Details

Time bar (total: 9.2s)

sample427.0ms

Algorithm
intervals
Results
76.0ms78×body1280valid
35.0ms250×body80valid
30.0ms49×body640valid
6.0ms15×body320valid
2.0ms9×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(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)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune674.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.3b

localize19.0ms

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)
2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite37.0ms

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))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
84.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491

prune447.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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:
9.0ms
(* (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)))
18.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
126.0ms
(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

prune717.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.0b
(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.1b
(* (log (* -1 x.re)) y.re)
2.2b
(* (atan2 x.im x.re) y.im)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
6×associate-*r*
3×exp-prod pow-prod-down
2×sub-neg diff-log exp-sum prod-exp log-pow *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×flip3-- exp-diff flip--
Counts
4 → 65
Calls
4 calls:
10.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
29.0ms
(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
17.0ms
(* (log (* -1 x.re)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series243.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
61.0ms
(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
63.0ms
(* (log (* -1 x.re)) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)

simplify114.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0259463
1927420
24704412
35001412

prune302.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.6b

regimes273.0ms

Accuracy

67.8% (5.2b remaining)

Error of 8.4b against oracle of 3.2b and baseline of 19.3b

bsearch159.0ms

Steps
ItersRangePoint
8
-8.232605307541833e-305
6.7289099023299e-310
1.15021295839907e-310

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03524
13924
23924

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s2067×body1280valid
1.1s8008×body80valid
911.0ms1461×body640valid
263.0ms604×body320valid
79.0ms279×body160valid