Details

Time bar (total: 6.6s)

sample363.0ms

Algorithm
intervals
Results
42.0ms70×body1280valid
21.0ms257×body80valid
16.0ms42×body640valid
7.0ms26×body320valid
3.0ms17×body160valid

simplify38.0ms

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: 34.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(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:
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)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(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

prune384.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.8b

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)
1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

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)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series233.0ms

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)))
89.0ms
(* (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

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
1.2b
(* (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)
9.0ms
(* (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:
102.0ms
(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)))
98.0ms
(* (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)

simplify54.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0341821
11379663
25001624

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))
1.2b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.im)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
22×add-exp-log
18×add-cube-cbrt unpow-prod-down *-un-lft-identity
16×associate-*r* associate-*l*
12×prod-exp add-cbrt-cube unswap-sqr
10×pow1 sqr-pow
7×swap-sqr
6×pow-to-exp pow-exp
4×expm1-log1p-u pow-prod-down *-commutative cbrt-unprod log1p-expm1-u unpow1/2 add-log-exp
1×pow2 sqrt-unprod rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 116
Calls
4 calls:
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)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)

series97.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (pow (hypot x.re x.im) 1/2) (pow (hypot x.re x.im) 1/2))
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify37.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0185530
1722425
25001410

prune492.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.8b

regimes201.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02111
12311
22311

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2032×body1280valid
670.0ms7994×body80valid
578.0ms1499×body640valid
172.0ms647×body320valid
48.0ms273×body160valid