Average Error: 0.1 → 0.1
Time: 5.3s
Precision: binary64
\[x + \frac{x - y}{2}\]
↓
\[-0.5 \cdot y + 1.5 \cdot x\]
x + \frac{x - y}{2}
↓
-0.5 \cdot y + 1.5 \cdot x
(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))
↓
(FPCore (x y) :precision binary64 (+ (* -0.5 y) (* 1.5 x)))
double code(double x, double y) {
	return x + ((x - y) / 2.0);
}
↓
double code(double x, double y) {
	return (-0.5 * y) + (1.5 * x);
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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)))