Average Error: 17.1 → 0.0
Time: 1.6s
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 r518231 = x;
        double r518232 = y;
        double r518233 = r518231 * r518232;
        double r518234 = r518232 * r518232;
        double r518235 = r518233 + r518234;
        double r518236 = z;
        double r518237 = r518232 * r518236;
        double r518238 = r518235 - r518237;
        double r518239 = r518238 - r518234;
        return r518239;
}
↓
double f(double x, double y, double z) {
        double r518240 = y;
        double r518241 = x;
        double r518242 = z;
        double r518243 = r518241 - r518242;
        double r518244 = r518240 * r518243;
        return r518244;
}

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

Original17.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.1

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

  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 2019356 
(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)))