Average Error: 17.7 → 0.0
Time: 1.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r589641 = x;
        double r589642 = y;
        double r589643 = r589641 * r589642;
        double r589644 = z;
        double r589645 = r589642 * r589644;
        double r589646 = r589643 - r589645;
        double r589647 = r589642 * r589642;
        double r589648 = r589646 - r589647;
        double r589649 = r589648 + r589647;
        return r589649;
}
↓
double f(double x, double y, double z) {
        double r589650 = y;
        double r589651 = x;
        double r589652 = z;
        double r589653 = r589651 - r589652;
        double r589654 = r589650 * r589653;
        return r589654;
}

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

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +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)))