Average Error: 17.2 → 0.0
Time: 2.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r510815 = x;
        double r510816 = y;
        double r510817 = r510815 * r510816;
        double r510818 = z;
        double r510819 = r510816 * r510818;
        double r510820 = r510817 - r510819;
        double r510821 = r510816 * r510816;
        double r510822 = r510820 - r510821;
        double r510823 = r510822 + r510821;
        return r510823;
}
↓
double f(double x, double y, double z) {
        double r510824 = y;
        double r510825 = x;
        double r510826 = r510824 * r510825;
        double r510827 = z;
        double r510828 = -r510827;
        double r510829 = r510824 * r510828;
        double r510830 = r510826 + r510829;
        return r510830;
}

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

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +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)))