Details

Time bar (total: 16.9s)

sample33.0ms

Algorithm
intervals
Results
22.0ms280×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
24.9b
(/ (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
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 y.im y.im (* y.re y.re))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series162.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(fma y.im y.im (* y.re y.re))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify3.1s

Counts
47 → 47
Iterations
IterNodes
done5000
44956
3991
2277
1109
068

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.5b

localize24.0ms

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))))
15.0b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.4b
(sqrt (fma y.im y.im (* y.re y.re)))
28.4b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite38.0ms

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:
19.0ms
(/ (/ (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))))
8.0ms
(/ (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)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (/ (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))))
142.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
57.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
66.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.2s

Counts
266 → 266
Iterations
IterNodes
done5064
34078
21154
1547
0262

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (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))
0.7b
(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
15.1b
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×add-sqr-sqrt
22×*-un-lft-identity times-frac add-cube-cbrt
20×add-cbrt-cube
13×associate-*l*
11×div-exp
9×pow1
8×prod-exp
6×cbrt-undiv associate-/l*
4×expm1-log1p-u associate-/r* cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-*r* div-inv
2×clear-num frac-2neg pow-prod-down associate-*l/ pow-flip unswap-sqr
1×associate-/r/ *-commutative fma-udef inv-pow
Counts
4 → 112
Calls
4 calls:
16.0ms
(* (/ (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))
21.0ms
(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
7.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
57.0ms
(fma x.im y.im (* y.re x.re))
226.0ms
(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
132.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify2.5s

Counts
124 → 124
Iterations
IterNodes
done5077
33511
21073
1308
0137

prune624.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.1b
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b
(fma y.im x.im (* y.re x.re))
15.0b
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

rewrite29.0ms

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)
16.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms
(fma y.im x.im (* y.re x.re))
9.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

series439.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(hypot y.im y.re)
165.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
56.0ms
(fma y.im x.im (* y.re x.re))
157.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

simplify2.3s

Counts
137 → 137
Iterations
IterNodes
done5010
33649
2923
1359
0170

prune789.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

regimes345.0ms

Accuracy

36% (7.1b remaining)

Error of 11.9b against oracle of 4.8b and baseline of 16.0b

bsearch102.0ms

Steps
ItersRangePoint
5
1.1557624945669879e+141
2.8347486911993956e+141
2.2908775229370544e+141
8
-4.843369791675614e+163
-3.80336143295907e+160
-4.434994773334765e+162

simplify6.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.2s8478×body80valid