Average Error: 7.6 → 2.0
Time: 17.9s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{y - z}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{y - z}}{t - z}
double f(double x, double y, double z, double t) {
        double r552642 = x;
        double r552643 = y;
        double r552644 = z;
        double r552645 = r552643 - r552644;
        double r552646 = t;
        double r552647 = r552646 - r552644;
        double r552648 = r552645 * r552647;
        double r552649 = r552642 / r552648;
        return r552649;
}
↓
double f(double x, double y, double z, double t) {
        double r552650 = x;
        double r552651 = y;
        double r552652 = z;
        double r552653 = r552651 - r552652;
        double r552654 = r552650 / r552653;
        double r552655 = t;
        double r552656 = r552655 - r552652;
        double r552657 = r552654 / r552656;
        return r552657;
}

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
Target8.2
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 7.6

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

  3. Applied associate-/r*2.0

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

  4. Final simplification2.0

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

Reproduce

herbie shell --seed 2019306 +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))))