Average Error: 7.4 → 1.6
Time: 20.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z}
double f(double x, double y, double z, double t) {
        double r35559127 = x;
        double r35559128 = y;
        double r35559129 = z;
        double r35559130 = r35559128 - r35559129;
        double r35559131 = t;
        double r35559132 = r35559131 - r35559129;
        double r35559133 = r35559130 * r35559132;
        double r35559134 = r35559127 / r35559133;
        return r35559134;
}
↓
double f(double x, double y, double z, double t) {
        double r35559135 = x;
        double r35559136 = cbrt(r35559135);
        double r35559137 = t;
        double r35559138 = z;
        double r35559139 = r35559137 - r35559138;
        double r35559140 = r35559136 / r35559139;
        double r35559141 = r35559136 * r35559136;
        double r35559142 = y;
        double r35559143 = r35559142 - r35559138;
        double r35559144 = r35559141 / r35559143;
        double r35559145 = r35559140 * r35559144;
        return r35559145;
}

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

Original7.4
Target7.8
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.4

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  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-frac1.6

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

  5. Final simplification1.6

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :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))))