Details

Time bar (total: 7.1s)

sample438.0ms

Algorithm
intervals
Results
60.0ms68×body1280valid
24.0ms264×body80valid
20.0ms52×body640valid
7.0ms24×body320valid
0.0ms2×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.6b

localize33.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

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)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune324.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.2b

localize15.0ms

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)
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite40.0ms

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:
8.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
13.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
79.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune273.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
6×associate-*r*
5×add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 49
Calls
3 calls:
8.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
8.0ms
(* (log x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series159.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
57.0ms
(* (log x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify69.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0208273
1698252
22248241
35002241

prune158.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize13.0ms

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)

rewrite72.0ms

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:
32.0ms
(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))))
13.0ms
(* y.re (log (/ -1 x.re)))
7.0ms
(* (atan2 x.im x.re) y.im)

series219.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(exp (- (+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))))
95.0ms
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
39.0ms
(* y.re (log (/ -1 x.re)))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify54.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0457961
11656899
25002884

prune382.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.0b

regimes360.0ms

Accuracy

64.7% (5.9b remaining)

Error of 9.4b against oracle of 3.4b and baseline of 20.2b

bsearch532.0ms

Steps
ItersRangePoint
8
4.3473897379746496e-92
2.3447525200782928e-88
4.421989942484377e-92
9
3.8871116002815187e-131
5.5601299630381306e-126
5.5106254525624743e-126
11
-7.519470916193732e-280
1.7139560852676268e-307
2.1213890303773e-310
8
-5.390430969028645e-31
-5.700837983803917e-35
-5.407292395185871e-32
10
-5371094.503416257
-3.843065465383605e-05
-1.3172646528039174

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07054
19154
29154

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2018×body1280valid
684.0ms7976×body80valid
593.0ms1497×body640valid
174.0ms637×body320valid
58.0ms314×body160valid