Average Error: 17.7 → 0.0
Time: 1.3s
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 r747870 = x;
        double r747871 = y;
        double r747872 = r747870 * r747871;
        double r747873 = z;
        double r747874 = r747871 * r747873;
        double r747875 = r747872 - r747874;
        double r747876 = r747871 * r747871;
        double r747877 = r747875 - r747876;
        double r747878 = r747877 + r747876;
        return r747878;
}
↓
double f(double x, double y, double z) {
        double r747879 = y;
        double r747880 = x;
        double r747881 = z;
        double r747882 = r747880 - r747881;
        double r747883 = r747879 * r747882;
        return r747883;
}

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 2019353 
(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)))