Details

Time bar (total: 6.7s)

sample19.0ms

Algorithm
intervals
Results
7.0ms340×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
077
1107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ sum-log add-cbrt-cube flip-+
Counts
1 → 11
Calls
1 calls:
3.0ms
(+ (* x.re y.im) (* x.im y.re))

series34.0ms

Counts
1 → 3
Calls
1 calls:
34.0ms
(+ (* x.re y.im) (* x.im y.re))

simplify1.7s

Counts
14 → 14
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
032160
199155
2318141
3860141
42086141
done5001141

prune34.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re y.im) (* x.im y.re))
0.2b
(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))
0.4b
(sqrt (+ (* x.re y.im) (* x.im y.re)))
0.4b
(sqrt (+ (* x.re y.im) (* x.im y.re)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
2.0ms
(+ (* x.re y.im) (* x.im y.re))
19.0ms
(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))
4.0ms
(sqrt (+ (* x.re y.im) (* x.im y.re)))
6.0ms
(sqrt (+ (* x.re y.im) (* x.im y.re)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.im) (* x.im y.re))
36.0ms
(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))
66.0ms
(sqrt (+ (* x.re y.im) (* x.im y.re)))
70.0ms
(sqrt (+ (* x.re y.im) (* x.im y.re)))

simplify1.7s

Counts
110 → 110
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01062066
12311475
27391367
327801320
done50011316

prune239.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re))))
1.6b
(+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3))
2.7b
(* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))
39.1b
(/ (+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3)) (+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
5×sum-cubes distribute-lft-out associate-/l*
4×distribute-rgt-in sub-neg associate-+r+ distribute-lft-in flip3-+ flip-+
3×associate-*r* pow-prod-down prod-exp associate-/r* cbrt-unprod
2×+-commutative associate-*r/ sum-log associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-exp associate-*l* clear-num *-commutative flip-- div-inv
Counts
4 → 91
Calls
4 calls:
10.0ms
(+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re))))
7.0ms
(+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3))
12.0ms
(* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))
40.0ms
(/ (+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3)) (+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re))))
191.0ms
(+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3))
72.0ms
(* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))
131.0ms
(/ (+ (pow (* x.re y.im) 3) (pow (* x.im y.re) 3)) (+ (* (* x.re y.im) (* x.re y.im)) (* (* x.im y.re) (- (* x.im y.re) (* y.im x.re)))))

simplify1.1s

Counts
103 → 103
Iterations

Useful iterations: 2 (274.0ms)

IterNodesCost
01683118
14372966
222182721
done50002721

prune320.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1107
done107

end0.0ms

sample497.0ms

Algorithm
intervals
Results
234.0ms10436×body80valid