Average Error: 0.1 → 0.1
Time: 2.0s
Precision: binary64
\[x + \frac{x - y}{2}\]
↓
\[x \cdot 1.5 - y \cdot 0.5\]
x + \frac{x - y}{2}
↓
x \cdot 1.5 - y \cdot 0.5
(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))
↓
(FPCore (x y) :precision binary64 (- (* x 1.5) (* y 0.5)))
double code(double x, double y) {
	return x + ((x - y) / 2.0);
}
↓
double code(double x, double y) {
	return (x * 1.5) - (y * 0.5);
}

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. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020224 
(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) 2.0)))