Average Error: 17.9 → 0.0
Time: 3.5s
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 r533232 = x;
        double r533233 = y;
        double r533234 = r533232 * r533233;
        double r533235 = z;
        double r533236 = r533233 * r533235;
        double r533237 = r533234 - r533236;
        double r533238 = r533233 * r533233;
        double r533239 = r533237 - r533238;
        double r533240 = r533239 + r533238;
        return r533240;
}
↓
double f(double x, double y, double z) {
        double r533241 = y;
        double r533242 = x;
        double r533243 = z;
        double r533244 = r533242 - r533243;
        double r533245 = r533241 * r533244;
        return r533245;
}

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

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

Derivation

  1. Initial program 17.9

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

  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 2020001 
(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)))