Details

Time bar (total: 45.8s)

sample58.0ms

Algorithm
intervals
Results
39.0ms268×body80valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
117
011

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize35.0ms

Local error

Found 1 expressions with local error:

24.9b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

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:
9.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series130.0ms

Counts
1 → 3
Calls
1 calls:
130.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify986.0ms

Counts
33 → 33
Iterations
IterNodes
42413
3689
2227
195
059

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (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))))
15.3b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.2b
(sqrt (fma y.im y.im (* y.re y.re)))
28.2b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite51.0ms

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:
20.0ms
(/ (/ (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))))
17.0ms
(/ (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)))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (/ (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))))
186.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
53.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.4s

Counts
266 → 266
Iterations
IterNodes
34174
21184
1542
0262

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
0.4b
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
0.5b
(fma x.im y.im (* y.re x.re))
15.3b
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite51.0ms

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:
11.0ms
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
16.0ms
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
0.0ms
(fma x.im y.im (* y.re x.re))
7.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series725.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
319.0ms
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
67.0ms
(fma x.im y.im (* y.re x.re))
211.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify5.8s

Counts
333 → 333
Iterations
IterNodes
22933
11159
0442

prune4.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 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))))
0.5b
(fma x.im y.im (* y.re x.re))
15.4b
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite50.0ms

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:
16.0ms
(/ (/ 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))))
0.0ms
(fma x.im y.im (* y.re x.re))
5.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series657.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))) (hypot y.im y.re))
176.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
72.0ms
(fma x.im y.im (* y.re x.re))
151.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify21.0s

Counts
335 → 335
Iterations
IterNodes
23247
11237
0462

prune4.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes413.0ms

Accuracy

37.3% (7.4b remaining)

Error of 12.5b against oracle of 5.1b and baseline of 16.9b

bsearch122.0ms

Steps
ItersRangePoint
7
2.1102039645699546e+151
5.958060973732056e+152
6.134295887350108e+151
9
-1.5743457092445136e+146
-1.7745971881998158e+137
-2.052205868896771e+142

simplify6.0ms

Iterations
IterNodes
222
122
020

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s8476×body80valid