Details

Time bar (total: 12.4s)

sample44.0ms

Algorithm
intervals
Results
21.0ms271×body80valid

simplify33.0ms

Counts
1 → 1
Iterations
IterNodes
done72
572
466
348
236
119
011

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
25.3b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
3 → 55
Calls
3 calls:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
30.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series190.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
48.0ms
(- (* x.im y.re) (* x.re y.im))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
64 → 64
Iterations
IterNodes
done5000
21834
1319
0101

prune455.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
16.4b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 86
Calls
4 calls:
6.0ms
(- (* x.im y.re) (* x.re y.im))
27.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* x.im y.re) (* x.re y.im))
141.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
98 → 98
Iterations
IterNodes
done5001
21227
1313
0121

prune737.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.0b

localize38.0ms

Local error

Found 4 expressions with local error:

16.4b
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
9×*-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod flip-+
8×associate-/r/
7×pow1
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/l/
1×clear-num associate-/r* frac-2neg flip3-- div-sub prod-exp cbrt-unprod div-inv flip--
Counts
4 → 77
Calls
4 calls:
34.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
47.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts
89 → 89
Iterations
IterNodes
done5001
33024
2956
1314
0110

prune683.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
0.6b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
25.1b
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r*
17×add-exp-log
11×add-cbrt-cube associate-/r/
8×div-exp add-log-exp
6×flip3-- div-inv flip-- associate-/l*
5×pow1
4×cbrt-undiv
2×rec-exp clear-num frac-2neg flip3-+ 1-exp flip-+ associate-/l/
1×+-commutative sum-log sub-neg diff-log pow-flip inv-pow
Counts
4 → 138
Calls
4 calls:
6.0ms
(+ (* y.re y.re) (* y.im y.im))
12.0ms
(- (* x.im y.re) (* x.re y.im))
30.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
35.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* y.re y.re) (* y.im y.im))
65.0ms
(- (* x.im y.re) (* x.re y.im))
187.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
76.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify1.7s

Counts
150 → 150
Iterations
IterNodes
done5000
23429
1589
0207

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.0b

regimes505.0ms

Accuracy

0% (3.2b remaining)

Error of 26.1b against oracle of 22.9b and baseline of 26.1b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done21
121
016

end0.0ms

sample1.2s

Algorithm
intervals
Results
705.0ms8499×body80valid