Average Error: 12.4 → 3.0
Time: 2.2s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\frac{x}{\frac{z}{y + z}}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\frac{x}{\frac{z}{y + z}}
double f(double x, double y, double z) {
        double r361576 = x;
        double r361577 = y;
        double r361578 = z;
        double r361579 = r361577 + r361578;
        double r361580 = r361576 * r361579;
        double r361581 = r361580 / r361578;
        return r361581;
}
↓
double f(double x, double y, double z) {
        double r361582 = x;
        double r361583 = z;
        double r361584 = y;
        double r361585 = r361584 + r361583;
        double r361586 = r361583 / r361585;
        double r361587 = r361582 / r361586;
        return r361587;
}

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

Original12.4
Target3.0
Herbie3.0
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Initial program 12.4

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

  3. Applied associate-/l*3.0

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

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

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

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