Details

Time bar (total: 29.4s)

sample352.0ms

Algorithm
intervals
Results
144.0ms63×body1280valid
47.0ms253×body80valid
39.0ms49×body640valid
14.0ms26×body320valid
7.0ms11×body160valid
3.0ms1×body2560valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize63.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
28.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite89.0ms

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)
36.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (atan2 x.im x.re) y.im)
277.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.4s

Counts
68 → 68
Iterations

Useful iterations: 3 (362.0ms)

IterNodesCost
098845
1198787
2443699
3826686
41659686
54107686
done5001686

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

localize87.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (139.0ms)

IterNodesCost
038852
191744
2205680
3444656
41114656
53182656
done5001656

prune739.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

localize61.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.8b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
15×add-sqr-sqrt sqrt-prod
12×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×unpow-prod-down cube-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 74
Calls
4 calls:
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series219.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.3s

Counts
86 → 86
Iterations

Useful iterations: 3 (344.0ms)

IterNodesCost
0771281
1188914
2409874
31355850
done5001850

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.6b

localize70.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
28.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite88.0ms

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:
25.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
41.0ms
(sin (+ (* (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)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
240.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
78.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.4s

Counts
71 → 71
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0961505
11921290
24071146
39361132
431481132
done50001125

prune466.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 20.6b

regimes747.0ms

Accuracy

78.2% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.6b

bsearch207.0ms

Steps
ItersRangePoint
9
-9.205433752799553e-305
1.5534809022725981e-305
-5.57158609869316e-309

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.8s2171×body1280valid
2.5s7991×body80valid
1.3s1450×body640valid
363.0ms586×body320valid
131.0ms52×body2560valid
83.0ms235×body160valid