Details

Time bar (total: 6.6s)

sample354.0ms

Algorithm
intervals
Results
30.0ms52×body1280valid
23.0ms250×body80valid
20.0ms52×body640valid
5.0ms18×body320valid
2.0ms10×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(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)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(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
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune304.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.4b

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))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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:
3.0ms
(- (* (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)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
88.0ms
(* (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)))

simplify78.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune265.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.8b

localize28.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381

prune336.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
0.1b
(* y.re (log (/ -1 x.re)))
1.5b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
52×log-prod
39×add-sqr-sqrt
36×times-frac
35×add-cube-cbrt *-un-lft-identity
26×distribute-rgt-in associate-+r+ distribute-lft-in
8×pow1
7×add-exp-log associate-*r* add-cbrt-cube
6×associate-*l*
5×add-log-exp
4×div-inv
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sum-log log-pow flip-+
Counts
3 → 100
Calls
3 calls:
7.0ms
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
7.0ms
(* y.re (log (/ -1 x.re)))
3.0ms
(* (atan2 x.im x.re) y.im)

series163.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(+ (* (atan2 x.im x.re) y.im) (* y.re (log (/ -1 x.re))))
39.0ms
(* y.re (log (/ -1 x.re)))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify47.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0389746
11420705
25002697

prune307.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 2.8b

regimes225.0ms

Accuracy

65.1% (5.6b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 19.8b

bsearch360.0ms

Steps
ItersRangePoint
8
1.8793537737921384e-32
3.9771376544151965e-29
5.924531193162435e-30
9
5.073148275473809e-159
2.88733846674046e-150
8.899433436760234e-153
9
-6.152941817396574e-304
2.4251123973937145e-305
2.98637517902405e-310
5
-3.595439683671731e-80
-1.748986179357307e-80
-1.9930388043660413e-80

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05845
18045
28345
38345

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2039×body1280valid
677.0ms7988×body80valid
606.0ms1558×body640valid
175.0ms664×body320valid
55.0ms284×body160valid