Average Error: 7.4 → 8.1
Time: 15.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{{\left(\sqrt[3]{x}\right)}^{3}}{{\left(\sqrt[3]{t - z}\right)}^{3} \cdot \left(y - z\right)}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{{\left(\sqrt[3]{x}\right)}^{3}}{{\left(\sqrt[3]{t - z}\right)}^{3} \cdot \left(y - z\right)}
double f(double x, double y, double z, double t) {
        double r613772 = x;
        double r613773 = y;
        double r613774 = z;
        double r613775 = r613773 - r613774;
        double r613776 = t;
        double r613777 = r613776 - r613774;
        double r613778 = r613775 * r613777;
        double r613779 = r613772 / r613778;
        return r613779;
}
↓
double f(double x, double y, double z, double t) {
        double r613780 = x;
        double r613781 = cbrt(r613780);
        double r613782 = 3.0;
        double r613783 = pow(r613781, r613782);
        double r613784 = t;
        double r613785 = z;
        double r613786 = r613784 - r613785;
        double r613787 = cbrt(r613786);
        double r613788 = pow(r613787, r613782);
        double r613789 = y;
        double r613790 = r613789 - r613785;
        double r613791 = r613788 * r613790;
        double r613792 = r613783 / r613791;
        return r613792;
}

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
Target8.2
Herbie8.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.4

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

  3. Applied associate-/r*2.3

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

  5. Applied add-cube-cbrt2.9

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

  6. Applied *-un-lft-identity2.9

    \[\leadsto \frac{\frac{x}{\color{blue}{1 \cdot \left(y - z\right)}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  7. Applied add-cube-cbrt3.1

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{1 \cdot \left(y - z\right)}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  8. Applied times-frac3.1

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \frac{\sqrt[3]{x}}{y - z}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  9. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{\sqrt[3]{t - z}}}\]

  10. Simplified1.3

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

  11. Final simplification8.1

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

Reproduce

herbie shell --seed 2019298 
(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))))