Average Error: 7.3 → 1.1
Time: 17.9s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}{y - z} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}{y - z} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r33855449 = x;
        double r33855450 = y;
        double r33855451 = z;
        double r33855452 = r33855450 - r33855451;
        double r33855453 = t;
        double r33855454 = r33855453 - r33855451;
        double r33855455 = r33855452 * r33855454;
        double r33855456 = r33855449 / r33855455;
        return r33855456;
}
↓
double f(double x, double y, double z, double t) {
        double r33855457 = x;
        double r33855458 = cbrt(r33855457);
        double r33855459 = t;
        double r33855460 = z;
        double r33855461 = r33855459 - r33855460;
        double r33855462 = cbrt(r33855461);
        double r33855463 = r33855458 / r33855462;
        double r33855464 = r33855463 * r33855463;
        double r33855465 = y;
        double r33855466 = r33855465 - r33855460;
        double r33855467 = r33855464 / r33855466;
        double r33855468 = r33855467 * r33855463;
        return r33855468;
}

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

Original7.3
Target7.8
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 7.3

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

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

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

  4. Applied times-frac2.2

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

  6. Applied add-cube-cbrt2.7

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

  7. Applied add-cube-cbrt2.9

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

  8. Applied times-frac2.9

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

  9. Applied associate-*r*1.1

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

  10. Simplified1.1

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

  11. Final simplification1.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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