Details

Time bar (total: 13.7s)

sample43.0ms

Algorithm
intervals
Results
21.0ms262×body80valid

simplify87.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
59014
69414
done9414

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
24.3b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite71.0ms

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 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
18.0ms
(- (* x.im y.re) (* x.re y.im))
50.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series197.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(- (* x.im y.re) (* x.re y.im))
145.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.6s

Counts
54 → 54
Iterations

Useful iterations: 3 (962.0ms)

IterNodesCost
088931
1222906
2890809
34246807
done5000807

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b
(- (* x.im y.re) (* x.re y.im))
14.7b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg pow-flip fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 139
Calls
4 calls:
6.0ms
(/ 1 (hypot y.re y.im))
48.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
17.0ms
(- (* x.im y.re) (* x.re y.im))
40.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series560.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 1 (hypot y.re y.im))
261.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
64.0ms
(- (* x.im y.re) (* x.re y.im))
172.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.2s

Counts
151 → 151
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01782462
15202280
233642015
done50001997

prune615.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b
(- (* y.re x.im) (* y.im x.re))
14.7b
(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
22.0ms
(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
18.0ms
(- (* y.re x.im) (* y.im x.re))
47.0ms
(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

series411.0ms

Counts
3 → 9
Calls
3 calls:
177.0ms
(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
53.0ms
(- (* y.re x.im) (* y.im x.re))
181.0ms
(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

simplify1.3s

Counts
130 → 130
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01852814
14752738
222792556
done50022506

prune509.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* y.re x.im) (hypot y.re y.im)) (hypot y.re y.im))
0.6b
(/ (/ (* y.im x.re) (hypot y.re y.im)) (hypot y.re y.im))
9.3b
(/ (* y.im x.re) (hypot y.re y.im))
9.4b
(/ (* y.re x.im) (hypot y.re y.im))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
16×associate-/l*
14×cbrt-undiv div-exp
12×associate-/r* div-inv
4×pow1 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 146
Calls
4 calls:
22.0ms
(/ (/ (* y.re x.im) (hypot y.re y.im)) (hypot y.re y.im))
14.0ms
(/ (/ (* y.im x.re) (hypot y.re y.im)) (hypot y.re y.im))
14.0ms
(/ (* y.im x.re) (hypot y.re y.im))
21.0ms
(/ (* y.re x.im) (hypot y.re y.im))

series583.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (/ (* y.re x.im) (hypot y.re y.im)) (hypot y.re y.im))
151.0ms
(/ (/ (* y.im x.re) (hypot y.re y.im)) (hypot y.re y.im))
109.0ms
(/ (* y.im x.re) (hypot y.re y.im))
146.0ms
(/ (* y.re x.im) (hypot y.re y.im))

simplify1.5s

Counts
158 → 158
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02102382
15232312
231282048
done50002000

prune738.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes317.0ms

Accuracy

40.4% (5.3b remaining)

Error of 5.9b against oracle of 0.6b and baseline of 9.6b

bsearch91.0ms

Steps
ItersRangePoint
6
4.8641680594845535e+57
6.917141905494778e+58
6.466645064161413e+58
9
-1.4354898932691594e+237
-7.52197164437044e+231
-7.628418106649201e+231

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02577
13155
done3155

end1.0ms

sample1.2s

Algorithm
intervals
Results
713.0ms8444×body80valid