Average Error: 8.0 → 2.2
Time: 4.6s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{t - z}}{y - z} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{t - z}}{y - z} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)
double f(double x, double y, double z, double t) {
        double r807925 = x;
        double r807926 = y;
        double r807927 = z;
        double r807928 = r807926 - r807927;
        double r807929 = t;
        double r807930 = r807929 - r807927;
        double r807931 = r807928 * r807930;
        double r807932 = r807925 / r807931;
        return r807932;
}
↓
double f(double x, double y, double z, double t) {
        double r807933 = x;
        double r807934 = t;
        double r807935 = z;
        double r807936 = r807934 - r807935;
        double r807937 = r807933 / r807936;
        double r807938 = y;
        double r807939 = r807938 - r807935;
        double r807940 = r807937 / r807939;
        double r807941 = 1.0;
        double r807942 = cbrt(r807941);
        double r807943 = r807942 * r807942;
        double r807944 = r807940 * r807943;
        return r807944;
}

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

Original8.0
Target8.7
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 8.0

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

  3. Applied *-un-lft-identity8.0

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

  4. Applied times-frac2.2

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

  6. Applied *-un-lft-identity2.2

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

  7. Applied add-cube-cbrt2.2

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

  8. Applied times-frac2.2

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

  9. Applied associate-*l*2.2

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

  10. Simplified2.2

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

  11. Final simplification2.2

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

Reproduce

herbie shell --seed 2020064 +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))))