Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[x \cdot y + 1 \cdot \left(x \cdot z - z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
x \cdot y + 1 \cdot \left(x \cdot z - z\right)
double f(double x, double y, double z) {
        double r144456 = x;
        double r144457 = y;
        double r144458 = r144456 * r144457;
        double r144459 = 1.0;
        double r144460 = r144456 - r144459;
        double r144461 = z;
        double r144462 = r144460 * r144461;
        double r144463 = r144458 + r144462;
        return r144463;
}
↓
double f(double x, double y, double z) {
        double r144464 = x;
        double r144465 = y;
        double r144466 = r144464 * r144465;
        double r144467 = 1.0;
        double r144468 = z;
        double r144469 = r144464 * r144468;
        double r144470 = r144469 - r144468;
        double r144471 = r144467 * r144470;
        double r144472 = r144466 + r144471;
        return r144472;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1\right) \cdot z\]
  2. Using strategy rm

  3. Applied flip3--12.0

    \[\leadsto x \cdot y + \color{blue}{\frac{{x}^{3} - {1}^{3}}{x \cdot x + \left(1 \cdot 1 + x \cdot 1\right)}} \cdot z\]

  4. Applied associate-*l/14.1

    \[\leadsto x \cdot y + \color{blue}{\frac{\left({x}^{3} - {1}^{3}\right) \cdot z}{x \cdot x + \left(1 \cdot 1 + x \cdot 1\right)}}\]

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto x \cdot y + 1 \cdot \left(x \cdot z - z\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))