Details

Time bar (total: 25.3s)

sample1.3s

Algorithm
intervals
Results
823.0ms60×body1280valid
125.0ms261×body80valid
114.0ms26×body640valid
27.0ms24×body320valid
10.0ms12×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done2059
62059
5808
4197
382
253
131
019

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize102.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

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:
11.0ms
(* (atan2 x.im x.re) y.im)
23.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(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)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.im)
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(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)))

simplify1.3s

Counts
72 → 72
Iterations
IterNodes
done2001
42001
3911
2425
1202
099

prune679.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (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)
1.2b
(* (atan2 x.im x.re) y.im)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite52.0ms

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* add-log-exp
4×insert-posit16
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 sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 70
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(- (* (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)
31.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.3s

Counts
82 → 82
Iterations
IterNodes
done2000
32000
2752
1307
0135

prune734.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.4b
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×pow1
9×*-un-lft-identity add-cube-cbrt
8×cbrt-div add-cbrt-cube sqrt-div associate-*l* add-exp-log
7×flip3-+ flip-+
6×associate-*r*
4×frac-times insert-posit16 add-log-exp
3×sqrt-prod
2×pow1/3 pow-prod-down associate-*l/ prod-exp associate-*r/ log-pow *-commutative cbrt-unprod unswap-sqr
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2 cube-unmult rem-cbrt-cube
Counts
4 → 75
Calls
4 calls:
36.0ms
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* 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)))
14.0ms
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

series254.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

simplify1.2s

Counts
87 → 87
Iterations
IterNodes
done2003
32003
2858
1345
0149

prune823.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.1b

localize98.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite43.0ms

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:
11.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.im)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
240.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
72 → 72
Iterations
IterNodes
done2001
42001
3911
2425
1202
099

prune720.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.1b

regimes491.0ms

Accuracy

75.9% (5.2b remaining)

Error of 8.7b against oracle of 3.6b and baseline of 25.0b

bsearch275.0ms

Steps
ItersRangePoint
10
-7.58300102256568e-301
1.7759471587980432e-306
-2.86513786455634e-310

simplify4.0ms

Iterations
IterNodes
done28
128
022

end0.0ms

sample11.4s

Algorithm
intervals
Results
4.2s1983×body1280valid
3.2s8010×body80valid
2.1s1460×body640valid
1.2s649×body320valid
226.0ms324×body160valid