Details

Time bar (total: 13.9s)

sample42.0ms

Algorithm
intervals
Results
20.0ms271×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
1.2b
(+ (* x.re y.re) (* x.im y.im))
24.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

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:
15.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* 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)))

series207.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ (* y.re y.re) (* y.im y.im))
44.0ms
(+ (* 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)))

simplify1.8s

Counts
62 → 62
Iterations

Useful iterations: 2 (218.0ms)

IterNodesCost
0991090
12701067
2866951
32515951
done5001951

prune263.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* x.re y.re) (* x.im y.im))
15.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite116.0ms

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:
18.0ms
(+ (* x.re y.re) (* x.im y.im))
60.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* x.re y.re) (* x.im y.im))
139.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
71.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
96 → 96
Iterations

Useful iterations: 3 (599.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune431.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* x.re y.re) (* x.im y.im))
15.8b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite135.0ms

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:
16.0ms
(+ (* x.re y.re) (* x.im y.im))
90.0ms
(* (+ (* 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)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* x.re y.re) (* x.im y.im))
184.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
48.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.9s

Counts
106 → 106
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01461886
13781642
211541474
337511458
done50011458

prune466.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.8b

localize37.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* x.re y.re) (* x.im y.im))
15.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite97.0ms

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:
10.0ms
(+ (* x.re y.re) (* x.im y.im))
40.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
25.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (* x.re y.re) (* x.im y.im))
176.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts
96 → 96
Iterations

Useful iterations: 3 (721.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune407.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 21.8b

regimes371.0ms

Accuracy

25% (2.2b remaining)

Error of 25.2b against oracle of 23.1b and baseline of 26.0b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02055
12755
done2755

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s8494×body80valid