Details

Time bar (total: 5.4s)

sample342.0ms

Algorithm
intervals
Results
35.0ms58×body1280valid
24.0ms259×body80valid
14.0ms37×body640valid
5.0ms20×body320valid
1.0ms4×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune26.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.8b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(cos (+ (* (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
4×sqrt-div
2×cos-sum flip3-+ pow1/2 flip-+
1×+-commutative *-commutative
Counts
4 → 9
Calls
4 calls:
2.0ms
(* (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)))
12.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify123.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0108126
1226126
2465126
31133126
43550126
55002126

prune109.0ms

Filtered
21 candidates to 17 candidates (81.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New18321
Fresh011
Picked101
Done000
Total19423

Merged error: 22.6b

Counts
23 → 4

localize19.0ms

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)
1.6b
(* (atan2 x.im x.re) y.im)
31.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1/2 sqrt-div exp-sum *-commutative
1×sub-neg flip3-+ exp-diff associate-*l* log-pow flip-+
Counts
4 → 9
Calls
4 calls:
6.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
3.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series238.0ms

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)))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 3 (21.0ms)

IterNodesCost
0139100
1311100
270296
3190295
4500295

prune89.0ms

Filtered
21 candidates to 16 candidates (76.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New17421
Fresh033
Picked011
Done000
Total17825

Merged error: 4.0b

Counts
25 → 8

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
1.6b
(* (atan2 x.im x.re) y.im)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-/r* div-inv associate-/l/
1×neg-sub0 exp-neg pow-to-exp unpow-prod-down frac-2neg exp-diff div-exp clear-num *-commutative sqr-pow
Counts
2 → 9
Calls
2 calls:
6.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
2.0ms
(* (atan2 x.im x.re) y.im)

series106.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify68.0ms

Algorithm
egg-herbie
Counts
15 → 15
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
09283
121883
261079
3277877
4500177

prune59.0ms

Filtered
15 candidates to 10 candidates (66.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New14115
Fresh156
Picked011
Done011
Total15823

Merged error: 4.0b

Counts
23 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
0.2b
(* y.re (log x.im))
1.6b
(* (atan2 x.im x.re) y.im)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
2×*-commutative
1×sub-neg flip3-- flip--
Counts
3 → 6
Calls
3 calls:
4.0ms
(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
2.0ms
(* y.re (log x.im))
2.0ms
(* (atan2 x.im x.re) y.im)

series135.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
37.0ms
(* y.re (log x.im))
19.0ms
(* (atan2 x.im x.re) y.im)

simplify106.0ms

Algorithm
egg-herbie
Counts
15 → 15
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
010681
126381
269370
3300970
4500170

prune17.0ms

Filtered
15 candidates to 5 candidates (33.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New15015
Fresh055
Picked011
Done022
Total15823

Merged error: 4.0b

Counts
23 → 8

regimes273.0ms

Accuracy

51.8% (7.7b remaining)

Error of 11.5b against oracle of 3.8b and baseline of 19.8b

bsearch292.0ms

Steps
ItersRangePoint
10
-2.6393627062331543e-300
2.6427537794451112e-306
2.4499326006478e-310
7
-4.61962456934001e-164
-2.804183003613989e-166
-7.760706787373968e-166
7
-2.4739378628411974e-101
-4.703758022750868e-103
-3.0234194298878746e-102

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05034
15834
25834

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1941×body1280valid
679.0ms7954×body80valid
566.0ms1445×body640valid
169.0ms629×body320valid
50.0ms285×body160valid