Average Error: 7.3 → 1.2
Time: 5.2s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}} \cdot \frac{\sqrt[3]{x}}{t - z}\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\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)
double f(double x, double y, double z, double t) {
        double r913810 = x;
        double r913811 = y;
        double r913812 = z;
        double r913813 = r913811 - r913812;
        double r913814 = t;
        double r913815 = r913814 - r913812;
        double r913816 = r913813 * r913815;
        double r913817 = r913810 / r913816;
        return r913817;
}
↓
double f(double x, double y, double z, double t) {
        double r913818 = x;
        double r913819 = cbrt(r913818);
        double r913820 = y;
        double r913821 = z;
        double r913822 = r913820 - r913821;
        double r913823 = cbrt(r913822);
        double r913824 = r913823 * r913823;
        double r913825 = r913819 / r913824;
        double r913826 = r913819 / r913823;
        double r913827 = t;
        double r913828 = r913827 - r913821;
        double r913829 = r913819 / r913828;
        double r913830 = r913826 * r913829;
        double r913831 = r913825 * r913830;
        return r913831;
}

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

Original7.3
Target8.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.3

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

  3. Applied add-cube-cbrt7.9

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

  4. Applied times-frac1.7

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

  8. Applied associate-*l*1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020060 +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))))