Average Error: 17.9 → 0.0
Time: 3.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r528216 = x;
        double r528217 = y;
        double r528218 = r528216 * r528217;
        double r528219 = r528217 * r528217;
        double r528220 = r528218 + r528219;
        double r528221 = z;
        double r528222 = r528217 * r528221;
        double r528223 = r528220 - r528222;
        double r528224 = r528223 - r528219;
        return r528224;
}
↓
double f(double x, double y, double z) {
        double r528225 = y;
        double r528226 = x;
        double r528227 = z;
        double r528228 = r528226 - r528227;
        double r528229 = r528225 * r528228;
        return r528229;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  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 2020001 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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