Details

Time bar (total: 41.2s)

sample784.0ms

Algorithm
intervals
Results
292.0ms35×body640valid
181.0ms53×body1280valid
111.0ms261×body80valid
22.0ms20×body320valid
5.0ms10×body160valid

simplify3.6s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize79.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
207.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
68 → 68
Iterations
IterNodes
54046
41624
3810
2409
1194
094

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.1b

localize47.0ms

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)
1.6b
(* (atan2 x.im x.re) y.im)
31.3b
(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*
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:
28.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
125.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.7s

Counts
81 → 81
Iterations
IterNodes
44041
31566
2690
1292
0133

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize65.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
6×add-cbrt-cube sqrt-div add-exp-log
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
5.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series182.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.0s

Counts
75 → 75
Iterations
IterNodes
53832
41501
3741
2352
1151
068

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im))
0.0b
(exp (- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im)))
0.2b
(* y.re (log x.re))
1.6b
(* (atan2 x.im x.re) y.im)

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×log-prod
15×*-un-lft-identity add-cube-cbrt
12×associate--l+
9×distribute-rgt-in pow1 distribute-lft-in add-log-exp
8×add-cbrt-cube exp-sum add-exp-log
7×associate-*r*
6×associate-*l*
3×exp-prod
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×flip3-- exp-diff log-pow flip--
Counts
4 → 82
Calls
4 calls:
13.0ms
(- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im))
29.0ms
(exp (- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im)))
12.0ms
(* y.re (log x.re))
11.0ms
(* (atan2 x.im x.re) y.im)

series269.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im))
79.0ms
(exp (- (* y.re (log x.re)) (* (atan2 x.im x.re) y.im)))
51.0ms
(* y.re (log x.re))
30.0ms
(* (atan2 x.im x.re) y.im)

simplify11.5s

Counts
94 → 94
Iterations
IterNodes
46111
31815
2663
1308
0145

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

regimes493.0ms

Accuracy

81.6% (6.2b remaining)

Error of 9.9b against oracle of 3.6b and baseline of 37.6b

bsearch296.0ms

Steps
ItersRangePoint
10
-1.0906968289144063e-304
2.8714006224246324e-294
1.04726288994103e-310

simplify6.0ms

Iterations
IterNodes
233
133
026

end0.0ms

sample10.3s

Algorithm
intervals
Results
3.4s1996×body1280valid
3.1s8017×body80valid
2.4s1536×body640valid
715.0ms668×body320valid
222.0ms307×body160valid