Average Error: 0.0 → 0.0
Time: 25.0s
Precision: binary64
Cost: 7488
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]
↓
\[x - \left(0.27061 \cdot x + 2.30753\right) \cdot \frac{1}{\mathsf{fma}\left(0.04481 \cdot x + 0.99229, x, 1\right)} \]
(FPCore (x)
 :precision binary64
 (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
↓
(FPCore (x)
 :precision binary64
 (-
  x
  (* (+ (* 0.27061 x) 2.30753) (/ 1.0 (fma (+ (* 0.04481 x) 0.99229) x 1.0)))))
double code(double x) {
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x)));
}
↓
double code(double x) {
	return x - (((0.27061 * x) + 2.30753) * (1.0 / fma(((0.04481 * x) + 0.99229), x, 1.0)));
}

function code(x)
	return Float64(x - Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(Float64(0.99229 + Float64(x * 0.04481)) * x))))
end
↓
function code(x)
	return Float64(x - Float64(Float64(Float64(0.27061 * x) + 2.30753) * Float64(1.0 / fma(Float64(Float64(0.04481 * x) + 0.99229), x, 1.0))))
end

code[x_] := N[(x - N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(x - N[(N[(N[(0.27061 * x), $MachinePrecision] + 2.30753), $MachinePrecision] * N[(1.0 / N[(N[(N[(0.04481 * x), $MachinePrecision] + 0.99229), $MachinePrecision] * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \left(0.27061 \cdot x + 2.30753\right) \cdot \frac{1}{\mathsf{fma}\left(0.04481 \cdot x + 0.99229, x, 1\right)}

Error

Derivation

  1. Initial program 0.0

    \[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]

  2. Applied egg-rr0.0

    \[\leadsto x - \color{blue}{\mathsf{fma}\left(0.27061, x, 2.30753\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(0.04481, x, 0.99229\right), x, 1\right)}} \]

  3. Applied egg-rr0.0

    \[\leadsto x - \mathsf{fma}\left(0.27061, x, 2.30753\right) \cdot \frac{1}{\mathsf{fma}\left(\color{blue}{0.04481 \cdot x + 0.99229}, x, 1\right)} \]

  4. Applied egg-rr0.0

    \[\leadsto x - \color{blue}{\left(0.27061 \cdot x + 2.30753\right)} \cdot \frac{1}{\mathsf{fma}\left(0.04481 \cdot x + 0.99229, x, 1\right)} \]

Alternatives

Alternative 1
Error0.0
Cost1088
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]
Alternative 2
Error0.9
Cost832
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + 0.99229 \cdot x} \]
Alternative 3
Error1.1
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;-2.30753\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 4
Error1.4
Cost192
\[x - 2.30753 \]
Alternative 5
Error32.3
Cost64
\[-2.30753 \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))