Average Error: 7.6 → 2.1
Time: 16.7s
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 r35345634 = x;
        double r35345635 = y;
        double r35345636 = z;
        double r35345637 = r35345635 - r35345636;
        double r35345638 = t;
        double r35345639 = r35345638 - r35345636;
        double r35345640 = r35345637 * r35345639;
        double r35345641 = r35345634 / r35345640;
        return r35345641;
}
↓
double f(double x, double y, double z, double t) {
        double r35345642 = x;
        double r35345643 = t;
        double r35345644 = z;
        double r35345645 = r35345643 - r35345644;
        double r35345646 = r35345642 / r35345645;
        double r35345647 = y;
        double r35345648 = r35345647 - r35345644;
        double r35345649 = r35345646 / r35345648;
        return r35345649;
}

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

Original7.6
Target8.1
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.6

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

  3. Applied *-un-lft-identity7.6

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

  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. Final simplification2.1

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

Reproduce

herbie shell --seed 2019170 
(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))))