| Alternative 1 | |
|---|---|
| Error | 0.4 |
| Cost | 13760 |
\[\left(\frac{\frac{\ell}{k}}{\tan k} \cdot \frac{2}{t}\right) \cdot \frac{\frac{\ell}{k}}{\sin k}
\]
Error
(FPCore (t l k) :precision binary64 (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
(FPCore (t l k) :precision binary64 (* (* (/ (/ l k) (tan k)) (/ 2.0 t)) (* (/ l k) (/ 1.0 (sin k)))))
double code(double t, double l, double k) {
return 2.0 / ((((pow(t, 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + pow((k / t), 2.0)) - 1.0));
}
double code(double t, double l, double k) {
return (((l / k) / tan(k)) * (2.0 / t)) * ((l / k) * (1.0 / sin(k)));
}
real(8) function code(t, l, k)
real(8), intent (in) :: t
real(8), intent (in) :: l
real(8), intent (in) :: k
code = 2.0d0 / (((((t ** 3.0d0) / (l * l)) * sin(k)) * tan(k)) * ((1.0d0 + ((k / t) ** 2.0d0)) - 1.0d0))
end function
real(8) function code(t, l, k)
real(8), intent (in) :: t
real(8), intent (in) :: l
real(8), intent (in) :: k
code = (((l / k) / tan(k)) * (2.0d0 / t)) * ((l / k) * (1.0d0 / sin(k)))
end function
public static double code(double t, double l, double k) {
return 2.0 / ((((Math.pow(t, 3.0) / (l * l)) * Math.sin(k)) * Math.tan(k)) * ((1.0 + Math.pow((k / t), 2.0)) - 1.0));
}
public static double code(double t, double l, double k) {
return (((l / k) / Math.tan(k)) * (2.0 / t)) * ((l / k) * (1.0 / Math.sin(k)));
}
def code(t, l, k): return 2.0 / ((((math.pow(t, 3.0) / (l * l)) * math.sin(k)) * math.tan(k)) * ((1.0 + math.pow((k / t), 2.0)) - 1.0))
def code(t, l, k): return (((l / k) / math.tan(k)) * (2.0 / t)) * ((l / k) * (1.0 / math.sin(k)))
function code(t, l, k) return Float64(2.0 / Float64(Float64(Float64(Float64((t ^ 3.0) / Float64(l * l)) * sin(k)) * tan(k)) * Float64(Float64(1.0 + (Float64(k / t) ^ 2.0)) - 1.0))) end
function code(t, l, k) return Float64(Float64(Float64(Float64(l / k) / tan(k)) * Float64(2.0 / t)) * Float64(Float64(l / k) * Float64(1.0 / sin(k)))) end
function tmp = code(t, l, k) tmp = 2.0 / (((((t ^ 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + ((k / t) ^ 2.0)) - 1.0)); end
function tmp = code(t, l, k) tmp = (((l / k) / tan(k)) * (2.0 / t)) * ((l / k) * (1.0 / sin(k))); end
code[t_, l_, k_] := N[(2.0 / N[(N[(N[(N[(N[Power[t, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[t_, l_, k_] := N[(N[(N[(N[(l / k), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(2.0 / t), $MachinePrecision]), $MachinePrecision] * N[(N[(l / k), $MachinePrecision] * N[(1.0 / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)}
\left(\frac{\frac{\ell}{k}}{\tan k} \cdot \frac{2}{t}\right) \cdot \left(\frac{\ell}{k} \cdot \frac{1}{\sin k}\right)
Results
Initial program 47.7
Simplified40.4
Applied egg-rr33.1
Taylor expanded in k around inf 22.4
Simplified7.2
Applied egg-rr1.5
Applied egg-rr0.4
Final simplification0.4
| Alternative 1 | |
|---|---|
| Error | 0.4 |
| Cost | 13760 |
| Alternative 2 | |
|---|---|
| Error | 24.2 |
| Cost | 7360 |
| Alternative 3 | |
|---|---|
| Error | 24.5 |
| Cost | 7300 |
| Alternative 4 | |
|---|---|
| Error | 29.0 |
| Cost | 960 |
herbie shell --seed 2022291
(FPCore (t l k)
:name "Toniolo and Linder, Equation (10-)"
:precision binary64
(/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))