Average Error: 0.7 → 0.9
Time: 5.7s
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 r216617 = 1.0;
        double r216618 = x;
        double r216619 = y;
        double r216620 = z;
        double r216621 = r216619 - r216620;
        double r216622 = t;
        double r216623 = r216619 - r216622;
        double r216624 = r216621 * r216623;
        double r216625 = r216618 / r216624;
        double r216626 = r216617 - r216625;
        return r216626;
}
↓
double f(double x, double y, double z, double t) {
        double r216627 = 1.0;
        double r216628 = x;
        double r216629 = cbrt(r216628);
        double r216630 = r216629 * r216629;
        double r216631 = y;
        double r216632 = z;
        double r216633 = r216631 - r216632;
        double r216634 = t;
        double r216635 = r216631 - r216634;
        double r216636 = r216633 * r216635;
        double r216637 = r216636 / r216629;
        double r216638 = r216630 / r216637;
        double r216639 = r216627 - r216638;
        return r216639;
}

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)))))