Details

Time bar (total: 17.8s)

sample32.0ms

Algorithm
intervals
Results
21.0ms268×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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 insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series129.0ms

Counts
1 → 3
Calls
1 calls:
129.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify887.0ms

Counts
33 → 33
Iterations
IterNodes
done2007
42007
3770
2232
196
059

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
18.6b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite27.0ms

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 insert-posit16 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 → 254
Calls
4 calls:
10.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
161.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
61.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
50.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify979.0ms

Counts
266 → 266
Iterations
IterNodes
done2006
32006
21154
1547
0262

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.0b
(fma x.im y.im (* y.re x.re))
0.0b
(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
18.6b
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Counts
4 → 125
Calls
4 calls:
0.0ms
(hypot y.im y.re)
0.0ms
(fma x.im y.im (* y.re x.re))
9.0ms
(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
5.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series438.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(hypot y.im y.re)
50.0ms
(fma x.im y.im (* y.re x.re))
173.0ms
(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
150.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify961.0ms

Counts
137 → 137
Iterations
IterNodes
done2000
32000
2892
1346
0171

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.im y.im (* y.re x.re))
0.0b
(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))) (hypot y.im y.re))
0.2b
(/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
18.7b
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite31.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
0.0ms
(fma x.im y.im (* y.re x.re))
11.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))) (hypot y.im y.re))
7.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
6.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series858.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma x.im y.im (* y.re x.re))
216.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))) (hypot y.im y.re))
465.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
126.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify1.1s

Counts
335 → 335
Iterations
IterNodes
done2000
22000
11263
0462

prune4.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

regimes393.0ms

Accuracy

31.5% (7.9b remaining)

Error of 13.0b against oracle of 5.2b and baseline of 16.6b

bsearch112.0ms

Steps
ItersRangePoint
11
3.256921449474541e+176
7.122284858877049e+195
4.711008584896772e+178
6
-8.126158358066474e+96
-1.2737663299885354e+96
-7.67400831190257e+96

simplify17.0ms

Iterations
IterNodes
done34
334
233
130
023

end0.0ms

sample1.3s

Algorithm
intervals
Results
987.0ms8453×body80valid