Average Error: 12.9 → 0.0
Time: 17.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y - y \cdot z
double f(double x, double y, double z) {
        double r355226 = x;
        double r355227 = y;
        double r355228 = r355226 * r355227;
        double r355229 = r355227 * r355227;
        double r355230 = r355228 - r355229;
        double r355231 = r355230 + r355229;
        double r355232 = z;
        double r355233 = r355227 * r355232;
        double r355234 = r355231 - r355233;
        return r355234;
}
↓
double f(double x, double y, double z) {
        double r355235 = x;
        double r355236 = y;
        double r355237 = r355235 * r355236;
        double r355238 = z;
        double r355239 = r355236 * r355238;
        double r355240 = r355237 - r355239;
        return r355240;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))