Details

Time bar (total: 7.2s)

sample361.0ms

Algorithm
intervals
Results
41.0ms68×body1280valid
24.0ms251×body80valid
17.0ms41×body640valid
7.0ms24×body320valid
2.0ms12×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune17.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(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)
3.0ms
(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)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms
(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 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune390.0ms

Filtered
78 candidates to 66 candidates (84.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.2b

localize18.0ms

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)
1.7b
(* (atan2 x.im x.re) y.im)
28.3b
(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:
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)))

series244.0ms

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)))
92.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(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

prune352.0ms

Filtered
91 candidates to 74 candidates (81.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y.re)
0.5b
(cbrt y.re)
0.5b
(cbrt y.re)
1.7b
(* (atan2 x.im x.re) y.im)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 59
Calls
4 calls:
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
0.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series534.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt y.re)
171.0ms
(cbrt y.re)
174.0ms
(cbrt y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify53.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune324.0ms

Filtered
71 candidates to 57 candidates (80.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y.re)
0.5b
(cbrt y.re)
1.7b
(* (atan2 x.im x.re) y.im)
10.2b
(log (exp (cbrt y.re)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×cbrt-prod
7×pow1 log-pow
6×add-exp-log exp-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod associate-*r* associate-*l*
2×pow1/3
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
0.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(log (exp (cbrt y.re)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
178.0ms
(log (exp (cbrt y.re)))

simplify50.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
0136234
1340211
2764205
31635202
45001202

prune337.0ms

Filtered
78 candidates to 61 candidates (78.2%)
Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.9b

regimes262.0ms

Accuracy

0% (0.5b 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
02413
12813
22813

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1983×body1280valid
695.0ms7943×body80valid
609.0ms1514×body640valid
175.0ms631×body320valid
63.0ms302×body160valid