Average Error: 0.6 → 0.7
Time: 3.4s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{y - t}
double f(double x, double y, double z, double t) {
        double r249711 = 1.0;
        double r249712 = x;
        double r249713 = y;
        double r249714 = z;
        double r249715 = r249713 - r249714;
        double r249716 = t;
        double r249717 = r249713 - r249716;
        double r249718 = r249715 * r249717;
        double r249719 = r249712 / r249718;
        double r249720 = r249711 - r249719;
        return r249720;
}
↓
double f(double x, double y, double z, double t) {
        double r249721 = 1.0;
        double r249722 = x;
        double r249723 = cbrt(r249722);
        double r249724 = r249723 * r249723;
        double r249725 = y;
        double r249726 = z;
        double r249727 = r249725 - r249726;
        double r249728 = r249724 / r249727;
        double r249729 = t;
        double r249730 = r249725 - r249729;
        double r249731 = r249723 / r249730;
        double r249732 = r249728 * r249731;
        double r249733 = r249721 - r249732;
        return r249733;
}

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 0.6

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

  3. Applied add-cube-cbrt0.8

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

  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. Final simplification0.7

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

Reproduce

herbie shell --seed 2020039 
(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)))))