Average Error: 17.8 → 0.0
Time: 1.5s
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 r478246 = x;
        double r478247 = y;
        double r478248 = r478246 * r478247;
        double r478249 = z;
        double r478250 = r478247 * r478249;
        double r478251 = r478248 - r478250;
        double r478252 = r478247 * r478247;
        double r478253 = r478251 - r478252;
        double r478254 = r478253 + r478252;
        return r478254;
}
↓
double f(double x, double y, double z) {
        double r478255 = y;
        double r478256 = x;
        double r478257 = z;
        double r478258 = r478256 - r478257;
        double r478259 = r478255 * r478258;
        return r478259;
}

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

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  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 2020064 +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)))