Details

Time bar (total: 23.5s)

sample52.0ms

Algorithm
intervals
Results
23.0ms272×body80valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
12315
26615
37215
done7215

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(- (* x.im y.re) (* x.re y.im))
27.2b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

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:
15.0ms
(+ (* y.re y.re) (* y.im y.im))
15.0ms
(- (* x.im y.re) (* x.re y.im))
54.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series282.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (* y.re y.re) (* y.im y.im))
73.0ms
(- (* x.im y.re) (* x.re y.im))
162.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts
64 → 64
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01021120
17141089
done5000999

prune248.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (* x.im y.re) (* x.re y.im))
16.6b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

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:
9.0ms
(- (* x.im y.re) (* x.re y.im))
29.0ms
(/ (- (* 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)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* x.im y.re) (* x.re y.im))
153.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.4s

Counts
98 → 98
Iterations

Useful iterations: done (4.4s)

IterNodesCost
01211814
17011682
done50001586

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (* x.im y.re) (* x.re y.im))
16.7b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite128.0ms

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×sqrt-div add-log-exp
5×unswap-sqr
4×prod-exp
3×flip3-- flip3-+ associate-*l* flip-- flip-+
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv sub-neg rec-exp diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
14.0ms
(- (* x.im y.re) (* x.re y.im))
79.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* x.im y.re) (* x.re y.im))
143.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
53.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify7.0s

Counts
107 → 107
Iterations

Useful iterations: done (7.0s)

IterNodesCost
01481896
127901625
done50001495

prune529.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (* x.im y.re) (* x.re y.im))
16.6b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite118.0ms

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:
17.0ms
(- (* x.im y.re) (* x.re y.im))
64.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* x.im y.re) (* x.re y.im))
222.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify5.5s

Counts
98 → 98
Iterations

Useful iterations: done (5.5s)

IterNodesCost
01211814
17011682
done50001586

prune484.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 24.2b

regimes271.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01527
12127
done2127

end0.0ms

sample1.2s

Algorithm
intervals
Results
752.0ms8480×body80valid