| Alternative 1 | |
|---|---|
| Error | 0.3 |
| Cost | 6848 |
\[t \cdot \sqrt{1.6 \cdot 10^{-63} \cdot \left(t \cdot t\right)}
\]
(FPCore (t) :precision binary64 (+ (* (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16))) (- -1.0 (* 2.0 (* t 2e-16)))))
(FPCore (t) :precision binary64 (sqrt (* 1.6e-63 (pow t 4.0))))
double code(double t) {
return ((1.0 + (t * 2e-16)) * (1.0 + (t * 2e-16))) + (-1.0 - (2.0 * (t * 2e-16)));
}
double code(double t) {
return sqrt((1.6e-63 * pow(t, 4.0)));
}
real(8) function code(t)
real(8), intent (in) :: t
code = ((1.0d0 + (t * 2d-16)) * (1.0d0 + (t * 2d-16))) + ((-1.0d0) - (2.0d0 * (t * 2d-16)))
end function
real(8) function code(t)
real(8), intent (in) :: t
code = sqrt((1.6d-63 * (t ** 4.0d0)))
end function
public static double code(double t) {
return ((1.0 + (t * 2e-16)) * (1.0 + (t * 2e-16))) + (-1.0 - (2.0 * (t * 2e-16)));
}
public static double code(double t) {
return Math.sqrt((1.6e-63 * Math.pow(t, 4.0)));
}
def code(t): return ((1.0 + (t * 2e-16)) * (1.0 + (t * 2e-16))) + (-1.0 - (2.0 * (t * 2e-16)))
def code(t): return math.sqrt((1.6e-63 * math.pow(t, 4.0)))
function code(t) return Float64(Float64(Float64(1.0 + Float64(t * 2e-16)) * Float64(1.0 + Float64(t * 2e-16))) + Float64(-1.0 - Float64(2.0 * Float64(t * 2e-16)))) end
function code(t) return sqrt(Float64(1.6e-63 * (t ^ 4.0))) end
function tmp = code(t) tmp = ((1.0 + (t * 2e-16)) * (1.0 + (t * 2e-16))) + (-1.0 - (2.0 * (t * 2e-16))); end
function tmp = code(t) tmp = sqrt((1.6e-63 * (t ^ 4.0))); end
code[t_] := N[(N[(N[(1.0 + N[(t * 2e-16), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(2.0 * N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[t_] := N[Sqrt[N[(1.6e-63 * N[Power[t, 4.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right)
\sqrt{1.6 \cdot 10^{-63} \cdot {t}^{4}}
Results
| Original | 61.8 |
|---|---|
| Target | 50.6 |
| Herbie | 0.2 |
Initial program 61.8
Simplified0.4
Taylor expanded in t around 0 0.4
Simplified0.4
Applied egg-rr0.2
Final simplification0.2
| Alternative 1 | |
|---|---|
| Error | 0.3 |
| Cost | 6848 |
| Alternative 2 | |
|---|---|
| Error | 0.4 |
| Cost | 320 |
herbie shell --seed 2022330
(FPCore (t)
:name "fma_test1"
:precision binary64
:pre (and (<= 0.9 t) (<= t 1.1))
:herbie-target
(fma (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16)) (- -1.0 (* 2.0 (* t 2e-16))))
(+ (* (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16))) (- -1.0 (* 2.0 (* t 2e-16)))))