Average Error: 12.9 → 0.0
Time: 5.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r547489 = x;
        double r547490 = y;
        double r547491 = r547489 * r547490;
        double r547492 = r547490 * r547490;
        double r547493 = r547491 - r547492;
        double r547494 = r547493 + r547492;
        double r547495 = z;
        double r547496 = r547490 * r547495;
        double r547497 = r547494 - r547496;
        return r547497;
}
↓
double f(double x, double y, double z) {
        double r547498 = y;
        double r547499 = x;
        double r547500 = z;
        double r547501 = r547499 - r547500;
        double r547502 = r547498 * r547501;
        return r547502;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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