Details

Time bar (total: 6.6s)

sample365.0ms

Algorithm
intervals
Results
41.0ms68×body1280valid
20.0ms245×body80valid
20.0ms53×body640valid
7.0ms26×body320valid
2.0ms12×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
27.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b
(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)))

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)))
9.0ms
(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:
20.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(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)))

simplify84.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207454
1556413
21286411
32863411
45002411

prune404.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize18.0ms

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)
2.4b
(* (atan2 x.im x.re) y.im)
27.0b
(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)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms
(* (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)))

simplify70.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune367.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
2.4b
(* (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)
1.0ms
(cbrt y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series550.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
180.0ms
(cbrt y.re)
17.0ms
(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
2.4b
(* (atan2 x.im x.re) y.im)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×log-prod
6×add-cube-cbrt *-un-lft-identity
5×add-exp-log
4×pow1 add-cbrt-cube
3×unpow-prod-down rem-log-exp associate-*r* associate-*l*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×pow-to-exp pow-prod-down pow-exp prod-exp log-pow *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
2 → 40
Calls
2 calls:
3.0ms
(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
3.0ms
(* (atan2 x.im x.re) y.im)

series171.0ms

Counts
2 → 6
Calls
2 calls:
155.0ms
(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify63.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0186359
1586307
22034291
35001281

prune168.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

regimes248.0ms

Accuracy

0% (0.6b remaining)

Error of 4.2b against oracle of 3.6b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02413
12813
22813

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2085×body1280valid
663.0ms7947×body80valid
547.0ms1412×body640valid
186.0ms684×body320valid
54.0ms308×body160valid