Details

Time bar (total: 14.6s)

sample49.0ms

Algorithm
intervals
Results
23.0ms266×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
24.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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:
16.0ms
(+ (* x.re y.re) (* x.im y.im))
44.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series170.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(+ (* x.re y.re) (* x.im y.im))
109.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify835.0ms

Counts
48 → 48
Iterations

Useful iterations: 2 (165.0ms)

IterNodesCost
086924
1238906
21009824
done5000824

prune529.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* 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))))
15.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite165.0ms

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:
68.0ms
(/ (/ (+ (* 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)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series344.0ms

Counts
4 → 12
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))))
142.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
276 → 276
Iterations

Useful iterations: done (1.9s)

IterNodesCost
030211076
17559987
237859426
done50009054

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
0.8b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.2b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×*-un-lft-identity times-frac
19×add-cube-cbrt
16×add-exp-log
15×associate-*r*
10×add-cbrt-cube
6×pow1
5×flip3-+ flip-+ add-log-exp
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×+-commutative pow-flip frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
3 → 86
Calls
3 calls:
12.0ms
(+ (* x.re y.re) (* x.im y.im))
16.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
64.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series215.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (* x.re y.re) (* x.im y.im))
53.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
123.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify4.7s

Counts
95 → 95
Iterations

Useful iterations: done (4.7s)

IterNodesCost
01271623
13751507
231791300
done50011294

prune305.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
0.5b
(/ (/ 1 1) (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im))))
24.3b
(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
221×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
38×add-exp-log
32×div-inv
31×associate-/r/
30×div-exp
18×associate-/r*
17×flip3-+ add-cbrt-cube flip-+
16×associate-/l*
10×1-exp
9×cbrt-undiv
5×add-log-exp
4×rec-exp
3×pow1 associate-/l/
2×frac-2neg clear-num
1×+-commutative sum-log
Counts
3 → 295
Calls
3 calls:
14.0ms
(+ (* x.re y.re) (* x.im y.im))
65.0ms
(/ (/ 1 1) (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im))))
48.0ms
(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im)))

series308.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(+ (* x.re y.re) (* x.im y.im))
177.0ms
(/ (/ 1 1) (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im))))
89.0ms
(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.6s

Counts
304 → 304
Iterations

Useful iterations: done (1.6s)

IterNodesCost
048111053
118309038
done50008745

prune553.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 22.1b

regimes174.0ms

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 25.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01325
11725
done1725

end0.0ms

sample1.2s

Algorithm
intervals
Results
722.0ms8411×body80valid