Average Error: 17.6 → 0.0
Time: 3.3s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r427549 = x;
        double r427550 = y;
        double r427551 = r427549 * r427550;
        double r427552 = r427550 * r427550;
        double r427553 = r427551 + r427552;
        double r427554 = z;
        double r427555 = r427550 * r427554;
        double r427556 = r427553 - r427555;
        double r427557 = r427556 - r427552;
        return r427557;
}
↓
double f(double x, double y, double z) {
        double r427558 = x;
        double r427559 = z;
        double r427560 = r427558 - r427559;
        double r427561 = y;
        double r427562 = r427560 * r427561;
        return r427562;
}

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

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

Reproduce

herbie shell --seed 2019308 
(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)))