Average Error: 17.3 → 0.0
Time: 7.5s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r24347986 = x;
        double r24347987 = y;
        double r24347988 = r24347986 * r24347987;
        double r24347989 = z;
        double r24347990 = r24347987 * r24347989;
        double r24347991 = r24347988 - r24347990;
        double r24347992 = r24347987 * r24347987;
        double r24347993 = r24347991 - r24347992;
        double r24347994 = r24347993 + r24347992;
        return r24347994;
}
↓
double f(double x, double y, double z) {
        double r24347995 = x;
        double r24347996 = z;
        double r24347997 = r24347995 - r24347996;
        double r24347998 = y;
        double r24347999 = r24347997 * r24347998;
        return r24347999;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original17.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.3

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"

  :herbie-target
  (* (- x z) y)

  (+ (- (- (* x y) (* y z)) (* y y)) (* y y)))