Average Error: 12.8 → 0.0
Time: 1.7s
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 r327261 = x;
        double r327262 = y;
        double r327263 = r327261 * r327262;
        double r327264 = r327262 * r327262;
        double r327265 = r327263 - r327264;
        double r327266 = r327265 + r327264;
        double r327267 = z;
        double r327268 = r327262 * r327267;
        double r327269 = r327266 - r327268;
        return r327269;
}
↓
double f(double x, double y, double z) {
        double r327270 = y;
        double r327271 = x;
        double r327272 = z;
        double r327273 = r327271 - r327272;
        double r327274 = r327270 * r327273;
        return r327274;
}

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

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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 2020089 
(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)))