Details

Time bar (total: 15.2s)

sample417.0ms

Algorithm
intervals
Results
48.0ms52×body1280valid
20.0ms258×body80valid
16.0ms37×body640valid
5.0ms21×body320valid
3.0ms15×body160valid

simplify966.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
29.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

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.re)
21.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
154.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.7s

Counts
68 → 68
Iterations

Useful iterations: 3 (224.0ms)

IterNodesCost
094836
1191778
2430690
3817677
41657677
54115677
done5002677

prune345.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.2b

localize17.0ms

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)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
32.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite51.0ms

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:
20.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms
(* (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)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (* (atan2 x.im x.re) y.im))
0.2b
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.7b
(* (atan2 x.im x.re) y.im)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
7×add-exp-log add-cbrt-cube associate-/l*
5×pow1 add-log-exp
4×sqr-pow
3×div-exp associate-*r* associate-*l* associate-/r*
1×cbrt-undiv pow-to-exp exp-prod exp-to-pow frac-2neg pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv rem-exp-log unswap-sqr
Counts
3 → 73
Calls
3 calls:
4.0ms
(exp (* (atan2 x.im x.re) y.im))
11.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)

series125.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(exp (* (atan2 x.im x.re) y.im))
83.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01401140
12581099
26751035
322511026
done50011024

prune248.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
0.5b
(exp (atan2 x.im x.re))
0.5b
(pow (exp (atan2 x.im x.re)) y.im)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
51×unpow-prod-down
49×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×sqr-pow
12×add-exp-log
9×div-exp
7×pow-to-exp pow-exp associate-/r* associate-/l*
6×exp-prod
5×add-cbrt-cube
4×pow1 pow-pow add-log-exp
3×pow-unpow
1×cbrt-undiv frac-2neg clear-num div-inv rem-exp-log
Counts
3 → 114
Calls
3 calls:
12.0ms
(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
2.0ms
(exp (atan2 x.im x.re))
4.0ms
(pow (exp (atan2 x.im x.re)) y.im)

series152.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(/ (pow x.re y.re) (pow (exp (atan2 x.im x.re)) y.im))
14.0ms
(exp (atan2 x.im x.re))
41.0ms
(pow (exp (atan2 x.im x.re)) y.im)

simplify1.8s

Counts
123 → 123
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01912002
13241897
29271849
341131840
done50011838

prune351.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.2b

regimes350.0ms

Accuracy

51.5% (7.6b remaining)

Error of 11.1b against oracle of 3.5b and baseline of 19.3b

bsearch157.0ms

Steps
ItersRangePoint
7
1.7675440002135593e-235
8.850619474871086e-234
5.166631344921751e-235
7
-2.303387199496212e-268
-9.432469785123202e-271
-2.9781961318465074e-269

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03456
14750
24950
done4950

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s2040×body1280valid
634.0ms8013×body80valid
516.0ms1407×body640valid
164.0ms636×body320valid
61.0ms346×body160valid