Average Error: 0.1 → 0.1
Time: 5.5s
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 r797160 = x;
        double r797161 = y;
        double r797162 = r797160 - r797161;
        double r797163 = 2.0;
        double r797164 = r797162 / r797163;
        double r797165 = r797160 + r797164;
        return r797165;
}
↓
double f(double x, double y) {
        double r797166 = 1.5;
        double r797167 = x;
        double r797168 = r797166 * r797167;
        double r797169 = 0.5;
        double r797170 = y;
        double r797171 = r797169 * r797170;
        double r797172 = r797168 - r797171;
        return r797172;
}

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. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(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)))