Average Error: 13.2 → 0.0
Time: 11.3s
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 r286003 = x;
        double r286004 = y;
        double r286005 = r286003 * r286004;
        double r286006 = r286004 * r286004;
        double r286007 = r286005 - r286006;
        double r286008 = r286007 + r286006;
        double r286009 = z;
        double r286010 = r286004 * r286009;
        double r286011 = r286008 - r286010;
        return r286011;
}
↓
double f(double x, double y, double z) {
        double r286012 = y;
        double r286013 = x;
        double r286014 = z;
        double r286015 = r286013 - r286014;
        double r286016 = r286012 * r286015;
        return r286016;
}

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 2020043 +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)))