Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\frac{x - y}{2 - \left(x + y\right)} \]
↓
\[\begin{array}{l} t_0 := \left(2 - x\right) - y\\ \mathsf{fma}\left(1, \frac{x}{t_0}, \frac{-y}{t_0}\right) \end{array} \]
(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (- 2.0 x) y))) (fma 1.0 (/ x t_0) (/ (- y) t_0))))
double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}
↓
double code(double x, double y) {
	double t_0 = (2.0 - x) - y;
	return fma(1.0, (x / t_0), (-y / t_0));
}

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end
↓
function code(x, y)
	t_0 = Float64(Float64(2.0 - x) - y)
	return fma(1.0, Float64(x / t_0), Float64(Float64(-y) / t_0))
end

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := Block[{t$95$0 = N[(N[(2.0 - x), $MachinePrecision] - y), $MachinePrecision]}, N[(1.0 * N[(x / t$95$0), $MachinePrecision] + N[((-y) / t$95$0), $MachinePrecision]), $MachinePrecision]]

\frac{x - y}{2 - \left(x + y\right)}
↓
\begin{array}{l}
t_0 := \left(2 - x\right) - y\\
\mathsf{fma}\left(1, \frac{x}{t_0}, \frac{-y}{t_0}\right)
\end{array}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)} \]

  2. Applied egg-rr0.8

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1, \frac{x}{\left(2 - x\right) - y}, -\frac{y}{\left(2 - x\right) - y}\right)} \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1, \frac{x}{\left(2 - x\right) - y}, \frac{-y}{\left(2 - x\right) - y}\right) \]

Reproduce

herbie shell --seed 2022160 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))