Average Error: 0.6 → 0.7
Time: 3.6s
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 r220472 = 1.0;
        double r220473 = x;
        double r220474 = y;
        double r220475 = z;
        double r220476 = r220474 - r220475;
        double r220477 = t;
        double r220478 = r220474 - r220477;
        double r220479 = r220476 * r220478;
        double r220480 = r220473 / r220479;
        double r220481 = r220472 - r220480;
        return r220481;
}
↓
double f(double x, double y, double z, double t) {
        double r220482 = 1.0;
        double r220483 = x;
        double r220484 = cbrt(r220483);
        double r220485 = r220484 * r220484;
        double r220486 = y;
        double r220487 = z;
        double r220488 = r220486 - r220487;
        double r220489 = r220485 / r220488;
        double r220490 = t;
        double r220491 = r220486 - r220490;
        double r220492 = r220484 / r220491;
        double r220493 = r220489 * r220492;
        double r220494 = r220482 - r220493;
        return r220494;
}

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

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

  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 2020039 +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)))))