Average Error: 13.2 → 0.0
Time: 1.3s
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 r417101 = x;
        double r417102 = y;
        double r417103 = r417101 * r417102;
        double r417104 = r417102 * r417102;
        double r417105 = r417103 - r417104;
        double r417106 = r417105 + r417104;
        double r417107 = z;
        double r417108 = r417102 * r417107;
        double r417109 = r417106 - r417108;
        return r417109;
}
↓
double f(double x, double y, double z) {
        double r417110 = y;
        double r417111 = x;
        double r417112 = z;
        double r417113 = r417111 - r417112;
        double r417114 = r417110 * r417113;
        return r417114;
}

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

Original13.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.2

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

  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 2020027 +o rules:numerics
(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)))