Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[x - y \cdot z\]
↓
\[\left(x + y \cdot z\right) \cdot \frac{x - y \cdot z}{x + y \cdot z}\]
x - y \cdot z
↓
\left(x + y \cdot z\right) \cdot \frac{x - y \cdot z}{x + y \cdot z}
double f(double x, double y, double z) {
        double r1515828 = x;
        double r1515829 = y;
        double r1515830 = z;
        double r1515831 = r1515829 * r1515830;
        double r1515832 = r1515828 - r1515831;
        return r1515832;
}
↓
double f(double x, double y, double z) {
        double r1515833 = x;
        double r1515834 = y;
        double r1515835 = z;
        double r1515836 = r1515834 * r1515835;
        double r1515837 = r1515833 + r1515836;
        double r1515838 = r1515833 - r1515836;
        double r1515839 = r1515838 / r1515837;
        double r1515840 = r1515837 * r1515839;
        return r1515840;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}}\]

Derivation

  1. Initial program 0.0

    \[x - y \cdot z\]
  2. Using strategy rm

  3. Applied flip--28.8

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

  5. Applied *-un-lft-identity28.8

    \[\leadsto \frac{x \cdot x - \left(y \cdot z\right) \cdot \left(y \cdot z\right)}{\color{blue}{1 \cdot \left(x + y \cdot z\right)}}\]

  6. Applied difference-of-squares28.8

    \[\leadsto \frac{\color{blue}{\left(x + y \cdot z\right) \cdot \left(x - y \cdot z\right)}}{1 \cdot \left(x + y \cdot z\right)}\]

  7. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x + y \cdot z}{1} \cdot \frac{x - y \cdot z}{x + y \cdot z}}\]

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (+ x (* y z)) (/ (+ x (* y z)) (- x (* y z))))

  (- x (* y z)))