Details

Time bar (total: 25.1s)

sample575.0ms

Algorithm
intervals
Results
273.0ms57×body1280valid
114.0ms249×body80valid
35.0ms42×body640valid
15.0ms25×body320valid
3.0ms7×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
019784
131784
253784
385784
4236784
51115784
done5000784

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize102.0ms

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)))

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:
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
212.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
68 → 68
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
09619880
119918842
256218842
3277918722
done500118722

prune718.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.8b

localize32.0ms

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)))

rewrite69.0ms

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:
27.0ms
(exp (- (* (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)
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
140.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts
81 → 81
Iterations

Useful iterations: done (1.1s)

IterNodesCost
013325655
129324757
295324677
done500024477

prune679.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* 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)))
40.2b
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

rewrite67.0ms

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 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 → 71
Calls
4 calls:
26.0ms
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

simplify1.3s

Counts
83 → 83
Iterations

Useful iterations: done (1.3s)

IterNodesCost
014529621
134227268
2112127228
done500023828

prune744.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize181.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×cos-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
215.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
218.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
212.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
51 → 51
Iterations

Useful iterations: 3 (226.0ms)

IterNodesCost
06823591
113923125
228923125
365223005
4187823005
done500023005

prune605.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.8b

regimes930.0ms

Accuracy

73.8% (5.7b remaining)

Error of 9.1b against oracle of 3.4b and baseline of 25.2b

bsearch613.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
7.830610238325062
0.033937663748779164
10
1.0104396359133627e-102
3.059160399966502e-92
2.3540707404960833e-92
9
-3.405412354409858e-300
-2.1744703393091546e-306
-2.2031366962120984e-306

simplify19.0ms

Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0381678
1521557
2551557
done551557

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.0s2090×body1280valid
2.4s8037×body80valid
1.6s1444×body640valid
417.0ms646×body320valid
112.0ms318×body160valid