Details

Time bar (total: 34.9s)

sample468.0ms

Algorithm
intervals
Results
119.0ms81×body1280valid
76.0ms39×body640valid
73.0ms259×body80valid
44.0ms8×body160valid
14.0ms16×body320valid
4.0ms2×body2560valid

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
65698
5805
4195
382
253
131
019

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize68.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 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 → 60
Calls
4 calls:
13.0ms
(* (atan2 x.im x.re) y.im)
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
262.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
72 → 72
Iterations
IterNodes
54090
41666
3854
2430
1206
0102

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.4b

localize101.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 43
Calls
4 calls:
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
211.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
209.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
55 → 55
Iterations
IterNodes
53217
41145
3535
2268
1145
073

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.4b

localize90.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0b
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum remove-posit16
Counts
4 → 50
Calls
4 calls:
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
1.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
223.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.6s

Counts
62 → 62
Iterations
IterNodes
53400
41265
3606
2306
1158
085

prune2.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.4b

localize148.0ms

Local error

Found 4 expressions with local error:

33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0b
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×sin-sum
1×remove-posit16
Counts
4 → 36
Calls
4 calls:
30.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
1.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series966.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
217.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
227.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
369.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify3.0s

Counts
48 → 48
Iterations
IterNodes
84754
71596
6856
5502
4301
3192
2123
178
055

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.4b

regimes957.0ms

Accuracy

77.4% (3.0b remaining)

Error of 22.3b against oracle of 19.3b and baseline of 32.4b

bsearch314.0ms

Steps
ItersRangePoint
8
-6.245387472968191e-307
2.5049244080050127e-307
-4.1355045148069e-310

simplify11.0ms

Iterations
IterNodes
239
139
029

end0.0ms

sample11.8s

Algorithm
intervals
Results
5.3s2254×body1280valid
2.7s7983×body80valid
2.3s1375×body640valid
562.0ms545×body320valid
196.0ms52×body2560valid
159.0ms223×body160valid