Average Error: 0.7 → 0.7
Time: 5.5s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{y - t}
double f(double x, double y, double z, double t) {
        double r231866 = 1.0;
        double r231867 = x;
        double r231868 = y;
        double r231869 = z;
        double r231870 = r231868 - r231869;
        double r231871 = t;
        double r231872 = r231868 - r231871;
        double r231873 = r231870 * r231872;
        double r231874 = r231867 / r231873;
        double r231875 = r231866 - r231874;
        return r231875;
}
↓
double f(double x, double y, double z, double t) {
        double r231876 = 1.0;
        double r231877 = x;
        double r231878 = cbrt(r231877);
        double r231879 = r231878 * r231878;
        double r231880 = y;
        double r231881 = z;
        double r231882 = r231880 - r231881;
        double r231883 = r231878 / r231882;
        double r231884 = t;
        double r231885 = r231880 - r231884;
        double r231886 = r231883 / r231885;
        double r231887 = r231879 * r231886;
        double r231888 = r231876 - r231887;
        return r231888;
}

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

Derivation

  1. Initial program 0.7

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.9

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

  4. Applied times-frac0.7

    \[\leadsto 1 - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t}}\]
  5. Using strategy rm

  6. Applied div-inv0.7

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

  7. Applied associate-*l*0.7

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

  8. Simplified0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1 (/ x (* (- y z) (- y t)))))