Average Error: 0.7 → 0.7
Time: 5.9s
Precision: binary64
\[[z, t] = \mathsf{sort}([z, t]) \\]
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[\begin{array}{l} t_1 := \sqrt[3]{y - t}\\ 1 - \frac{x \cdot \frac{\frac{1}{y - z}}{t_1}}{t_1 \cdot t_1} \end{array} \]
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))
↓
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (cbrt (- y t))))
   (- 1.0 (/ (* x (/ (/ 1.0 (- y z)) t_1)) (* t_1 t_1)))))
double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}
↓
double code(double x, double y, double z, double t) {
	double t_1 = cbrt((y - t));
	return 1.0 - ((x * ((1.0 / (y - z)) / t_1)) / (t_1 * t_1));
}

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}
↓
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.cbrt((y - t));
	return 1.0 - ((x * ((1.0 / (y - z)) / t_1)) / (t_1 * t_1));
}

function code(x, y, z, t)
	return Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
end
↓
function code(x, y, z, t)
	t_1 = cbrt(Float64(y - t))
	return Float64(1.0 - Float64(Float64(x * Float64(Float64(1.0 / Float64(y - z)) / t_1)) / Float64(t_1 * t_1)))
end

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Power[N[(y - t), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 - N[(N[(x * N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
\begin{array}{l}
t_1 := \sqrt[3]{y - t}\\
1 - \frac{x \cdot \frac{\frac{1}{y - z}}{t_1}}{t_1 \cdot t_1}
\end{array}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

  2. Applied div-inv_binary640.8

    \[\leadsto 1 - \color{blue}{x \cdot \frac{1}{\left(y - z\right) \cdot \left(y - t\right)}} \]

  3. Applied associate-/r*_binary640.8

    \[\leadsto 1 - x \cdot \color{blue}{\frac{\frac{1}{y - z}}{y - t}} \]

  4. Applied add-cube-cbrt_binary641.0

    \[\leadsto 1 - x \cdot \frac{\frac{1}{y - z}}{\color{blue}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}}} \]

  5. Applied *-un-lft-identity_binary641.0

    \[\leadsto 1 - x \cdot \frac{\color{blue}{1 \cdot \frac{1}{y - z}}}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}} \]

  6. Applied times-frac_binary641.0

    \[\leadsto 1 - x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{\frac{1}{y - z}}{\sqrt[3]{y - t}}\right)} \]

  7. Applied associate-*r*_binary641.0

    \[\leadsto 1 - \color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}\right) \cdot \frac{\frac{1}{y - z}}{\sqrt[3]{y - t}}} \]

  8. Applied un-div-inv_binary641.0

    \[\leadsto 1 - \color{blue}{\frac{x}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}} \cdot \frac{\frac{1}{y - z}}{\sqrt[3]{y - t}} \]

  9. Applied associate-*l/_binary640.7

    \[\leadsto 1 - \color{blue}{\frac{x \cdot \frac{\frac{1}{y - z}}{\sqrt[3]{y - t}}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}} \]

  10. Final simplification0.7

    \[\leadsto 1 - \frac{x \cdot \frac{\frac{1}{y - z}}{\sqrt[3]{y - t}}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))