Average Error: 0.7 → 0.6
Time: 19.6s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}} \cdot \frac{\sqrt[3]{x}}{\frac{y - t}{\sqrt[3]{\sqrt[3]{x}}}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{x}}{\frac{y - z}{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}} \cdot \frac{\sqrt[3]{x}}{\frac{y - t}{\sqrt[3]{\sqrt[3]{x}}}}
double f(double x, double y, double z, double t) {
        double r284330 = 1.0;
        double r284331 = x;
        double r284332 = y;
        double r284333 = z;
        double r284334 = r284332 - r284333;
        double r284335 = t;
        double r284336 = r284332 - r284335;
        double r284337 = r284334 * r284336;
        double r284338 = r284331 / r284337;
        double r284339 = r284330 - r284338;
        return r284339;
}
↓
double f(double x, double y, double z, double t) {
        double r284340 = 1.0;
        double r284341 = x;
        double r284342 = cbrt(r284341);
        double r284343 = y;
        double r284344 = z;
        double r284345 = r284343 - r284344;
        double r284346 = cbrt(r284342);
        double r284347 = r284346 * r284346;
        double r284348 = r284345 / r284347;
        double r284349 = r284342 / r284348;
        double r284350 = t;
        double r284351 = r284343 - r284350;
        double r284352 = r284351 / r284346;
        double r284353 = r284342 / r284352;
        double r284354 = r284349 * r284353;
        double r284355 = r284340 - r284354;
        return r284355;
}

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. Using strategy rm

  6. Applied add-cube-cbrt1.0

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

  7. Applied times-frac0.6

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

  8. Applied times-frac0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2019351 +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)))))