Details

Time bar (total: 3.0s)

sample21.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157
done157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
25.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
10.0ms
(+ (* x.re y.re) (* x.im y.im))
29.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series149.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(+ (* x.re y.re) (* x.im y.im))
84.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify131.0ms

Counts
62 → 62
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0272527
11164479
24451477
35003477
done5003477

prune163.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
17.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite57.0ms

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:
9.0ms
(+ (* x.re y.re) (* x.im y.im))
30.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x.re y.re) (* x.im y.im))
111.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0273893
1868840
22693828
35001828
done5001828

prune263.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
18.0b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

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))
53.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* x.re y.re) (* x.im y.im))
112.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0385911
11913826
25002802
done5002802

prune264.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
0.9b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.5b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
6×flip3-+ flip-+
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv +-commutative frac-times rec-exp 1-exp associate-*l/ sum-log cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 97
Calls
4 calls:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
7.0ms
(+ (* x.re y.re) (* x.im y.im))
13.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(+ (* x.re y.re) (* x.im y.im))
37.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
83.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify51.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0393853
12037749
25003720
done5003720

prune217.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.8b

regimes137.0ms

Accuracy

0% (2.8b remaining)

Error of 25.9b against oracle of 23.1b and baseline of 25.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02214
12214
done2214

end0.0ms

sample548.0ms

Algorithm
intervals
Results
277.0ms8463×body80valid