Details

Time bar (total: 53.6s)

sample36.0ms

Algorithm
intervals
Results
22.0ms268×body80valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
117
011

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize33.0ms

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)))

rewrite11.0ms

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

series111.0ms

Counts
1 → 3
Calls
1 calls:
111.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts
33 → 33
Iterations
IterNodes
42413
3689
2227
195
059

prune249.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.3b

localize43.0ms

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)))

rewrite26.0ms

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))))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (/ (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))))
151.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
60.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
56.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts
266 → 266
Iterations
IterNodes
34174
21184
1542
0262

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.im y.im (* y.re x.re))
0.1b
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
1.2b
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
18.6b
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite53.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×fma-udef pow-flip inv-pow
Counts
4 → 321
Calls
4 calls:
0.0ms
(fma x.im y.im (* y.re x.re))
12.0ms
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
18.0ms
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
9.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series616.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma x.im y.im (* y.re x.re))
107.0ms
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
242.0ms
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
218.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify7.4s

Counts
333 → 333
Iterations
IterNodes
22985
11161
0442

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.im y.im (* y.re x.re))
0.1b
(/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
0.3b
(/ (/ 1 (hypot y.im y.re)) (/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
18.6b
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
1985×times-frac
859×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
108×div-inv
100×add-exp-log
78×div-exp
60×associate-/r*
32×add-cbrt-cube
19×cbrt-undiv associate-/l*
17×rec-exp 1-exp
16×associate-/r/
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 798
Calls
4 calls:
0.0ms
(fma x.im y.im (* y.re x.re))
17.0ms
(/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
26.0ms
(/ (/ 1 (hypot y.im y.re)) (/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
9.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series718.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(fma x.im y.im (* y.re x.re))
157.0ms
(/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
268.0ms
(/ (/ 1 (hypot y.im y.re)) (/ 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
223.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify32.0s

Counts
810 → 810
Iterations
IterNodes
14019
01198

prune2.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.3b

regimes511.0ms

Accuracy

30.6% (8.0b remaining)

Error of 13.2b against oracle of 5.2b and baseline of 16.7b

bsearch126.0ms

Steps
ItersRangePoint
11
3.256921449474541e+176
7.122284858877049e+195
6.658964062989261e+180
7
-1.2737663299885354e+96
-6.766972193909726e+93
-1.0287542866145704e+96

simplify4.0ms

Iterations
IterNodes
224
124
023

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.7s8453×body80valid