Average Error: 17.4 → 0.0
Time: 1.8s
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 r598364 = x;
        double r598365 = y;
        double r598366 = r598364 * r598365;
        double r598367 = z;
        double r598368 = r598365 * r598367;
        double r598369 = r598366 - r598368;
        double r598370 = r598365 * r598365;
        double r598371 = r598369 - r598370;
        double r598372 = r598371 + r598370;
        return r598372;
}
↓
double f(double x, double y, double z) {
        double r598373 = y;
        double r598374 = x;
        double r598375 = z;
        double r598376 = r598374 - r598375;
        double r598377 = r598373 * r598376;
        return r598377;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  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 2020081 +o rules:numerics
(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)))