Details

Time bar (total: 17.5s)

sample35.0ms

Algorithm
intervals
Results
19.0ms269×body80valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.0b
(fma x.re y.re (* x.im y.im))
24.7b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 52
Calls
3 calls:
0.0ms
(fma y.im y.im (* y.re y.re))
0.0ms
(fma x.re y.re (* x.im y.im))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series227.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(fma y.im y.im (* y.re y.re))
53.0ms
(fma x.re y.re (* x.im y.im))
120.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify3.0s

Counts
61 → 61
Iterations
IterNodes
done5000
43914
3787
2257
1117
076

prune340.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.3b

localize29.0ms

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))))
15.2b
(/ (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)))

rewrite23.0ms

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)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (/ (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))))
148.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
67.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
45.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.6s

Counts
266 → 266
Iterations
IterNodes
done5064
34078
21154
1547
0262

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.2b
(* (/ (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)))
15.3b
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite41.0ms

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×hypot-udef associate-/r/ *-commutative inv-pow
Counts
4 → 112
Calls
4 calls:
0.0ms
(hypot y.im y.re)
10.0ms
(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
21.0ms
(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
9.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(hypot y.im y.re)
142.0ms
(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
308.0ms
(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
124.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify2.4s

Counts
124 → 124
Iterations
IterNodes
done5123
33254
21062
1312
0139

prune686.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.0b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
15.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite14.0ms

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.re y.re (* x.im y.im))
8.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series399.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(hypot y.im y.re)
74.0ms
(fma x.re y.re (* x.im y.im))
133.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
132.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.7s

Counts
137 → 137
Iterations
IterNodes
done6169
33334
2872
1346
0172

prune841.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

regimes378.0ms

Accuracy

35.4% (7.0b remaining)

Error of 12.9b against oracle of 5.9b and baseline of 16.7b

bsearch119.0ms

Steps
ItersRangePoint
10
1.2561864524018759e+175
1.0510968897587459e+188
6.204871618360054e+176
9
-6.307110292048232e+194
-4.525432705928785e+186
-5.086126503497258e+188

simplify4.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample1.1s

Algorithm
intervals
Results
827.0ms8439×body80valid