Average Error: 7.3 → 1.3
Time: 4.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r810847 = x;
        double r810848 = y;
        double r810849 = z;
        double r810850 = r810848 - r810849;
        double r810851 = t;
        double r810852 = r810851 - r810849;
        double r810853 = r810850 * r810852;
        double r810854 = r810847 / r810853;
        return r810854;
}
↓
double f(double x, double y, double z, double t) {
        double r810855 = x;
        double r810856 = cbrt(r810855);
        double r810857 = r810856 * r810856;
        double r810858 = y;
        double r810859 = z;
        double r810860 = r810858 - r810859;
        double r810861 = cbrt(r810860);
        double r810862 = r810861 * r810861;
        double r810863 = r810857 / r810862;
        double r810864 = t;
        double r810865 = r810864 - r810859;
        double r810866 = cbrt(r810865);
        double r810867 = r810866 * r810866;
        double r810868 = r810863 / r810867;
        double r810869 = r810856 / r810861;
        double r810870 = r810869 / r810866;
        double r810871 = r810868 * r810870;
        return r810871;
}

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

Derivation

  1. Initial program 7.3

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

  3. Applied associate-/r*2.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.7

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

  6. Applied add-cube-cbrt3.0

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

  7. Applied add-cube-cbrt3.1

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

  8. Applied times-frac3.1

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

  9. Applied times-frac1.3

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

  10. Final simplification1.3

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

Reproduce

herbie shell --seed 2020062 
(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))))