Average Error: 0.0 → 0.0
Time: 7.5s
Precision: binary64
Cost: 7488
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
↓
\[\frac{2.30753 + x \cdot 0.27061}{1 + \mathsf{fma}\left(x \cdot 0.04481, x, x \cdot 0.99229\right)} - x \]
(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
↓
(FPCore (x)
 :precision binary64
 (-
  (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (fma (* x 0.04481) x (* x 0.99229))))
  x))
double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}
↓
double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + fma((x * 0.04481), x, (x * 0.99229)))) - x;
}

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

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost7360
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \mathsf{fma}\left(x, 0.04481, 0.99229\right)} - x \]
Alternative 2
Error0.0
Cost1088
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x \]
Alternative 3
Error0.7
Cost576
\[\frac{1}{0.4333638132548656 + x \cdot 0.37920088514346545} - x \]
Alternative 4
Error1.1
Cost392
\[\begin{array}{l} \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;2.30753\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
Alternative 5
Error1.5
Cost192
\[2.30753 - x \]
Alternative 6
Error31.5
Cost64
\[2.30753 \]

Error

Reproduce

herbie shell --seed 2022330 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))