Details

Time bar (total: 12.9s)

sample42.0ms

Algorithm
intervals
Results
24.0ms259×body80valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01115
12114
24014
35614
47614
59014
69414
done9414

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (* x.im y.re) (* x.re y.im))
25.3b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite61.0ms

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:
17.0ms
(- (* x.im y.re) (* x.re y.im))
43.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series214.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(- (* x.im y.re) (* x.re y.im))
147.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.3s

Counts
54 → 54
Iterations

Useful iterations: 3 (948.0ms)

IterNodesCost
088931
1222906
2890809
34246807
done5000807

prune227.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)))
0.9b
(- (* x.im y.re) (* x.re y.im))
15.2b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot y.re y.im)
53.0ms
(* (/ 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))
49.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series553.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(hypot y.re y.im)
244.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
52.0ms
(- (* x.im y.re) (* x.re y.im))
176.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.9s

Counts
128 → 128
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01712225
14982088
225101825
done50011817

prune423.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.5b
(fma y.re x.im (- (* y.im x.re)))
15.2b
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.re y.im)
12.0ms
(/ (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma y.re x.im (- (* y.im x.re)))
5.0ms
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

series481.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(hypot y.re y.im)
169.0ms
(/ (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
71.0ms
(fma y.re x.im (- (* y.im x.re)))
170.0ms
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

simplify751.0ms

Counts
133 → 133
Iterations

Useful iterations: done (745.0ms)

IterNodesCost
01682712
13682653
216472463
done50022417

prune610.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)))
0.5b
(fma y.re x.im (- (* y.im x.re)))
15.2b
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
1.0ms
(hypot y.re y.im)
33.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)))
0.0ms
(fma y.re x.im (- (* y.im x.re)))
6.0ms
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

series560.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(hypot y.re y.im)
260.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im)))
69.0ms
(fma y.re x.im (- (* y.im x.re)))
166.0ms
(/ (fma y.re x.im (- (* y.im x.re))) (hypot y.re y.im))

simplify2.6s

Counts
119 → 119
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01472085
14002033
222651702
done50011694

prune526.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

regimes231.0ms

Accuracy

34.7% (7.0b remaining)

Error of 12.8b against oracle of 5.8b and baseline of 16.6b

bsearch65.0ms

Steps
ItersRangePoint
7
1.1507004734249195e+75
6.28375514977393e+76
6.152282888480768e+76
7
-9.986183728447351e+162
-4.4878019732439455e+160
-1.5651675657811871e+162

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01934
12534
22734
done2734

end0.0ms

sample921.0ms

Algorithm
intervals
Results
568.0ms8444×body80valid