Average Error: 12.8 → 0.0
Time: 8.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(-z\right) \cdot y + y \cdot x\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(-z\right) \cdot y + y \cdot x
double f(double x, double y, double z) {
        double r27077391 = x;
        double r27077392 = y;
        double r27077393 = r27077391 * r27077392;
        double r27077394 = r27077392 * r27077392;
        double r27077395 = r27077393 - r27077394;
        double r27077396 = r27077395 + r27077394;
        double r27077397 = z;
        double r27077398 = r27077392 * r27077397;
        double r27077399 = r27077396 - r27077398;
        return r27077399;
}
↓
double f(double x, double y, double z) {
        double r27077400 = z;
        double r27077401 = -r27077400;
        double r27077402 = y;
        double r27077403 = r27077401 * r27077402;
        double r27077404 = x;
        double r27077405 = r27077402 * r27077404;
        double r27077406 = r27077403 + r27077405;
        return r27077406;
}

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

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

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

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