Average Error: 7.7 → 1.1
Time: 14.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}{y - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}{y - z}
double f(double x, double y, double z, double t) {
        double r814321 = x;
        double r814322 = y;
        double r814323 = z;
        double r814324 = r814322 - r814323;
        double r814325 = t;
        double r814326 = r814325 - r814323;
        double r814327 = r814324 * r814326;
        double r814328 = r814321 / r814327;
        return r814328;
}
↓
double f(double x, double y, double z, double t) {
        double r814329 = x;
        double r814330 = cbrt(r814329);
        double r814331 = r814330 * r814330;
        double r814332 = t;
        double r814333 = z;
        double r814334 = r814332 - r814333;
        double r814335 = cbrt(r814334);
        double r814336 = r814335 * r814335;
        double r814337 = r814331 / r814336;
        double r814338 = r814330 / r814335;
        double r814339 = y;
        double r814340 = r814339 - r814333;
        double r814341 = r814338 / r814340;
        double r814342 = r814337 * r814341;
        return r814342;
}

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

Target

Original7.7
Target8.6
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.7

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity7.7

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

  4. Applied times-frac2.2

    \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}}\]
  5. Using strategy rm

  6. Applied associate-*l/2.1

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

  7. Simplified2.1

    \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{y - z}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity2.1

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

  10. Applied add-cube-cbrt2.7

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

  11. Applied add-cube-cbrt2.9

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

  12. Applied times-frac2.9

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

  13. Applied times-frac1.1

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

  14. Simplified1.1

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

  15. Final simplification1.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))