Average Error: 0.7 → 0.9
Time: 5.4s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\left(y - z\right) \cdot \left(y - t\right)}{\sqrt[3]{x}}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\left(y - z\right) \cdot \left(y - t\right)}{\sqrt[3]{x}}}
double f(double x, double y, double z, double t) {
        double r238814 = 1.0;
        double r238815 = x;
        double r238816 = y;
        double r238817 = z;
        double r238818 = r238816 - r238817;
        double r238819 = t;
        double r238820 = r238816 - r238819;
        double r238821 = r238818 * r238820;
        double r238822 = r238815 / r238821;
        double r238823 = r238814 - r238822;
        return r238823;
}
↓
double f(double x, double y, double z, double t) {
        double r238824 = 1.0;
        double r238825 = x;
        double r238826 = cbrt(r238825);
        double r238827 = r238826 * r238826;
        double r238828 = y;
        double r238829 = z;
        double r238830 = r238828 - r238829;
        double r238831 = t;
        double r238832 = r238828 - r238831;
        double r238833 = r238830 * r238832;
        double r238834 = r238833 / r238826;
        double r238835 = r238827 / r238834;
        double r238836 = r238824 - r238835;
        return r238836;
}

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 associate-/l*0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2020001 
(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)))))