Details

Time bar (total: 12.2s)

sample46.0ms

Algorithm
intervals
Results
21.0ms265×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01115
11713
22113
done2113

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
27.8b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite13.0ms

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:
1.0ms
(fma x.re y.re (* x.im y.im))
10.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series220.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(fma x.re y.re (* x.im y.im))
166.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.7s

Counts
45 → 45
Iterations

Useful iterations: 3 (325.0ms)

IterNodesCost
065725
1104714
2392624
32082622
done5001622

prune252.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(fma y.re x.re (* y.im x.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
17.6b
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite64.0ms

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)
1.0ms
(fma y.re x.re (* y.im x.im))
41.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
16.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series580.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(hypot y.re y.im)
56.0ms
(fma y.re x.re (* y.im x.im))
287.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
166.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify3.1s

Counts
119 → 119
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01451955
13941902
225571596
done50001579

prune539.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b
(fma x.im y.im (* x.re y.re))
17.6b
(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

rewrite31.0ms

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 x.im y.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma x.im y.im (* x.re y.re))
13.0ms
(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

series494.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot y.re y.im)
179.0ms
(/ (/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
69.0ms
(fma x.im y.im (* x.re y.re))
195.0ms
(/ (fma x.im y.im (* x.re y.re)) (hypot y.re y.im))

simplify1.0s

Counts
133 → 133
Iterations

Useful iterations: done (998.0ms)

IterNodesCost
01682544
13632481
217772306
done50022264

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))))
0.5b
(fma x.im y.im (* y.re x.re))
17.6b
(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

rewrite80.0ms

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:
11.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
51.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))))
0.0ms
(fma x.im y.im (* y.re x.re))
5.0ms
(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

series615.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
240.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))))
49.0ms
(fma x.im y.im (* y.re x.re))
106.0ms
(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

simplify529.0ms

Counts
252 → 252
Iterations

Useful iterations: done (520.0ms)

IterNodesCost
02915363
19564821
done50004337

prune846.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.3b

regimes217.0ms

Accuracy

27.6% (10.5b remaining)

Error of 12.9b against oracle of 2.4b and baseline of 16.9b

bsearch89.0ms

Steps
ItersRangePoint
8
1.267959276101694e+93
1.0044135886792885e+96
9.741722452995778e+95
7
-1.1968959000014948e+107
-2.2592652681113707e+105
-4.379830691407506e+106

simplify8.0ms

Iterations

Useful iterations: 3 (5.0ms)

IterNodesCost
02035
12635
23035
33434
done3434

end0.0ms

sample1.1s

Algorithm
intervals
Results
626.0ms8462×body80valid