Details

Time bar (total: 7.5s)

sample338.0ms

Algorithm
intervals
Results
211.0ms44×body640valid
53.0ms71×body1280valid
27.0ms248×body80valid
11.0ms22×body320valid
3.0ms2×body2560valid
2.0ms10×body160valid

simplify526.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0499636
1499636

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 33.4b

Counts
2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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×sin-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
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series86.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sin (+ (* (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: 0 (67.0ms)

IterNodesCost
04835689
14835689

prune143.0ms

Filtered
56 candidates to 68 candidates (-21.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New61768
Fresh000
Picked011
Done000
Total61869

Merged error: 18.5b

Counts
69 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (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
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series173.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
04945851
14945851

prune118.0ms

Filtered
48 candidates to 51 candidates (-6.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New49251
Fresh156
Picked101
Done011
Total51859

Merged error: 18.5b

Counts
59 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (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:
56.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify122.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (116.0ms)

IterNodesCost
04711916
14711916

prune121.0ms

Filtered
44 candidates to 44 candidates (0.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New42244
Fresh066
Picked011
Done011
Total421052

Merged error: 18.5b

Counts
52 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (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:
56.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify121.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (115.0ms)

IterNodesCost
04711916
14711916

prune78.0ms

Filtered
44 candidates to 44 candidates (0.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New44044
Fresh077
Picked011
Done022
Total441054

Merged error: 18.5b

Counts
54 → 10

regimes596.0ms

Accuracy

77.6% (3.1b remaining)

Error of 22.6b against oracle of 19.4b and baseline of 33.4b

bsearch89.0ms

Steps
ItersRangePoint
7
-7.401970125053545e-302
-3.357329548787188e-303
-3.407855708985085e-303

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03965
13965

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.6s2254×body1280valid
873.0ms7977×body80valid
679.0ms1376×body640valid
196.0ms572×body320valid
77.0ms45×body2560valid
54.0ms228×body160valid

Profiling

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