Average Error: 12.1 → 2.4
Time: 12.7s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\frac{x}{\frac{z}{z + y}}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\frac{x}{\frac{z}{z + y}}
double f(double x, double y, double z) {
        double r21699863 = x;
        double r21699864 = y;
        double r21699865 = z;
        double r21699866 = r21699864 + r21699865;
        double r21699867 = r21699863 * r21699866;
        double r21699868 = r21699867 / r21699865;
        return r21699868;
}
↓
double f(double x, double y, double z) {
        double r21699869 = x;
        double r21699870 = z;
        double r21699871 = y;
        double r21699872 = r21699870 + r21699871;
        double r21699873 = r21699870 / r21699872;
        double r21699874 = r21699869 / r21699873;
        return r21699874;
}

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

Original12.1
Target2.4
Herbie2.4
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Initial program 12.1

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

  3. Applied associate-/l*2.4

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

  4. Final simplification2.4

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))