Details

Time bar (total: 23.4s)

sample606.0ms

Algorithm
intervals
Results
349.0ms44×body640valid
65.0ms56×body1280valid
41.0ms260×body80valid
9.0ms18×body320valid
3.0ms8×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5000
51115
4236
385
253
131
019

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize65.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
30.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite66.0ms

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 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 → 56
Calls
4 calls:
10.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(cos (+ (* (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)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
205.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts
68 → 68
Iterations
IterNodes
done5001
32850
2554
1199
096

prune651.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)
1.8b
(* (atan2 x.im x.re) y.im)
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite64.0ms

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*
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 → 69
Calls
4 calls:
32.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
16.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
121.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts
81 → 81
Iterations
IterNodes
done5000
2953
1293
0133

prune681.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b
(exp (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b
(* (log (- x.re)) y.re)
1.8b
(* (atan2 x.im x.re) y.im)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt add-log-exp
8×add-cbrt-cube add-exp-log
7×associate-*l*
6×associate-*r*
3×exp-prod
2×sub-neg diff-log exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×flip3-- exp-diff log-pow flip--
Counts
4 → 64
Calls
4 calls:
16.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
15.0ms
(exp (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im)))
6.0ms
(* (log (- x.re)) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)

series406.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
125.0ms
(exp (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im)))
88.0ms
(* (log (- x.re)) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
done5000
21031
1274
0120

prune617.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
4.3b
(cbrt (atan2 x.im x.re))
4.3b
(cbrt (atan2 x.im x.re))
4.3b
(cbrt (atan2 x.im x.re))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
18.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))

series300.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
81.0ms
(cbrt (atan2 x.im x.re))
71.0ms
(cbrt (atan2 x.im x.re))
63.0ms
(cbrt (atan2 x.im x.re))

simplify1.6s

Counts
85 → 85
Iterations
IterNodes
done5000
2545
1105
049

prune598.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

regimes475.0ms

Accuracy

66.9% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 19.9b

bsearch563.0ms

Steps
ItersRangePoint
9
-1.8790274713376555e-304
4.616381127637937e-308
2.92295118775524e-310
10
-7.768730768275641e-269
-2.2402272282629534e-287
-7.58660889710456e-269
7
-3.192839627708737e-253
-3.105046959787587e-255
-3.1609365710248735e-255

simplify22.0ms

Iterations
IterNodes
done53
253
150
039

end0.0ms

sample8.2s

Algorithm
intervals
Results
2.7s7972×body80valid
2.5s2032×body1280valid
1.8s1517×body640valid
434.0ms679×body320valid
97.0ms309×body160valid