Average Error: 7.5 → 1.1
Time: 10.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}\]
\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}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}
double f(double x, double y, double z, double t) {
        double r16433882 = x;
        double r16433883 = y;
        double r16433884 = z;
        double r16433885 = r16433883 - r16433884;
        double r16433886 = t;
        double r16433887 = r16433886 - r16433884;
        double r16433888 = r16433885 * r16433887;
        double r16433889 = r16433882 / r16433888;
        return r16433889;
}
↓
double f(double x, double y, double z, double t) {
        double r16433890 = x;
        double r16433891 = cbrt(r16433890);
        double r16433892 = r16433891 * r16433891;
        double r16433893 = y;
        double r16433894 = z;
        double r16433895 = r16433893 - r16433894;
        double r16433896 = cbrt(r16433895);
        double r16433897 = r16433896 * r16433896;
        double r16433898 = r16433892 / r16433897;
        double r16433899 = t;
        double r16433900 = r16433899 - r16433894;
        double r16433901 = r16433891 / r16433896;
        double r16433902 = r16433900 / r16433901;
        double r16433903 = r16433898 / r16433902;
        return r16433903;
}

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

Derivation

  1. Initial program 7.5

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

  3. Applied associate-/r*2.1

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

  5. Applied add-cube-cbrt2.7

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

  6. Applied add-cube-cbrt2.9

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

  7. Applied times-frac2.9

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

  8. Applied associate-/l*1.1

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

  9. Final simplification1.1

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

Reproduce

herbie shell --seed 2019156 
(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))))