Details

Time bar (total: 11.8s)

sample47.0ms

Algorithm
intervals
Results
22.0ms271×body80valid

simplify23.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* x.re y.re) (* x.im y.im))
23.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
13.0ms
(+ (* y.re y.re) (* y.im y.im))
13.0ms
(+ (* x.re y.re) (* x.im y.im))
66.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series221.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (* y.re y.re) (* y.im y.im))
51.0ms
(+ (* x.re y.re) (* x.im y.im))
131.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
62 → 62

prune283.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.4b
(/ (+ (* x.re y.re) (* x.im 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)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
107.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
64.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
149.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
71.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify939.0ms

Counts
276 → 276

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.5b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
28×add-exp-log times-frac
26×*-un-lft-identity
24×add-cube-cbrt associate-*r*
23×sqrt-prod
18×add-cbrt-cube
9×div-exp
8×pow1 flip3-+ sqrt-div prod-exp flip-+
6×associate-/r* associate-/l/
5×cbrt-undiv unswap-sqr
4×frac-times associate-*l/ associate-/r/ cbrt-unprod add-log-exp
3×associate-*l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ un-div-inv div-inv
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
65.0ms
(/ (* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
67.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
153.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts
134 → 134

prune641.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* x.re y.re) (* x.im y.im))
0.5b
(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
23.7b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
222×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
39×add-exp-log
32×div-inv
31×associate-/r/
30×div-exp
18×flip3-+ associate-/r* add-cbrt-cube flip-+
16×associate-/l*
10×1-exp
9×cbrt-undiv
8×add-log-exp
4×pow1 rec-exp
3×associate-/l/
2×+-commutative frac-2neg clear-num sum-log
Counts
4 → 306
Calls
4 calls:
10.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
48.0ms
(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
51.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* y.re y.re) (* y.im y.im))
50.0ms
(+ (* x.re y.re) (* x.im y.im))
203.0ms
(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
82.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify719.0ms

Counts
318 → 318

prune1.0s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 21.0b

regimes369.0ms

Accuracy

-2.2% (3.1b remaining)

Error of 26.9b against oracle of 23.8b and baseline of 26.8b

bsearch0.0ms

simplify26.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
737.0ms8479×body80valid