Details

Time bar (total: 30.6s)

sample510.0ms

Algorithm
intervals
Results
162.0ms60×body1280valid
103.0ms40×body640valid
71.0ms254×body80valid
15.0ms15×body320valid
8.0ms12×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5000
5862
4202
382
253
131
019

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.re)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

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)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.re)
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
232.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
72 → 72
Iterations
IterNodes
done5002
42613
31002
2431
1198
097

prune613.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.5b

localize48.0ms

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.6b
(* (atan2 x.im x.re) y.im)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite66.0ms

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:
42.0ms
(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)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
133.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.8s

Counts
85 → 85
Iterations
IterNodes
done5000
31979
2731
1297
0137

prune603.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize113.0ms

Local error

Found 4 expressions with local error:

24.4b
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite38.0ms

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-+
Counts
4 → 56
Calls
4 calls:
11.0ms
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.9s

Counts
68 → 68
Iterations
IterNodes
done5002
54148
41376
3590
2266
1130
060

prune732.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize110.0ms

Local error

Found 4 expressions with local error:

24.4b
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite67.0ms

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-+
Counts
4 → 56
Calls
4 calls:
28.0ms
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.1s

Counts
68 → 68
Iterations
IterNodes
done5002
54148
41376
3590
2266
1130
060

prune931.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.1b

regimes610.0ms

Accuracy

69.4% (5.0b remaining)

Error of 8.6b against oracle of 3.6b and baseline of 20.1b

bsearch828.0ms

Steps
ItersRangePoint
8
-2.439564962497264e-306
1.2873264571255324e-307
-4.2640896224449e-310
3
-3.6539480182871386e-164
-2.7629713230024924e-164
-2.9130712528480477e-164
5
-4.535964318370555e-06
-1.254342544040049e-06
-1.8407009899098441e-06

simplify14.0ms

Iterations
IterNodes
done46
146
036

end0.0ms

sample10.9s

Algorithm
intervals
Results
4.1s2062×body1280valid
3.1s7998×body80valid
2.3s1438×body640valid
633.0ms682×body320valid
195.0ms316×body160valid