| Alternative 1 | |
|---|---|
| Error | 0.0 |
| Cost | 7360 |
\[\left(1 - v \cdot v\right) \cdot \sqrt{0.125 \cdot \left(1 + v \cdot \left(v \cdot -3\right)\right)}
\]
(FPCore (v) :precision binary64 (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
(FPCore (v)
:precision binary64
(*
(sqrt
(*
(/
(+ 1.0 (* (pow v 6.0) -27.0))
(+ 1.0 (* (* v v) (+ 3.0 (* (* v v) 9.0)))))
0.125))
(- 1.0 (* v v))))double code(double v) {
return ((sqrt(2.0) / 4.0) * sqrt((1.0 - (3.0 * (v * v))))) * (1.0 - (v * v));
}
double code(double v) {
return sqrt((((1.0 + (pow(v, 6.0) * -27.0)) / (1.0 + ((v * v) * (3.0 + ((v * v) * 9.0))))) * 0.125)) * (1.0 - (v * v));
}
real(8) function code(v)
real(8), intent (in) :: v
code = ((sqrt(2.0d0) / 4.0d0) * sqrt((1.0d0 - (3.0d0 * (v * v))))) * (1.0d0 - (v * v))
end function
real(8) function code(v)
real(8), intent (in) :: v
code = sqrt((((1.0d0 + ((v ** 6.0d0) * (-27.0d0))) / (1.0d0 + ((v * v) * (3.0d0 + ((v * v) * 9.0d0))))) * 0.125d0)) * (1.0d0 - (v * v))
end function
public static double code(double v) {
return ((Math.sqrt(2.0) / 4.0) * Math.sqrt((1.0 - (3.0 * (v * v))))) * (1.0 - (v * v));
}
public static double code(double v) {
return Math.sqrt((((1.0 + (Math.pow(v, 6.0) * -27.0)) / (1.0 + ((v * v) * (3.0 + ((v * v) * 9.0))))) * 0.125)) * (1.0 - (v * v));
}
def code(v): return ((math.sqrt(2.0) / 4.0) * math.sqrt((1.0 - (3.0 * (v * v))))) * (1.0 - (v * v))
def code(v): return math.sqrt((((1.0 + (math.pow(v, 6.0) * -27.0)) / (1.0 + ((v * v) * (3.0 + ((v * v) * 9.0))))) * 0.125)) * (1.0 - (v * v))
function code(v) return Float64(Float64(Float64(sqrt(2.0) / 4.0) * sqrt(Float64(1.0 - Float64(3.0 * Float64(v * v))))) * Float64(1.0 - Float64(v * v))) end
function code(v) return Float64(sqrt(Float64(Float64(Float64(1.0 + Float64((v ^ 6.0) * -27.0)) / Float64(1.0 + Float64(Float64(v * v) * Float64(3.0 + Float64(Float64(v * v) * 9.0))))) * 0.125)) * Float64(1.0 - Float64(v * v))) end
function tmp = code(v) tmp = ((sqrt(2.0) / 4.0) * sqrt((1.0 - (3.0 * (v * v))))) * (1.0 - (v * v)); end
function tmp = code(v) tmp = sqrt((((1.0 + ((v ^ 6.0) * -27.0)) / (1.0 + ((v * v) * (3.0 + ((v * v) * 9.0))))) * 0.125)) * (1.0 - (v * v)); end
code[v_] := N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] / 4.0), $MachinePrecision] * N[Sqrt[N[(1.0 - N[(3.0 * N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[v_] := N[(N[Sqrt[N[(N[(N[(1.0 + N[(N[Power[v, 6.0], $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(v * v), $MachinePrecision] * N[(3.0 + N[(N[(v * v), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.125), $MachinePrecision]], $MachinePrecision] * N[(1.0 - N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
\sqrt{\frac{1 + {v}^{6} \cdot -27}{1 + \left(v \cdot v\right) \cdot \left(3 + \left(v \cdot v\right) \cdot 9\right)} \cdot 0.125} \cdot \left(1 - v \cdot v\right)
Results
Initial program 0.0
Applied egg-rr0.0
Applied egg-rr0.0
Simplified0.0
Final simplification0.0
| Alternative 1 | |
|---|---|
| Error | 0.0 |
| Cost | 7360 |
| Alternative 2 | |
|---|---|
| Error | 0.3 |
| Cost | 6976 |
| Alternative 3 | |
|---|---|
| Error | 0.6 |
| Cost | 6464 |
herbie shell --seed 2022330
(FPCore (v)
:name "Falkner and Boettcher, Appendix B, 2"
:precision binary64
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))