Average Error: 12.9 → 0.0
Time: 17.6s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r317402 = x;
        double r317403 = y;
        double r317404 = r317402 * r317403;
        double r317405 = r317403 * r317403;
        double r317406 = r317404 - r317405;
        double r317407 = r317406 + r317405;
        double r317408 = z;
        double r317409 = r317403 * r317408;
        double r317410 = r317407 - r317409;
        return r317410;
}
↓
double f(double x, double y, double z) {
        double r317411 = x;
        double r317412 = z;
        double r317413 = r317411 - r317412;
        double r317414 = y;
        double r317415 = r317413 * r317414;
        return r317415;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))