Details

Time bar (total: 29.9s)

sample337.0ms

Algorithm
intervals
Results
80.0ms47×body640valid
68.0ms65×body1280valid
40.0ms255×body80valid
12.0ms15×body320valid
2.0ms6×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize48.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.re)
30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite88.0ms

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:
14.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
282.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.0s

Counts
68 → 68
Iterations

Useful iterations: 3 (334.0ms)

IterNodesCost
097845
1196787
2437699
3824686
41659686
54095686
done5001686

prune569.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.9b

localize41.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube add-log-exp
3×flip3-+ sqrt-prod flip-+
2×pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 sin-sum
Counts
4 → 49
Calls
4 calls:
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series776.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
123.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
444.0ms
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
61 → 61
Iterations

Useful iterations: 3 (321.0ms)

IterNodesCost
01091110
12261052
2480904
31039898
42984898
done5000898

prune758.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.9b

localize42.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b
(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.3b
(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
33.9b
(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×cbrt-prod unpow-prod-down pow-unpow sqrt-prod
2×cbrt-div flip3-+ sqrt-div flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow1/3 sin-sum pow1/3 pow-exp sqr-pow
Counts
4 → 54
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
52.0ms
(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series828.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
177.0ms
(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
448.0ms
(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts
66 → 66
Iterations

Useful iterations: 3 (420.0ms)

IterNodesCost
01321155
12711035
2569904
31302897
44174897
done5000897

prune653.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.9b

localize44.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×add-exp-log
7×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum associate-*r* *-commutative unswap-sqr
Counts
4 → 57
Calls
4 calls:
25.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
250.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.6s

Counts
69 → 69
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
01091040
1242979
2539815
31125768
42497754
done5001754

prune590.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.9b

regimes732.0ms

Accuracy

75.7% (3.4b remaining)

Error of 22.8b against oracle of 19.4b and baseline of 33.4b

bsearch286.0ms

Steps
ItersRangePoint
9
-1.2051837121686706e-306
9.463584260948629e-306
-5.70557298521433e-309

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.6s2214×body1280valid
2.7s8010×body80valid
1.5s1390×body640valid
294.0ms539×body320valid
174.0ms203×body160valid
114.0ms41×body2560valid