Average Error: 12.9 → 0.0
Time: 1.3s
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 r754195 = x;
        double r754196 = y;
        double r754197 = r754195 * r754196;
        double r754198 = r754196 * r754196;
        double r754199 = r754197 - r754198;
        double r754200 = r754199 + r754198;
        double r754201 = z;
        double r754202 = r754196 * r754201;
        double r754203 = r754200 - r754202;
        return r754203;
}
↓
double f(double x, double y, double z) {
        double r754204 = y;
        double r754205 = x;
        double r754206 = z;
        double r754207 = r754205 - r754206;
        double r754208 = r754204 * r754207;
        return r754208;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  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 2019353 
(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)))