Average Error: 0.5 → 0.7
Time: 5.2s
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 r217344 = 1.0;
        double r217345 = x;
        double r217346 = y;
        double r217347 = z;
        double r217348 = r217346 - r217347;
        double r217349 = t;
        double r217350 = r217346 - r217349;
        double r217351 = r217348 * r217350;
        double r217352 = r217345 / r217351;
        double r217353 = r217344 - r217352;
        return r217353;
}
↓
double f(double x, double y, double z, double t) {
        double r217354 = 1.0;
        double r217355 = x;
        double r217356 = cbrt(r217355);
        double r217357 = r217356 * r217356;
        double r217358 = y;
        double r217359 = z;
        double r217360 = r217358 - r217359;
        double r217361 = r217357 / r217360;
        double r217362 = t;
        double r217363 = r217358 - r217362;
        double r217364 = r217356 / r217363;
        double r217365 = r217361 * r217364;
        double r217366 = r217354 - r217365;
        return r217366;
}

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 0.5

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  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 1978988140 
(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)))))