Average Error: 17.2 → 0.0
Time: 2.3s
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 r629467 = x;
        double r629468 = y;
        double r629469 = r629467 * r629468;
        double r629470 = z;
        double r629471 = r629468 * r629470;
        double r629472 = r629469 - r629471;
        double r629473 = r629468 * r629468;
        double r629474 = r629472 - r629473;
        double r629475 = r629474 + r629473;
        return r629475;
}
↓
double f(double x, double y, double z) {
        double r629476 = y;
        double r629477 = x;
        double r629478 = z;
        double r629479 = r629477 - r629478;
        double r629480 = r629476 * r629479;
        return r629480;
}

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

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2020047 
(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)))