Average Error: 17.4 → 0.0
Time: 3.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r574290 = x;
        double r574291 = y;
        double r574292 = r574290 * r574291;
        double r574293 = z;
        double r574294 = r574291 * r574293;
        double r574295 = r574292 - r574294;
        double r574296 = r574291 * r574291;
        double r574297 = r574295 - r574296;
        double r574298 = r574297 + r574296;
        return r574298;
}
↓
double f(double x, double y, double z) {
        double r574299 = y;
        double r574300 = x;
        double r574301 = z;
        double r574302 = r574300 - r574301;
        double r574303 = r574299 * r574302;
        return r574303;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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