Average Error: 0.1 → 0
Time: 1.2s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[\mathsf{fma}\left(1.5 \cdot 1, x, -y \cdot 0.5\right)\]
x + \frac{x - y}{2}
↓
\mathsf{fma}\left(1.5 \cdot 1, x, -y \cdot 0.5\right)
double code(double x, double y) {
	return ((double) (x + ((double) (((double) (x - y)) / 2.0))));
}
↓
double code(double x, double y) {
	return ((double) fma(((double) (1.5 * 1.0)), x, ((double) -(((double) (y * 0.5))))));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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. Using strategy rm

  4. Applied *-un-lft-identity0.1

    \[\leadsto 1.5 \cdot \color{blue}{\left(1 \cdot x\right)} - 0.5 \cdot y\]

  5. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(1.5 \cdot 1\right) \cdot x} - 0.5 \cdot y\]

  6. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.5 \cdot 1, x, -0.5 \cdot y\right)}\]

  7. Simplified0

    \[\leadsto \mathsf{fma}\left(1.5 \cdot 1, x, \color{blue}{-y \cdot 0.5}\right)\]

  8. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.5 \cdot 1, x, -y \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2020113 +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)))