Details

Time bar (total: 8.4s)

sample433.0ms

Algorithm
intervals
Results
72.0ms74×body1280valid
44.0ms251×body80valid
34.0ms56×body640valid
7.0ms16×body320valid
4.0ms13×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b
(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)))

series242.0ms

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)))
151.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune320.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (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)
1.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
8.0ms
(exp (- (* (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)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune296.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* sqrt-prod
4×sqrt-div add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 66
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.im)
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)))

series108.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify69.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0145348
1428322
21017320
32145320
45002320

prune358.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
4.1b
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
8×add-exp-log log-pow add-cbrt-cube
7×associate-*l*
6×exp-prod associate-*r* sqrt-prod
4×add-log-exp
3×log-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 70
Calls
4 calls:
3.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series182.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0256510
1732441
21709432
33785432
45002432

prune282.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.1b

regimes342.0ms

Accuracy

62% (6.1b remaining)

Error of 9.9b against oracle of 3.8b and baseline of 20.0b

bsearch294.0ms

Steps
ItersRangePoint
10
1.0928630698256826e-243
1.0310911336826013e-231
8.595292827844492e-243
9
-3.5260362984931933e-177
-8.373869441468036e-184
-1.3201057596803101e-183

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04940
16140
26140

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.7s1987×body1280valid
1.4s7946×body80valid
852.0ms1377×body640valid
293.0ms636×body320valid
86.0ms270×body160valid