Details

Time bar (total: 11.4s)

sample60.0ms

Algorithm
intervals
Results
41.0ms272×body80valid

simplify60.0ms

Counts
1 → 1
Iterations
IterNodes
done70
570
466
348
236
119
011

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(- (* x.im y.re) (* x.re y.im))
25.8b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

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* insert-posit16 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 → 58
Calls
3 calls:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
13.0ms
(- (* x.im y.re) (* x.re y.im))
49.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
55.0ms
(- (* x.im y.re) (* x.re y.im))
137.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify929.0ms

Counts
67 → 67
Iterations
IterNodes
done2001
32001
21186
1305
0104

prune365.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 270
Calls
4 calls:
60.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.0ms
(/ (- (* 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)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
121.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts
282 → 282
Iterations
IterNodes
done2000
22000
1745
0310

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.7b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(- (* x.im y.re) (* x.re y.im))
25.8b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

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* insert-posit16 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 → 58
Calls
3 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
13.0ms
(- (* x.im y.re) (* x.re y.im))
39.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series182.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (* y.re y.re) (* y.im y.im))
53.0ms
(- (* x.im y.re) (* x.re y.im))
91.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
67 → 67
Iterations
IterNodes
done2001
32001
21186
1305
0104

prune400.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
17.0b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 165
Calls
4 calls:
97.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
51.0ms
(/ (- (* 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)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
163.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
47.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts
177 → 177
Iterations
IterNodes
done2005
32005
21840
1596
0199

prune870.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.7b

regimes430.0ms

Accuracy

0% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done14
114
011

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8470×body80valid