Average Error: 13.2 → 0.0
Time: 15.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r411417 = x;
        double r411418 = y;
        double r411419 = r411417 * r411418;
        double r411420 = r411418 * r411418;
        double r411421 = r411419 - r411420;
        double r411422 = r411421 + r411420;
        double r411423 = z;
        double r411424 = r411418 * r411423;
        double r411425 = r411422 - r411424;
        return r411425;
}
↓
double f(double x, double y, double z) {
        double r411426 = x;
        double r411427 = z;
        double r411428 = r411426 - r411427;
        double r411429 = y;
        double r411430 = r411428 * r411429;
        return r411430;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(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)))