Details

Time bar (total: 8.2s)

sample22.0ms

Algorithm
intervals
Results
10.0ms277×body80valid

simplify31.0ms

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: 27.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.8b
(- (* x.im y.re) (* x.re y.im))
26.6b
(/ (- (* 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:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
87.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
64 → 64
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01021120
12891097
21023981
33795981
done5001980

prune179.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* x.im y.re) (* x.re y.im))
15.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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))
11.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* x.im y.re) (* x.re y.im))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify987.0ms

Counts
98 → 98
Iterations

Useful iterations: done (984.0ms)

IterNodesCost
01211814
13041682
28541574
325011558
done50001557

prune281.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
585×sqrt-prod
567×times-frac
302×add-sqr-sqrt
299×add-cube-cbrt *-un-lft-identity
50×sqrt-div
33×associate-/l*
22×associate-/r/
14×flip3-+ flip-+
11×div-inv
9×add-exp-log associate-/r* add-cbrt-cube
7×pow1
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
2×div-sub
1×frac-2neg clear-num associate-/l/
Counts
4 → 402
Calls
4 calls:
32.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify967.0ms

Counts
414 → 414
Iterations

Useful iterations: done (940.0ms)

IterNodesCost
043620421
1102318015
2236316855
done500016853

prune766.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize19.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series150.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
72 → 72
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
038852
191744
2207680
3459656
41009656
52575656
done5001656

prune308.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes148.0ms

Accuracy

-5.8% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.7b

bsearch48.0ms

Steps
ItersRangePoint
10
6.409730244873951e+265
3.5402997186520582e+277
2.966297851011323e+277

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01840
12340
done2340

end0.0ms

sample536.0ms

Algorithm
intervals
Results
318.0ms8494×body80valid