Average Error: 7.5 → 1.7
Time: 5.8s
Precision: binary64
\[[y, t] = \mathsf{sort}([y, t]) \\]
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
↓
\[\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (* (/ (pow (cbrt x) 2.0) (- y z)) (/ (cbrt x) (- t z))))
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) {
	return (pow(cbrt(x), 2.0) / (y - z)) * (cbrt(x) / (t - z));
}

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
Target8.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

  1. Initial program 7.5

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

  2. Applied add-cube-cbrt_binary648.1

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

  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 pow2_binary641.7

    \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

  5. Final simplification1.7

    \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

Reproduce

herbie shell --seed 2022068 
(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))))