Details

Time bar (total: 7.0s)

sample355.0ms

Algorithm
intervals
Results
39.0ms66×body1280valid
24.0ms262×body80valid
19.0ms48×body640valid
6.0ms23×body320valid
2.0ms9×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (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)))
32.7b
(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)
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)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune328.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.0b

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)
1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:
4.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
8.0ms
(* (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)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
96.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(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
11×pow1
10×add-sqr-sqrt
9×add-exp-log
7×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum associate-*r* *-commutative unswap-sqr
Counts
4 → 57
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(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)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify135.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (129.0ms)

IterNodesCost
0232495
1586443
21587439
34527432
45002431

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×add-exp-log
7×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum associate-*r* *-commutative unswap-sqr
Counts
4 → 57
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
139.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify132.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (126.0ms)

IterNodesCost
0232495
1586443
21587439
34527432
45002431

prune390.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.7b

regimes304.0ms

Accuracy

82.2% (5.3b remaining)

Error of 8.6b against oracle of 3.3b and baseline of 33.1b

bsearch117.0ms

Steps
ItersRangePoint
10
-3.1733683408219374e-304
1.957129954217898e-303
7.7747768769685e-312

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
14216
24216

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1976×body1280valid
672.0ms8021×body80valid
564.0ms1424×body640valid
169.0ms618×body320valid
53.0ms298×body160valid