Average Error: 12.8 → 0.0
Time: 1.8s
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 r511616 = x;
        double r511617 = y;
        double r511618 = r511616 * r511617;
        double r511619 = r511617 * r511617;
        double r511620 = r511618 - r511619;
        double r511621 = r511620 + r511619;
        double r511622 = z;
        double r511623 = r511617 * r511622;
        double r511624 = r511621 - r511623;
        return r511624;
}
↓
double f(double x, double y, double z) {
        double r511625 = y;
        double r511626 = x;
        double r511627 = z;
        double r511628 = r511626 - r511627;
        double r511629 = r511625 * r511628;
        return r511629;
}

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

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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 2020089 +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)))