Average Error: 7.1 → 2.1
Time: 4.0s
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 r759807 = x;
        double r759808 = y;
        double r759809 = z;
        double r759810 = r759808 - r759809;
        double r759811 = t;
        double r759812 = r759811 - r759809;
        double r759813 = r759810 * r759812;
        double r759814 = r759807 / r759813;
        return r759814;
}
↓
double f(double x, double y, double z, double t) {
        double r759815 = x;
        double r759816 = y;
        double r759817 = z;
        double r759818 = r759816 - r759817;
        double r759819 = r759815 / r759818;
        double r759820 = t;
        double r759821 = r759820 - r759817;
        double r759822 = r759819 / r759821;
        return r759822;
}

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

Original7.1
Target7.9
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 7.1

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

  3. Applied associate-/r*2.1

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2020021 +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))))