Details

Time bar (total: 15.8s)

sample23.0ms

Algorithm
intervals
Results
11.0ms271×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
011284
117234
221234
done21234

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize24.0ms

Local error

Found 1 expressions with local error:

22.6b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series98.0ms

Counts
1 → 3
Calls
1 calls:
98.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.1s

Counts
32 → 32
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05811094
19510821
224010181
390610181
4439610181
done500010181

prune209.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
14.2b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
27.1b
(sqrt (fma y.re y.re (* y.im y.im)))
27.1b
(sqrt (fma y.re y.re (* y.im y.im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 250
Calls
4 calls:
14.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
1.0ms
(sqrt (fma y.re y.re (* y.im y.im)))
2.0ms
(sqrt (fma y.re y.re (* y.im y.im)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im)))) (sqrt (fma y.re y.re (* y.im y.im))))
134.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.re y.re (* y.im y.im))))
49.0ms
(sqrt (fma y.re y.re (* y.im y.im)))
54.0ms
(sqrt (fma y.re y.re (* y.im y.im)))

simplify1.9s

Counts
262 → 262
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0259153997
1565143728
22237120927
done5000118367

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.8b
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
14.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×associate-/r*
32×add-exp-log
23×div-inv
20×add-cbrt-cube
19×div-exp
10×cbrt-undiv
9×associate-/l*
6×associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×hypot-udef pow-flip inv-pow
Counts
4 → 317
Calls
4 calls:
0.0ms
(hypot y.re y.im)
15.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
16.0ms
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series587.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(hypot y.re y.im)
110.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
202.0ms
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
202.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify1.5s

Counts
329 → 329
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0439175285
11219152551
done5000150782

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
14.4b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×hypot-udef pow-flip inv-pow associate-/l/
Counts
4 → 319
Calls
4 calls:
0.0ms
(hypot y.re y.im)
35.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
14.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
8.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(hypot y.re y.im)
234.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
208.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
149.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify1.2s

Counts
331 → 331
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0459177395
11314151107
done5000145394

prune1.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes465.0ms

Accuracy

34.2% (7.5b remaining)

Error of 13.5b against oracle of 6.0b and baseline of 17.4b

bsearch108.0ms

Steps
ItersRangePoint
6
7.997843383138597e+191
8.056208352901572e+192
8.747123436813268e+191
10
-3.959953710600684e+125
-7.632284195501427e+113
-2.0458466692374305e+123

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
021697
126697
done26697

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8463×body80valid