Average Error: 7.5 → 1.9
Time: 3.9s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}
double f(double x, double y, double z, double t) {
        double r697774 = x;
        double r697775 = y;
        double r697776 = z;
        double r697777 = r697775 - r697776;
        double r697778 = t;
        double r697779 = r697778 - r697776;
        double r697780 = r697777 * r697779;
        double r697781 = r697774 / r697780;
        return r697781;
}
↓
double f(double x, double y, double z, double t) {
        double r697782 = x;
        double r697783 = cbrt(r697782);
        double r697784 = r697783 * r697783;
        double r697785 = y;
        double r697786 = z;
        double r697787 = r697785 - r697786;
        double r697788 = r697784 / r697787;
        double r697789 = t;
        double r697790 = r697789 - r697786;
        double r697791 = r697783 / r697790;
        double r697792 = r697788 * r697791;
        return r697792;
}

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
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt8.0

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

  4. Applied times-frac1.9

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

  5. Final simplification1.9

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

Reproduce

herbie shell --seed 2020083 
(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 (* (- y z) (- t z)))))

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