Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\left(1 \cdot y + x \cdot y\right) - x\]
\left(x + 1\right) \cdot y - x
↓
\left(1 \cdot y + x \cdot y\right) - x
double f(double x, double y) {
        double r265312 = x;
        double r265313 = 1.0;
        double r265314 = r265312 + r265313;
        double r265315 = y;
        double r265316 = r265314 * r265315;
        double r265317 = r265316 - r265312;
        return r265317;
}
↓
double f(double x, double y) {
        double r265318 = 1.0;
        double r265319 = y;
        double r265320 = r265318 * r265319;
        double r265321 = x;
        double r265322 = r265321 * r265319;
        double r265323 = r265320 + r265322;
        double r265324 = r265323 - r265321;
        return r265324;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied flip-+11.0

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

  4. Applied associate-*l/13.1

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

  5. Taylor expanded around inf 0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))