Details

Time bar (total: 30.8s)

sample690.0ms

Algorithm
intervals
Results
210.0ms255×body80valid
149.0ms55×body1280valid
130.0ms47×body640valid
9.0ms10×body320valid
5.0ms6×body160valid
3.0ms1×body2560valid

simplify3.2s

Counts
1 → 1
Iterations
IterNodes
done5001
5808
4197
382
253
131
019

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize99.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.re)
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite57.0ms

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:
11.0ms
(* (atan2 x.im x.re) y.re)
24.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
190.0ms
(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)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.9s

Counts
72 → 72
Iterations
IterNodes
done5000
42080
3861
2414
1203
0100

prune699.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.6b

localize91.0ms

Local error

Found 4 expressions with local error:

8.0b
(cbrt (* (atan2 x.im x.re) y.re))
29.5b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite82.0ms

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×cbrt-prod sin-sum pow1/3
Counts
4 → 51
Calls
4 calls:
6.0ms
(cbrt (* (atan2 x.im x.re) y.re))
60.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (* (atan2 x.im x.re) y.re))
267.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.8s

Counts
63 → 63
Iterations
IterNodes
done5001
41714
3756
2366
1198
0102

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.6b

localize126.0ms

Local error

Found 4 expressions with local error:

29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.6s

Counts
76 → 76
Iterations
IterNodes
done5001
53254
4995
3435
2196
192
039

prune815.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.6b

localize121.0ms

Local error

Found 4 expressions with local error:

29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.9b
(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×remove-posit16
Counts
4 → 57
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms
(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series202.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify2.6s

Counts
69 → 69
Iterations
IterNodes
done5001
53242
41006
3447
2207
1103
048

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.6b

regimes678.0ms

Accuracy

76.1% (3.3b remaining)

Error of 22.2b against oracle of 18.9b and baseline of 32.6b

bsearch359.0ms

Steps
ItersRangePoint
10
-6.011308145746772e-298
1.697267822885472e-307
-1.39623527537587e-310

simplify12.0ms

Iterations
IterNodes
done39
139
029

end0.0ms

sample11.4s

Algorithm
intervals
Results
4.2s2157×body1280valid
3.6s7975×body80valid
2.4s1384×body640valid
530.0ms555×body320valid
159.0ms230×body160valid
142.0ms42×body2560valid