Average Error: 12.8 → 0.0
Time: 13.8s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r444227 = x;
        double r444228 = y;
        double r444229 = r444227 * r444228;
        double r444230 = r444228 * r444228;
        double r444231 = r444229 - r444230;
        double r444232 = r444231 + r444230;
        double r444233 = z;
        double r444234 = r444228 * r444233;
        double r444235 = r444232 - r444234;
        return r444235;
}
↓
double f(double x, double y, double z) {
        double r444236 = x;
        double r444237 = y;
        double r444238 = r444236 * r444237;
        double r444239 = z;
        double r444240 = -r444239;
        double r444241 = r444240 * r444237;
        double r444242 = r444238 + r444241;
        return r444242;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

Target

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))