Details

Time bar (total: 15.3s)

sample49.0ms

Algorithm
intervals
Results
26.0ms273×body80valid

simplify23.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
26.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
15.0ms
(+ (* x.re y.re) (* x.im y.im))
55.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series160.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(+ (* x.re y.re) (* x.im y.im))
121.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts
48 → 48

prune166.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.1b

localize20.0ms

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))))
15.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite164.0ms

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:
90.0ms
(/ (/ (+ (* 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))))
37.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (/ (+ (* 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))))
152.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify935.0ms

Counts
276 → 276

prune855.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.8b

localize19.0ms

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))))
15.9b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite194.0ms

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:
67.0ms
(/ (* (+ (* 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))))
80.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
20.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (* (+ (* 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))))
163.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
61.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts
134 → 134

prune530.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im))))
15.9b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
9×associate-/l*
8×flip3-+ div-exp flip-+
7×pow1
6×sqrt-div div-inv
4×cbrt-undiv add-log-exp
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
40.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im))))
41.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im))))
117.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
54.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts
205 → 205

prune916.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.8b

regimes295.0ms

Accuracy

16.7% (2.5b remaining)

Error of 25.8b against oracle of 23.3b and baseline of 26.3b

bsearch2.0ms

simplify4.7s

end0.0ms

sample1.1s

Algorithm
intervals
Results
619.0ms8474×body80valid