Details

Time bar (total: 10.7s)

sample20.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
24.5b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite3.0ms

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
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series129.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(fma x.re y.re (* x.im y.im))
91.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.5s

Counts
45 → 45
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
065725
1104714
2318622
3965622
42936622
done5000622

prune151.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.3b
(fma y.re x.re (* x.im y.im))
0.3b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
15.3b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite20.0ms

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:
0.0ms
(hypot y.re y.im)
0.0ms
(fma y.re x.re (* x.im y.im))
14.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
2.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series375.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(hypot y.re y.im)
40.0ms
(fma y.re x.re (* x.im y.im))
181.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
99.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify788.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
01461955
13681833
214221579
done50021579

prune337.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
0.3b
(fma y.re x.re (* x.im y.im))
0.3b
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
15.4b
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
143×add-sqr-sqrt
107×*-un-lft-identity
100×add-exp-log
96×add-cube-cbrt
50×div-exp
44×associate-*r*
32×add-cbrt-cube
28×prod-exp
17×rec-exp 1-exp
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv associate-*l*
11×div-inv
9×pow1
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-flip pow-prod-down inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 240
Calls
4 calls:
5.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
0.0ms
(fma y.re x.re (* x.im y.im))
32.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
2.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
40.0ms
(fma y.re x.re (* x.im y.im))
181.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
90.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

simplify2.3s

Counts
252 → 252
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02915363
18434825
226554048
done50004042

prune576.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
15.3b
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

rewrite13.0ms

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×hypot-udef frac-2neg clear-num
1×associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
6.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
2.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

series330.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(hypot y.re y.im)
47.0ms
(hypot y.re y.im)
121.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
111.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

simplify2.3s

Counts
133 → 133
Iterations

Useful iterations: 3 (615.0ms)

IterNodesCost
01612502
13392439
211232262
335962208
done50002208

prune392.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.8b

regimes214.0ms

Accuracy

26.8% (10.4b remaining)

Error of 12.9b against oracle of 2.5b and baseline of 16.8b

bsearch68.0ms

Steps
ItersRangePoint
5
8.957497130921995e+173
2.753131322655158e+174
9.568321133628251e+173
9
-2.4646235951984806e+94
-5.042571483055581e+85
-2.417601261285543e+94

simplify7.0ms

Iterations

Useful iterations: 2 (2.0ms)

IterNodesCost
02343
13139
23435
34135
44435
54635
done4635

end0.0ms

sample513.0ms

Algorithm
intervals
Results
300.0ms8488×body80valid