Details

Time bar (total: 14.8s)

sample38.0ms

Algorithm
intervals
Results
18.0ms265×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
27.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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:
9.0ms
(+ (* x.re y.re) (* x.im y.im))
43.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series171.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(+ (* x.re y.re) (* x.im y.im))
110.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify836.0ms

Counts
48 → 48
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
086924
1238906
21009824
done5000824

prune188.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
17.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (* x.re y.re) (* x.im y.im))
123.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify802.0ms

Counts
96 → 96
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
01171780
12801649
211731543
done50001541

prune460.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
17.7b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×flip3-+ sqrt-div flip-+ add-log-exp
5×unswap-sqr
4×prod-exp
3×associate-*l*
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rec-exp 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
63.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (* x.re y.re) (* x.im y.im))
142.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
37.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.7s

Counts
106 → 106
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01461886
14081701
223411478
done50021474

prune499.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
0.6b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
27.5b
(* (+ (* 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:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
15.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
69.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series232.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (* x.re y.re) (* x.im y.im))
71.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
109.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify4.5s

Counts
95 → 95
Iterations

Useful iterations: done (4.5s)

IterNodesCost
01271623
13751507
231791300
done50011294

prune338.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.2b

regimes308.0ms

Accuracy

3.9% (2.9b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 26.0b

bsearch54.0ms

Steps
ItersRangePoint
8
1.267959276101694e+93
1.0044135886792885e+96
1.7284643974157362e+95

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01941
12641
done2641

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8462×body80valid