Average Error: 13.1 → 3.0
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\frac{x}{\frac{y}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\frac{x}{\frac{y}{y - z}}
double f(double x, double y, double z) {
        double r1061888 = x;
        double r1061889 = y;
        double r1061890 = z;
        double r1061891 = r1061889 - r1061890;
        double r1061892 = r1061888 * r1061891;
        double r1061893 = r1061892 / r1061889;
        return r1061893;
}
↓
double f(double x, double y, double z) {
        double r1061894 = x;
        double r1061895 = y;
        double r1061896 = z;
        double r1061897 = r1061895 - r1061896;
        double r1061898 = r1061895 / r1061897;
        double r1061899 = r1061894 / r1061898;
        return r1061899;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.1
Target3.1
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 13.1

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

  3. Applied associate-/l*3.0

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

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))