to-exp pow-exp
5×log-pow
4×expm1-log1p-u pow-prod-down log1p-expm1-u unpow1/2
3×exp-prod exp-sum *-commutative cbrt-unprod
2×pow2 pow-sqr pow-prod-up rem-exp-log
1×sub-neg exp-diff sqrt-unprod diff-log prod-diff rem-square-sqrt
Counts
4 → 119
Calls
4 calls:
15.0ms
(exp (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms
(* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re)
8.0ms
(* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))
3.0ms
(* (atan2 x.im x.re) y.im)

series265.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(exp (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
100.0ms
(* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re)
45.0ms
(* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify59.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0341821
11379663
25001624

prune424.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
1.9b
(* (atan2 x.im x.re) y.im)
1.9b
(* (atan2 x.im x.re) y.im)
1.9b
(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×cbrt-div
1×flip3-- pow1/3 flip--
Counts
4 → 75
Calls
4 calls:
4.0ms
(cbrt (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)

series241.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(cbrt (- (* (log (* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))) y.re) (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify124.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0237555
1742520
23568517
35001507

prune377.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

regimes198.0ms

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
03145
13345
23345

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2000×body1280valid
655.0ms7920×body80valid
542.0ms1392×body640valid
173.0ms649×body320valid
52.0ms285×body160valid