Details

Time bar (total: 29.3s)

sample554.0ms

Algorithm
intervals
Results
196.0ms72×body1280valid
101.0ms44×body640valid
89.0ms257×body80valid
27.0ms26×body320valid
3.0ms4×body160valid

simplify3.5s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.re)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
12.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.re)
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
226.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
72 → 72
Iterations
IterNodes
54112
41680
3849
2410
1197
097

prune696.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×associate-*l*
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r*
4×insert-posit16
3×exp-prod log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×rem-sqrt-square sub-neg flip3-+ exp-diff diff-log flip-+
Counts
4 → 73
Calls
4 calls:
26.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
10.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
137.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
29.0ms
(* (atan2 x.im x.re) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.0s

Counts
85 → 85
Iterations
IterNodes
44065
31573
2686
1296
0137

prune713.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.1b
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r*
4×insert-posit16 add-log-exp
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square flip3-+ flip-+ remove-posit16
Counts
4 → 66
Calls
4 calls:
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
28.0ms
(* (atan2 x.im x.re) y.im)
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms
(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.4s

Counts
78 → 78
Iterations
IterNodes
42188
31180
2581
1254
0120

prune927.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize97.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.re)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite58.0ms

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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.re)
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
189.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
72 → 72
Iterations
IterNodes
54112
41680
3849
2410
1197
097

prune669.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

regimes796.0ms

Accuracy

74.2% (5.3b remaining)

Error of 8.9b against oracle of 3.5b and baseline of 24.2b

bsearch275.0ms

Steps
ItersRangePoint
10
-2.0138937375136724e-306
1.6865852339130767e-299
-1.7421973940893e-310

simplify6.0ms

Iterations
IterNodes
226
126
021

end0.0ms

sample10.5s

Algorithm
intervals
Results
3.9s1909×body1280valid
3.0s8008×body80valid
2.4s1502×body640valid
671.0ms641×body320valid
173.0ms327×body160valid