Average Error: 13.2 → 0.0
Time: 1.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r504191 = x;
        double r504192 = y;
        double r504193 = r504191 * r504192;
        double r504194 = r504192 * r504192;
        double r504195 = r504193 - r504194;
        double r504196 = r504195 + r504194;
        double r504197 = z;
        double r504198 = r504192 * r504197;
        double r504199 = r504196 - r504198;
        return r504199;
}
↓
double f(double x, double y, double z) {
        double r504200 = y;
        double r504201 = x;
        double r504202 = r504200 * r504201;
        double r504203 = z;
        double r504204 = -r504203;
        double r504205 = r504200 * r504204;
        double r504206 = r504202 + r504205;
        return r504206;
}

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

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(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)))