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 r198586 = 1.0;
        double r198587 = x;
        double r198588 = y;
        double r198589 = z;
        double r198590 = r198588 - r198589;
        double r198591 = t;
        double r198592 = r198588 - r198591;
        double r198593 = r198590 * r198592;
        double r198594 = r198587 / r198593;
        double r198595 = r198586 - r198594;
        return r198595;
}
↓
double f(double x, double y, double z, double t) {
        double r198596 = 1.0;
        double r198597 = x;
        double r198598 = cbrt(r198597);
        double r198599 = r198598 * r198598;
        double r198600 = y;
        double r198601 = z;
        double r198602 = r198600 - r198601;
        double r198603 = t;
        double r198604 = r198600 - r198603;
        double r198605 = r198602 * r198604;
        double r198606 = r198605 / r198598;
        double r198607 = r198599 / r198606;
        double r198608 = r198596 - r198607;
        return r198608;
}

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 +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)))))