Average Error: 7.5 → 1.2
Time: 10.1s
Precision: binary64
\[[y, t] = \mathsf{sort}([y, t]) \\]
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
↓
\[\begin{array}{l} t_1 := \sqrt[3]{y - z}\\ \frac{\sqrt[3]{x}}{t_1 \cdot t_1} \cdot \left(\frac{\sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{t_1}\right) \end{array} \]
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (cbrt (- y z))))
   (* (/ (cbrt x) (* t_1 t_1)) (* (/ (cbrt x) (- t z)) (/ (cbrt x) t_1)))))
double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}
↓
double code(double x, double y, double z, double t) {
	double t_1 = cbrt((y - z));
	return (cbrt(x) / (t_1 * t_1)) * ((cbrt(x) / (t - z)) * (cbrt(x) / t_1));
}

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

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

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

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

Target

Original7.5
Target8.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

  1. Initial program 7.5

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

  2. Applied add-cube-cbrt_binary648.0

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

  3. Applied times-frac_binary641.7

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

  4. Applied add-cube-cbrt_binary641.8

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

  5. Applied times-frac_binary641.8

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

  6. Applied associate-*l*_binary641.2

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

  7. Simplified1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2022129 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))