Average Error: 0.6 → 0.6
Time: 3.5s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
double f(double x, double y, double z, double t) {
        double r184818 = 1.0;
        double r184819 = x;
        double r184820 = y;
        double r184821 = z;
        double r184822 = r184820 - r184821;
        double r184823 = t;
        double r184824 = r184820 - r184823;
        double r184825 = r184822 * r184824;
        double r184826 = r184819 / r184825;
        double r184827 = r184818 - r184826;
        return r184827;
}
↓
double f(double x, double y, double z, double t) {
        double r184828 = 1.0;
        double r184829 = x;
        double r184830 = y;
        double r184831 = z;
        double r184832 = r184830 - r184831;
        double r184833 = t;
        double r184834 = r184830 - r184833;
        double r184835 = r184832 * r184834;
        double r184836 = r184829 / r184835;
        double r184837 = r184828 - r184836;
        return r184837;
}

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 div-inv0.6

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

  5. Applied add-cube-cbrt0.6

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

  6. Applied times-frac0.7

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

  7. Simplified0.7

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

  8. Simplified0.7

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

  10. Applied frac-times0.6

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

  11. Applied associate-*r/0.6

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

  12. Simplified0.6

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

  13. Final simplification0.6

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

Reproduce

herbie shell --seed 2020034 +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)))))