Average Error: 17.6 → 0.0
Time: 3.2s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r484419 = x;
        double r484420 = y;
        double r484421 = r484419 * r484420;
        double r484422 = r484420 * r484420;
        double r484423 = r484421 + r484422;
        double r484424 = z;
        double r484425 = r484420 * r484424;
        double r484426 = r484423 - r484425;
        double r484427 = r484426 - r484422;
        return r484427;
}
↓
double f(double x, double y, double z) {
        double r484428 = y;
        double r484429 = x;
        double r484430 = r484428 * r484429;
        double r484431 = z;
        double r484432 = -r484431;
        double r484433 = r484428 * r484432;
        double r484434 = r484430 + r484433;
        return r484434;
}

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

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))