Details

Time bar (total: 22.8s)

sample914.0ms

Algorithm
intervals
Results
482.0ms249×body80valid
74.0ms57×body1280valid
63.0ms42×body640valid
15.0ms25×body320valid
3.0ms7×body160valid

simplify1.8s

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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize92.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (atan2 x.im x.re) y.im)
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(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)))

simplify1.5s

Counts
68 → 68
Iterations
IterNodes
done5001
32779
2562
1199
096

prune775.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.8b

localize60.0ms

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)
1.7b
(* (atan2 x.im x.re) y.im)
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite81.0ms

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:
37.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
129.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify825.0ms

Counts
81 → 81
Iterations
IterNodes
done5000
2953
1293
0133

prune792.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
28.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.2b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×cbrt-prod
14×*-un-lft-identity add-cube-cbrt
10×pow1
9×sqrt-prod
8×add-cbrt-cube associate-*l* add-exp-log
6×unpow-prod-down cube-prod associate-*r*
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 82
Calls
4 calls:
16.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series261.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.3s

Counts
94 → 94
Iterations
IterNodes
done5000
21788
1366
0147

prune942.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize47.0ms

Local error

Found 3 expressions with local error:

0.1b
(exp (* y.im (atan2 x.im x.re)))
0.5b
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
1.7b
(* y.im (atan2 x.im x.re))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
57×add-sqr-sqrt
55×*-un-lft-identity add-cube-cbrt
52×unpow-prod-down
17×associate-/l*
9×add-exp-log
7×add-cbrt-cube
5×pow1 div-exp div-inv add-log-exp
4×sqr-pow
3×associate-/r* associate-*r* associate-*l*
2×pow-exp associate-/l/
1×neg-sub0 pow-to-exp cbrt-undiv exp-prod pow-neg clear-num frac-2neg exp-to-pow pow-prod-down prod-exp *-commutative cbrt-unprod pow-sub unswap-sqr rem-exp-log
Counts
3 → 116
Calls
3 calls:
6.0ms
(exp (* y.im (atan2 x.im x.re)))
35.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
11.0ms
(* y.im (atan2 x.im x.re))

series197.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(exp (* y.im (atan2 x.im x.re)))
152.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
21.0ms
(* y.im (atan2 x.im x.re))

simplify1.1s

Counts
125 → 125
Iterations
IterNodes
done5001
21903
1482
0254

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes973.0ms

Accuracy

62.8% (8.0b remaining)

Error of 11.7b against oracle of 3.7b and baseline of 25.2b

bsearch1.0s

Steps
ItersRangePoint
9
5.1798647897020696e-05
7.830610238325062
0.11072392652887969
10
1.0104396359133627e-102
3.059160399966502e-92
1.1112862032308682e-97
9
-3.405412354409858e-300
-2.1744703393091546e-306
-2.2031366962120984e-306
9
-1.2878017345991347e-78
-2.7289543354637992e-86
-3.862547000878271e-82
7
-5.301633519238957e-21
-2.137872795194052e-22
-1.4369310699094394e-21

simplify8.0ms

Iterations
IterNodes
done64
264
161
049

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.7s2090×body1280valid
2.3s8037×body80valid
1.9s1444×body640valid
411.0ms646×body320valid
110.0ms318×body160valid