Average Error: 17.2 → 0.0
Time: 22.4s
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 r271259 = x;
        double r271260 = y;
        double r271261 = r271259 * r271260;
        double r271262 = r271260 * r271260;
        double r271263 = r271261 + r271262;
        double r271264 = z;
        double r271265 = r271260 * r271264;
        double r271266 = r271263 - r271265;
        double r271267 = r271266 - r271262;
        return r271267;
}
↓
double f(double x, double y, double z) {
        double r271268 = y;
        double r271269 = x;
        double r271270 = z;
        double r271271 = r271269 - r271270;
        double r271272 = r271268 * r271271;
        return r271272;
}

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

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2019304 +o rules:numerics
(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)))