Average Error: 0.0 → 0.0
Time: 8.4s
Precision: binary64
Cost: 7488
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]
↓
\[x + \frac{-1}{\mathsf{fma}\left(x, x \cdot 0.04481 + 0.99229, 1\right)} \cdot \left(2.30753 - x \cdot -0.27061\right) \]
(FPCore (x)
 :precision binary64
 (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
↓
(FPCore (x)
 :precision binary64
 (+
  x
  (*
   (/ -1.0 (fma x (+ (* x 0.04481) 0.99229) 1.0))
   (- 2.30753 (* x -0.27061)))))
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 + ((-1.0 / fma(x, ((x * 0.04481) + 0.99229), 1.0)) * (2.30753 - (x * -0.27061)));
}

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(-1.0 / fma(x, Float64(Float64(x * 0.04481) + 0.99229), 1.0)) * Float64(2.30753 - Float64(x * -0.27061))))
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[(-1.0 / N[(x * N[(N[(x * 0.04481), $MachinePrecision] + 0.99229), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(2.30753 - N[(x * -0.27061), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

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

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost1088
\[x - \frac{2.30753 - x \cdot -0.27061}{1 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \]
Alternative 2
Error0.6
Cost576
\[x + \frac{1}{x \cdot -0.37920088514346545 + -0.4333638132548656} \]
Alternative 3
Error1.0
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -3.6:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;-2.30753\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 4
Error1.3
Cost192
\[x + -2.30753 \]
Alternative 5
Error31.9
Cost64
\[-2.30753 \]

Error

Reproduce

herbie shell --seed 2023016 
(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)))))