Details

Time bar (total: 14.5s)

sample40.0ms

Algorithm
intervals
Results
17.0ms272×body80valid

simplify65.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57015
done7015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
28.4b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite68.0ms

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×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
14.0ms
(- (* x.im y.re) (* x.re y.im))
53.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series182.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(- (* x.im y.re) (* x.re y.im))
115.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts
50 → 50
Iterations

Useful iterations: 3 (828.0ms)

IterNodesCost
089954
1252936
2858854
32877850
done5000850

prune169.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.7b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
62.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
177.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts
278 → 278
Iterations

Useful iterations: done (1.4s)

IterNodesCost
030711144
174010034
218859365
done50019059

prune933.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.5b

localize32.0ms

Local error

Found 4 expressions with local error:

11.4b
(/ (* x.im y.re) (sqrt (+ (* y.im y.im) (* y.re y.re))))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.im y.im) (* y.re y.re)))
31.7b
(sqrt (+ (* y.im y.im) (* y.re y.re)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
15×sqrt-prod
14×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
8×sqrt-div
7×pow1
6×times-frac associate-/r*
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-undiv div-exp associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
36.0ms
(/ (* x.im y.re) (sqrt (+ (* y.im y.im) (* y.re y.re))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
16.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (* x.im y.re) (sqrt (+ (* y.im y.im) (* y.re y.re))))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
64.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

simplify2.7s

Counts
86 → 86
Iterations

Useful iterations: 3 (920.0ms)

IterNodesCost
01081174
12441042
2715934
32510912
done5000912

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.0b

localize15.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ y.im (/ (sqrt (+ (* y.im y.im) (* y.re y.re))) x.re))
31.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(sqrt (+ (* y.im y.im) (* y.re y.re)))
31.7b
(sqrt (+ (* y.im y.im) (* y.re y.re)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
85×add-sqr-sqrt
82×add-cube-cbrt *-un-lft-identity
45×sqrt-prod
22×associate-/r*
9×add-exp-log add-cbrt-cube
7×pow1
6×sqrt-div
5×div-inv
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ associate-/l*
1×frac-2neg clear-num associate-/r/
Counts
4 → 151
Calls
4 calls:
32.0ms
(/ y.im (/ (sqrt (+ (* y.im y.im) (* y.re y.re))) x.re))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
8.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ y.im (/ (sqrt (+ (* y.im y.im) (* y.re y.re))) x.re))
47.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
50.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

simplify2.8s

Counts
163 → 163
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
02433273
15222943
214332815
338492795
done50012795

prune794.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.0b

regimes253.0ms

Accuracy

0% (0.3b remaining)

Error of 22.7b against oracle of 22.4b and baseline of 22.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
11734
done1734

end0.0ms

sample908.0ms

Algorithm
intervals
Results
430.0ms8509×body80valid