Average Error: 12.9 → 0.0
Time: 1.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r597097 = x;
        double r597098 = y;
        double r597099 = r597097 * r597098;
        double r597100 = r597098 * r597098;
        double r597101 = r597099 - r597100;
        double r597102 = r597101 + r597100;
        double r597103 = z;
        double r597104 = r597098 * r597103;
        double r597105 = r597102 - r597104;
        return r597105;
}
↓
double f(double x, double y, double z) {
        double r597106 = y;
        double r597107 = x;
        double r597108 = z;
        double r597109 = r597107 - r597108;
        double r597110 = r597106 * r597109;
        return r597110;
}

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. 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 2020035 
(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)))