Details

Time bar (total: 7.1s)

sample20.0ms

Algorithm
intervals
Results
9.0ms274×body80valid

simplify37.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
1.0b
(- (* x.im y.re) (* x.re y.im))
27.9b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
36.0ms
(- (* x.im y.re) (* x.re y.im))
86.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts
64 → 64
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01021120
12891097
21023981
33795981
done5000980

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* x.im y.re) (* x.re y.im))
16.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
2.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
98 → 98
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01211814
13041690
28551590
324971560
done50001559

prune302.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))
17.6b
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
20.0b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
6×times-frac associate-/r*
4×pow1 cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
2×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(+ (* y.re y.re) (* y.im y.im))
7.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series149.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* y.re y.re) (* y.im y.im))
27.0ms
(+ (* y.re y.re) (* y.im y.im))
47.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify765.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
01111120
13061096
21173880
done5002880

prune217.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
20.0b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
31.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×times-frac
34×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
24×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
8×pow1 sqrt-div
6×cbrt-undiv div-exp associate-/r/
5×flip3-+ prod-exp cbrt-unprod flip-+
4×add-log-exp
3×associate-/r* div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 130
Calls
4 calls:
41.0ms
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
46.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify905.0ms

Counts
142 → 142
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
01983016
15792843
220162349
done50002299

prune406.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.7b

regimes128.0ms

Accuracy

0% (1.3b remaining)

Error of 23.7b against oracle of 22.4b and baseline of 23.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01543
11843
done1843

end0.0ms

sample507.0ms

Algorithm
intervals
Results
292.0ms8491×body80valid