Average Error: 17.5 → 0.0
Time: 14.6s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r651929 = x;
        double r651930 = y;
        double r651931 = r651929 * r651930;
        double r651932 = r651930 * r651930;
        double r651933 = r651931 + r651932;
        double r651934 = z;
        double r651935 = r651930 * r651934;
        double r651936 = r651933 - r651935;
        double r651937 = r651936 - r651932;
        return r651937;
}
↓
double f(double x, double y, double z) {
        double r651938 = x;
        double r651939 = y;
        double r651940 = r651938 * r651939;
        double r651941 = z;
        double r651942 = -r651941;
        double r651943 = r651942 * r651939;
        double r651944 = r651940 + r651943;
        return r651944;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

    \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto y \cdot \color{blue}{\left(x + \left(-z\right)\right)}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{y \cdot x + y \cdot \left(-z\right)}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{x \cdot y} + y \cdot \left(-z\right)\]

  7. Simplified0.0

    \[\leadsto x \cdot y + \color{blue}{\left(-z\right) \cdot y}\]

  8. Final simplification0.0

    \[\leadsto x \cdot y + \left(-z\right) \cdot y\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))