Average Error: 17.2 → 0.0
Time: 18.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r564429 = x;
        double r564430 = y;
        double r564431 = r564429 * r564430;
        double r564432 = z;
        double r564433 = r564430 * r564432;
        double r564434 = r564431 - r564433;
        double r564435 = r564430 * r564430;
        double r564436 = r564434 - r564435;
        double r564437 = r564436 + r564435;
        return r564437;
}
↓
double f(double x, double y, double z) {
        double r564438 = x;
        double r564439 = y;
        double r564440 = r564438 * r564439;
        double r564441 = z;
        double r564442 = -r564441;
        double r564443 = r564442 * r564439;
        double r564444 = r564440 + r564443;
        return r564444;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. 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 2020047 
(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)))