Average Error: 12.7 → 0.0
Time: 5.3s
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 r454761 = x;
        double r454762 = y;
        double r454763 = r454761 * r454762;
        double r454764 = r454762 * r454762;
        double r454765 = r454763 - r454764;
        double r454766 = r454765 + r454764;
        double r454767 = z;
        double r454768 = r454762 * r454767;
        double r454769 = r454766 - r454768;
        return r454769;
}
↓
double f(double x, double y, double z) {
        double r454770 = y;
        double r454771 = x;
        double r454772 = z;
        double r454773 = r454771 - r454772;
        double r454774 = r454770 * r454773;
        return r454774;
}

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

Original12.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.7

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

  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 2019298 
(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)))