Details

Time bar (total: 8.1s)

sample391.0ms

Algorithm
intervals
Results
45.0ms56×body1280valid
37.0ms252×body80valid
20.0ms36×body640valid
7.0ms17×body320valid
3.0ms10×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.9b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
32.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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)
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
145.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune385.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize19.0ms

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)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
32.9b
(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)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
97.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify69.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0308585
1921522
22504484
35002467

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (pow (hypot x.re x.im) y.re))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.3b
(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
2.2b
(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt exp-prod
11×add-cube-cbrt *-un-lft-identity
7×add-exp-log log-prod add-log-exp
6×pow1 unpow-prod-down add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×rem-log-exp associate-*r* associate-*l* rem-exp-log
2×sqr-pow
1×neg-sub0 distribute-lft-neg-in exp-neg pow-to-exp neg-mul-1 distribute-rgt-neg-in exp-diff pow-prod-down neg-log pow-exp prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
3.0ms
(exp (pow (hypot x.re x.im) y.re))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
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)

series332.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(exp (pow (hypot x.re x.im) y.re))
24.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
156.0ms
(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)

simplify138.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0294551
1994487
24741467
35001467

prune367.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (pow (hypot x.re x.im) y.re))
0.3b
(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (atan2 x.im x.re)) (- y.im))))
0.5b
(exp (atan2 x.im x.re))
0.5b
(pow (exp (atan2 x.im x.re)) (- y.im))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×exp-prod
10×pow-unpow
9×unpow-prod-down
7×log-prod
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in rem-log-exp sqr-pow
2×pow-to-exp pow-exp rem-exp-log
1×neg-sub0 pow-neg neg-mul-1 log-pow pow-sub
Counts
4 → 81
Calls
4 calls:
5.0ms
(exp (pow (hypot x.re x.im) y.re))
3.0ms
(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (atan2 x.im x.re)) (- y.im))))
1.0ms
(exp (atan2 x.im x.re))
3.0ms
(pow (exp (atan2 x.im x.re)) (- y.im))

series358.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(exp (pow (hypot x.re x.im) y.re))
171.0ms
(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (atan2 x.im x.re)) (- y.im))))
14.0ms
(exp (atan2 x.im x.re))
40.0ms
(pow (exp (atan2 x.im x.re)) (- y.im))

simplify39.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0342599
11148542
25002531

prune381.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

regimes182.0ms

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
0239
1279
2279

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s2028×body1280valid
1.1s7956×body80valid
806.0ms1397×body640valid
289.0ms698×body320valid
90.0ms317×body160valid