Average Error: 7.6 → 1.5
Time: 18.6s
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 r418761 = x;
        double r418762 = y;
        double r418763 = z;
        double r418764 = r418762 - r418763;
        double r418765 = t;
        double r418766 = r418765 - r418763;
        double r418767 = r418764 * r418766;
        double r418768 = r418761 / r418767;
        return r418768;
}
↓
double f(double x, double y, double z, double t) {
        double r418769 = x;
        double r418770 = cbrt(r418769);
        double r418771 = r418770 * r418770;
        double r418772 = y;
        double r418773 = z;
        double r418774 = r418772 - r418773;
        double r418775 = r418771 / r418774;
        double r418776 = t;
        double r418777 = r418776 - r418773;
        double r418778 = r418770 / r418777;
        double r418779 = r418775 * r418778;
        return r418779;
}

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

Original7.6
Target8.2
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.6

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

  3. Applied add-cube-cbrt8.1

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

  4. Applied times-frac1.5

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

  5. Final simplification1.5

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(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))))