Details

Time bar (total: 25.2s)

sample449.0ms

Algorithm
intervals
Results
88.0ms256×body80valid
56.0ms56×body1280valid
26.0ms41×body640valid
8.0ms20×body320valid
1.0ms4×body160valid

simplify1.6s

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize109.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite73.0ms

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:
11.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(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:
23.0ms
(* (atan2 x.im x.re) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
262.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts
68 → 68
Iterations
IterNodes
done5001
32779
2562
1199
096

prune624.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize59.0ms

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)
2.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite45.0ms

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:
16.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
136.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify690.0ms

Counts
81 → 81
Iterations
IterNodes
done5000
2953
1293
0133

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
0.0b
(exp (* y.im (atan2 x.im x.re)))
2.4b
(* y.im (atan2 x.im x.re))

rewrite38.0ms

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:
21.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
3.0ms
(exp (* y.im (atan2 x.im x.re)))
5.0ms
(* y.im (atan2 x.im x.re))

series203.0ms

Counts
3 → 9
Calls
3 calls:
156.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* y.im (atan2 x.im x.re))))
31.0ms
(exp (* y.im (atan2 x.im x.re)))
15.0ms
(* y.im (atan2 x.im x.re))

simplify1.1s

Counts
125 → 125
Iterations
IterNodes
done5000
21897
1482
0254

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
0.0b
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
2.7b
(pow (exp y.im) (atan2 x.im x.re))
2.7b
(pow (exp y.im) (atan2 x.im x.re))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
598×times-frac
418×unpow-prod-down
374×cbrt-prod
334×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
294×sqrt-prod
66×sqr-pow
40×associate-/l*
24×div-inv
20×associate-/r*
8×pow-pow add-exp-log
6×pow1 pow-unpow exp-prod add-cbrt-cube
4×cbrt-div add-log-exp associate-/l/
2×neg-sub0 pow-to-exp cbrt-undiv pow-neg clear-num frac-2neg div-exp pow-exp pow-sub
Counts
4 → 528
Calls
4 calls:
37.0ms
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
31.0ms
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
6.0ms
(pow (exp y.im) (atan2 x.im x.re))
7.0ms
(pow (exp y.im) (atan2 x.im x.re))

series521.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
220.0ms
(/ (cbrt (pow (/ -1 x.re) (- y.re))) (sqrt (pow (exp y.im) (atan2 x.im x.re))))
41.0ms
(pow (exp y.im) (atan2 x.im x.re))
43.0ms
(pow (exp y.im) (atan2 x.im x.re))

simplify1.3s

Counts
540 → 540
Iterations
IterNodes
done5001
22760
1744
0486

prune4.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes792.0ms

Accuracy

80.1% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 30.9b

bsearch237.0ms

Steps
ItersRangePoint
9
-8.047445764076778e-305
9.039519750896997e-304
2.00937700819994e-310

simplify6.0ms

Iterations
IterNodes
done39
339
238
132
023

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.5s2015×body1280valid
1.7s8005×body80valid
1.5s1389×body640valid
413.0ms648×body320valid
165.0ms319×body160valid