Average Error: 12.7 → 0.0
Time: 1.5s
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 r477385 = x;
        double r477386 = y;
        double r477387 = r477385 * r477386;
        double r477388 = r477386 * r477386;
        double r477389 = r477387 - r477388;
        double r477390 = r477389 + r477388;
        double r477391 = z;
        double r477392 = r477386 * r477391;
        double r477393 = r477390 - r477392;
        return r477393;
}
↓
double f(double x, double y, double z) {
        double r477394 = y;
        double r477395 = x;
        double r477396 = z;
        double r477397 = r477395 - r477396;
        double r477398 = r477394 * r477397;
        return r477398;
}

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

Original12.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.7

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

  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 2019356 
(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)))