Average Error: 7.9 → 2.0
Time: 14.7s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{t - z}}{y - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{t - z}}{y - z}
double f(double x, double y, double z, double t) {
        double r517836 = x;
        double r517837 = y;
        double r517838 = z;
        double r517839 = r517837 - r517838;
        double r517840 = t;
        double r517841 = r517840 - r517838;
        double r517842 = r517839 * r517841;
        double r517843 = r517836 / r517842;
        return r517843;
}
↓
double f(double x, double y, double z, double t) {
        double r517844 = x;
        double r517845 = t;
        double r517846 = z;
        double r517847 = r517845 - r517846;
        double r517848 = r517844 / r517847;
        double r517849 = y;
        double r517850 = r517849 - r517846;
        double r517851 = r517848 / r517850;
        return r517851;
}

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

Original7.9
Target8.5
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.9

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

  3. Applied *-un-lft-identity7.9

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

  4. Applied times-frac2.0

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

  6. Applied associate-*l/2.0

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

  7. Simplified2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2019235 +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))))