Average Error: 17.5 → 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 r502046 = x;
        double r502047 = y;
        double r502048 = r502046 * r502047;
        double r502049 = z;
        double r502050 = r502047 * r502049;
        double r502051 = r502048 - r502050;
        double r502052 = r502047 * r502047;
        double r502053 = r502051 - r502052;
        double r502054 = r502053 + r502052;
        return r502054;
}
↓
double f(double x, double y, double z) {
        double r502055 = y;
        double r502056 = x;
        double r502057 = z;
        double r502058 = r502056 - r502057;
        double r502059 = r502055 * r502058;
        return r502059;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020027 +o rules:numerics
(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)))