Average Error: 0.6 → 0.8
Time: 9.7s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \left(\sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}} \cdot \sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}}\right) \cdot \sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \left(\sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}} \cdot \sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}}\right) \cdot \sqrt[3]{\frac{x}{\left(y - z\right) \cdot \left(y - t\right)}}
double f(double x, double y, double z, double t) {
        double r170265 = 1.0;
        double r170266 = x;
        double r170267 = y;
        double r170268 = z;
        double r170269 = r170267 - r170268;
        double r170270 = t;
        double r170271 = r170267 - r170270;
        double r170272 = r170269 * r170271;
        double r170273 = r170266 / r170272;
        double r170274 = r170265 - r170273;
        return r170274;
}
↓
double f(double x, double y, double z, double t) {
        double r170275 = 1.0;
        double r170276 = x;
        double r170277 = y;
        double r170278 = z;
        double r170279 = r170277 - r170278;
        double r170280 = t;
        double r170281 = r170277 - r170280;
        double r170282 = r170279 * r170281;
        double r170283 = r170276 / r170282;
        double r170284 = cbrt(r170283);
        double r170285 = r170284 * r170284;
        double r170286 = r170285 * r170284;
        double r170287 = r170275 - r170286;
        return r170287;
}

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 add-cube-cbrt0.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2019291 
(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)))))