Details

Time bar (total: 31.7s)

sample44.0ms

Algorithm
intervals
Results
31.0ms270×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
117
011

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
28.2b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series190.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(fma x.re y.re (* x.im y.im))
121.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts
47 → 47
Iterations
IterNodes
43206
3937
2297
1105
067

prune603.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.8b

localize40.0ms

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))))
18.7b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
33.4b
(sqrt (fma y.im y.im (* y.re y.re)))
33.4b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite32.0ms

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:
17.0ms
(/ (/ (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)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (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))))
157.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
77.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
75.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts
266 → 266
Iterations
IterNodes
34174
21184
1542
0262

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize20.0ms

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)))
0.6b
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
18.7b
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite35.0ms

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))
6.0ms
(/ (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))))
5.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series651.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma x.im y.im (* y.re x.re))
110.0ms
(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
292.0ms
(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
190.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify7.1s

Counts
333 → 333
Iterations
IterNodes
22985
11161
0442

prune3.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×times-frac
27×*-un-lft-identity add-exp-log
25×add-cube-cbrt
17×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv
4×cbrt-unprod
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
2×rec-exp 1-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Counts
3 → 100
Calls
3 calls:
5.0ms
(fma x.im y.im (* y.re x.re))
14.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
7.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series447.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(fma x.im y.im (* y.re x.re))
215.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
165.0ms
(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify9.4s

Counts
109 → 109
Iterations
IterNodes
33758
21102
1361
0142

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.4b

regimes444.0ms

Accuracy

35.5% (7.6b remaining)

Error of 12.7b against oracle of 5.2b and baseline of 16.9b

bsearch146.0ms

Steps
ItersRangePoint
9
5.794242328935301e+149
4.804137794702964e+156
3.85213929759163e+150
5
-2.3145197442357917e+201
-5.993537297213248e+200
-1.1964723101605788e+201

simplify12.0ms

Iterations
IterNodes
431
331
228
125
020

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s8484×body80valid