Details

Time bar (total: 27.7s)

sample321.0ms

Algorithm
intervals
Results
127.0ms94×body1280valid
39.0ms256×body80valid
38.0ms54×body640valid
10.0ms20×body320valid
4.0ms2×body2560valid
2.0ms9×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01937
13137
25336
38536
422036
5102336
done500036

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.0b

localize79.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite90.0ms

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:
13.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
248.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts
68 → 68
Iterations

Useful iterations: 3 (673.0ms)

IterNodesCost
098845
1202787
2554701
32840686
done5001686

prune624.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.6b

localize52.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (fabs (sqrt (+ (* x.re x.re) (* x.im x.im))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

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:
15.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sin (+ (* (log (fabs (sqrt (+ (* x.re x.re) (* x.im x.im))))) y.im) (* (atan2 x.im x.re) y.re)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
179.0ms
(sin (+ (* (log (fabs (sqrt (+ (* x.re x.re) (* x.im x.im))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify739.0ms

Counts
68 → 68
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
096877
1207820
2842720
done5000718

prune583.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.6b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (fabs x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 59
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sin (+ (* (log (fabs x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
108.0ms
(sin (+ (* (log (fabs x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify6.1s

Counts
71 → 71
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0110714
1226681
2696605
34307595
done5000595

prune538.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
1.6b
(* (atan2 x.im x.re) y.im)
27.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(sin (+ (* (log (fabs x.im)) y.im) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
11×add-exp-log
9×add-cube-cbrt *-un-lft-identity associate-*r*
8×add-cbrt-cube
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cbrt-prod sqrt-prod
2×sqrt-div *-commutative
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+ unswap-sqr
Counts
4 → 62
Calls
4 calls:
46.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
14.0ms
(* (atan2 x.im x.re) y.im)
29.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sin (+ (* (log (fabs x.im)) y.im) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
21.0ms
(* (atan2 x.im x.re) y.im)
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
169.0ms
(sin (+ (* (log (fabs x.im)) y.im) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

simplify1.2s

Counts
74 → 74
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0133922
1299881
21257773
done5000731

prune622.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

regimes546.0ms

Accuracy

37.7% (10.1b remaining)

Error of 17.6b against oracle of 7.5b and baseline of 23.7b

bsearch903.0ms

Steps
ItersRangePoint
9
9.793266657720577e-149
4.534244796144556e-143
6.089823661559196e-145
8
1.9260611924290092e-256
8.532008566463438e-254
2.69879743510774e-254
6
1.37932645896813e-293
9.075716005402557e-293
1.4058484354712057e-293
7
-3.530882493372637e-42
-8.421206599817505e-44
-4.0002364356805634e-43

simplify22.0ms

Iterations

Useful iterations: done (21.0ms)

IterNodesCost
054181
173158
276113
379113
done79112

end0.0ms

sample9.3s

Algorithm
intervals
Results
3.2s2244×body1280valid
2.4s7960×body80valid
1.8s1449×body640valid
628.0ms50×body2560valid
302.0ms524×body320valid
84.0ms231×body160valid