Details

Time bar (total: 7.2s)

sample440.0ms

Algorithm
intervals
Results
60.0ms65×body1280valid
23.0ms257×body80valid
19.0ms48×body640valid
7.0ms25×body320valid
2.0ms10×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
30.5b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite54.0ms

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×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
158.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (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)
1.8b
(* (atan2 x.im x.re) y.im)
31.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
15.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
98.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune264.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
0.0b
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
0.1b
(* y.re (log (/ -1 x.re)))
1.8b
(* (atan2 x.im x.re) y.im)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
52×log-prod
43×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
36×times-frac
26×distribute-rgt-in associate-+r+ distribute-lft-in
10×exp-prod add-log-exp
9×pow1
8×add-exp-log add-cbrt-cube
7×associate-*r*
6×associate-*l*
4×div-inv
3×distribute-lft-neg-in distribute-rgt-neg-in rem-exp-log
2×pow-prod-down neg-log prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative neg-sub0 exp-neg neg-mul-1 distribute-neg-in flip3-+ exp-diff exp-sum log-pow flip-+
Counts
4 → 123
Calls
4 calls:
35.0ms
(exp (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
14.0ms
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
14.0ms
(* y.re (log (/ -1 x.re)))
7.0ms
(* (atan2 x.im x.re) y.im)

series258.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(exp (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
111.0ms
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
41.0ms
(* y.re (log (/ -1 x.re)))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify51.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0457961
11656899
25002884

prune407.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
1.8b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log cbrt-prod add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×cbrt-div distribute-neg-frac
1×neg-mul-1 flip3-+ pow1/3 flip-+
Counts
4 → 74
Calls
4 calls:
9.0ms
(cbrt (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
7.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.im)

series265.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(cbrt (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
19.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.im)

simplify104.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0242558
1749526
23635517
35002517

prune330.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.5b

regimes268.0ms

Accuracy

60.4% (6.4b remaining)

Error of 10.1b against oracle of 3.6b and baseline of 19.9b

bsearch227.0ms

Steps
ItersRangePoint
10
5.7510339643397785e-08
5459.192962656793
0.9896125733904901
9
-3.9417628294913115e-252
-3.5512611144321106e-261
-5.066092175636721e-261

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05246
17146
27146

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2032×body1280valid
680.0ms7973×body80valid
593.0ms1520×body640valid
176.0ms663×body320valid
63.0ms340×body160valid