Average Error: 12.5 → 0.0
Time: 29.6s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y - z \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y - z \cdot y
double f(double x, double y, double z) {
        double r18627139 = x;
        double r18627140 = y;
        double r18627141 = r18627139 * r18627140;
        double r18627142 = r18627140 * r18627140;
        double r18627143 = r18627141 - r18627142;
        double r18627144 = r18627143 + r18627142;
        double r18627145 = z;
        double r18627146 = r18627140 * r18627145;
        double r18627147 = r18627144 - r18627146;
        return r18627147;
}
↓
double f(double x, double y, double z) {
        double r18627148 = x;
        double r18627149 = y;
        double r18627150 = r18627148 * r18627149;
        double r18627151 = z;
        double r18627152 = r18627151 * r18627149;
        double r18627153 = r18627150 - r18627152;
        return r18627153;
}

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

Original12.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.5

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
  2. Using strategy rm

  3. Applied associate-+l-7.6

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

  4. Applied associate--l-7.6

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

  5. Simplified0.0

    \[\leadsto x \cdot y - \color{blue}{z \cdot y}\]

  6. Final simplification0.0

    \[\leadsto x \cdot y - z \cdot y\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

  :herbie-target
  (* (- x z) y)

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))