Average Error: 12.6 → 0.0
Time: 2.0s
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 r733340 = x;
        double r733341 = y;
        double r733342 = r733340 * r733341;
        double r733343 = r733341 * r733341;
        double r733344 = r733342 - r733343;
        double r733345 = r733344 + r733343;
        double r733346 = z;
        double r733347 = r733341 * r733346;
        double r733348 = r733345 - r733347;
        return r733348;
}
↓
double f(double x, double y, double z) {
        double r733349 = y;
        double r733350 = x;
        double r733351 = z;
        double r733352 = r733350 - r733351;
        double r733353 = r733349 * r733352;
        return r733353;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original12.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.6

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

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt31.4

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

  5. Applied associate-*r*31.4

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

  7. Applied associate-*l*31.4

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(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)))