Average Error: 17.5 → 0.0
Time: 14.2s
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 r612661 = x;
        double r612662 = y;
        double r612663 = r612661 * r612662;
        double r612664 = z;
        double r612665 = r612662 * r612664;
        double r612666 = r612663 - r612665;
        double r612667 = r612662 * r612662;
        double r612668 = r612666 - r612667;
        double r612669 = r612668 + r612667;
        return r612669;
}
↓
double f(double x, double y, double z) {
        double r612670 = x;
        double r612671 = y;
        double r612672 = r612670 * r612671;
        double r612673 = z;
        double r612674 = -r612673;
        double r612675 = r612674 * r612671;
        double r612676 = r612672 + r612675;
        return r612676;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020042 +o rules:numerics
(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)))