Average Error: 12.4 → 0.0
Time: 15.5s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r647243 = x;
        double r647244 = y;
        double r647245 = r647243 * r647244;
        double r647246 = r647244 * r647244;
        double r647247 = r647245 - r647246;
        double r647248 = r647247 + r647246;
        double r647249 = z;
        double r647250 = r647244 * r647249;
        double r647251 = r647248 - r647250;
        return r647251;
}
↓
double f(double x, double y, double z) {
        double r647252 = x;
        double r647253 = z;
        double r647254 = r647252 - r647253;
        double r647255 = y;
        double r647256 = r647254 * r647255;
        return r647256;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))