Details

Time bar (total: 6.8s)

sample220.0ms

Algorithm
intervals
Results
83.0ms77×body1280valid
46.0ms253×body80valid
29.0ms41×body640valid
13.0ms26×body320valid
3.0ms8×body160valid
2.0ms1×body2560valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0499636
1499636

prune16.0ms

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: 32.5b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

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:
4.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series100.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify53.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
05058689

prune151.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New61768
Fresh000
Picked101
Done000
Total62769

Merged error: 19.3b

Counts
69 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum
Counts
4 → 53
Calls
4 calls:
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (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
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify42.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
04945688
14945688

prune140.0ms

Filtered
52 candidates to 65 candidates (-25.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New65065
Fresh066
Picked011
Done000
Total65772

Merged error: 19.3b

Counts
72 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

11.1b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×unpow-prod-down cube-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 59
Calls
4 calls:
5.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify44.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
051121134

prune157.0ms

Filtered
53 candidates to 71 candidates (-34.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New69271
Fresh055
Picked011
Done011
Total69978

Merged error: 19.3b

Counts
78 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 46
Calls
4 calls:
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
63.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify52.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04890786
14890786

prune144.0ms

Filtered
52 candidates to 58 candidates (-11.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New54458
Fresh156
Picked101
Done022
Total561167

Merged error: 19.3b

Counts
67 → 11

regimes552.0ms

Accuracy

80.3% (2.9b remaining)

Error of 22.3b against oracle of 19.4b and baseline of 34.0b

bsearch98.0ms

Steps
ItersRangePoint
9
-1.1320017857953323e-301
8.126837495347253e-308
7.9933606979313e-311

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03965
13965

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s2226×body1280valid
941.0ms7968×body80valid
740.0ms1433×body640valid
198.0ms527×body320valid
70.0ms47×body2560valid
60.0ms250×body160valid

Profiling

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