Average Error: 0.1 → 0
Time: 8.1s
Precision: binary64
Cost: 6720
\[x + \frac{x - y}{2} \]
↓
\[\mathsf{fma}\left(x, 1.5, -0.5 \cdot y\right) \]
(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))
↓
(FPCore (x y) :precision binary64 (fma x 1.5 (* -0.5 y)))
double code(double x, double y) {
	return x + ((x - y) / 2.0);
}
↓
double code(double x, double y) {
	return fma(x, 1.5, (-0.5 * y));
}

function code(x, y)
	return Float64(x + Float64(Float64(x - y) / 2.0))
end
↓
function code(x, y)
	return fma(x, 1.5, Float64(-0.5 * y))
end

code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * 1.5 + N[(-0.5 * y), $MachinePrecision]), $MachinePrecision]

x + \frac{x - y}{2}
↓
\mathsf{fma}\left(x, 1.5, -0.5 \cdot y\right)

Error

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 in x around 0 0.1

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

  3. Applied egg-rr0

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

Alternatives

Alternative 1
Error15.3
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{elif}\;x \leq 2200000:\\ \;\;\;\;-0.5 \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
Alternative 2
Error16.9
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
Alternative 3
Error0.1
Cost448
\[x + \frac{x - y}{2} \]
Alternative 4
Error31.8
Cost192
\[x \cdot 1.5 \]

Error

Reproduce

herbie shell --seed 2023010 
(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)))