Average Error: 17.9 → 0.0
Time: 3.4s
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 r565432 = x;
        double r565433 = y;
        double r565434 = r565432 * r565433;
        double r565435 = z;
        double r565436 = r565433 * r565435;
        double r565437 = r565434 - r565436;
        double r565438 = r565433 * r565433;
        double r565439 = r565437 - r565438;
        double r565440 = r565439 + r565438;
        return r565440;
}
↓
double f(double x, double y, double z) {
        double r565441 = y;
        double r565442 = x;
        double r565443 = z;
        double r565444 = r565442 - r565443;
        double r565445 = r565441 * r565444;
        return r565445;
}

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)))