Average Error: 17.7 → 0.0
Time: 11.6s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r442306 = x;
        double r442307 = y;
        double r442308 = r442306 * r442307;
        double r442309 = r442307 * r442307;
        double r442310 = r442308 + r442309;
        double r442311 = z;
        double r442312 = r442307 * r442311;
        double r442313 = r442310 - r442312;
        double r442314 = r442313 - r442309;
        return r442314;
}
↓
double f(double x, double y, double z) {
        double r442315 = x;
        double r442316 = z;
        double r442317 = r442315 - r442316;
        double r442318 = y;
        double r442319 = r442317 * r442318;
        return r442319;
}

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

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto y \cdot \color{blue}{\left(x + \left(-z\right)\right)}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{y \cdot x + y \cdot \left(-z\right)}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(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)))