Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[1.5 \cdot x - 0.5 \cdot y\]
x + \frac{x - y}{2}
↓
1.5 \cdot x - 0.5 \cdot y
double f(double x, double y) {
        double r431707 = x;
        double r431708 = y;
        double r431709 = r431707 - r431708;
        double r431710 = 2.0;
        double r431711 = r431709 / r431710;
        double r431712 = r431707 + r431711;
        return r431712;
}
↓
double f(double x, double y) {
        double r431713 = 1.5;
        double r431714 = x;
        double r431715 = r431713 * r431714;
        double r431716 = 0.5;
        double r431717 = y;
        double r431718 = r431716 * r431717;
        double r431719 = r431715 - r431718;
        return r431719;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt32.2

    \[\leadsto \color{blue}{\sqrt{x + \frac{x - y}{2}} \cdot \sqrt{x + \frac{x - y}{2}}}\]
  4. Using strategy rm

  5. Applied pow1/232.2

    \[\leadsto \color{blue}{{\left(x + \frac{x - y}{2}\right)}^{\frac{1}{2}}} \cdot \sqrt{x + \frac{x - y}{2}}\]

  6. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{1.5 \cdot x - 0.5 \cdot y}\]

  7. Final simplification0.1

    \[\leadsto 1.5 \cdot x - 0.5 \cdot y\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2)))