Average Error: 0.1 → 0.1
Time: 2.4s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
↓
\[1 - \left(x \cdot \left(x \cdot 0.12\right) + x \cdot 0.253\right) \]
(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))
↓
(FPCore (x) :precision binary64 (- 1.0 (+ (* x (* x 0.12)) (* x 0.253))))
double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
double code(double x) {
	return 1.0 - ((x * (x * 0.12)) + (x * 0.253));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - ((x * (x * 0.12d0)) + (x * 0.253d0))
end function

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
public static double code(double x) {
	return 1.0 - ((x * (x * 0.12)) + (x * 0.253));
}

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))
↓
def code(x):
	return 1.0 - ((x * (x * 0.12)) + (x * 0.253))

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end
↓
function code(x)
	return Float64(1.0 - Float64(Float64(x * Float64(x * 0.12)) + Float64(x * 0.253)))
end

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end
↓
function tmp = code(x)
	tmp = 1.0 - ((x * (x * 0.12)) + (x * 0.253));
end

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(1.0 - N[(N[(x * N[(x * 0.12), $MachinePrecision]), $MachinePrecision] + N[(x * 0.253), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(x \cdot \left(x \cdot 0.12\right) + x \cdot 0.253\right)

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, -0.12, -0.253\right), 1\right)} \]

  3. Taylor expanded in x around 0 0.2

    \[\leadsto \color{blue}{1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)} \]

  4. Applied add-sqr-sqrt_binary6432.3

    \[\leadsto 1 - \left(0.12 \cdot {\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}}^{2} + 0.253 \cdot x\right) \]

  5. Applied unpow-prod-down_binary6432.3

    \[\leadsto 1 - \left(0.12 \cdot \color{blue}{\left({\left(\sqrt{x}\right)}^{2} \cdot {\left(\sqrt{x}\right)}^{2}\right)} + 0.253 \cdot x\right) \]

  6. Applied add-sqr-sqrt_binary6432.3

    \[\leadsto 1 - \left(\color{blue}{\left(\sqrt{0.12} \cdot \sqrt{0.12}\right)} \cdot \left({\left(\sqrt{x}\right)}^{2} \cdot {\left(\sqrt{x}\right)}^{2}\right) + 0.253 \cdot x\right) \]

  7. Applied unswap-sqr_binary6432.3

    \[\leadsto 1 - \left(\color{blue}{\left(\sqrt{0.12} \cdot {\left(\sqrt{x}\right)}^{2}\right) \cdot \left(\sqrt{0.12} \cdot {\left(\sqrt{x}\right)}^{2}\right)} + 0.253 \cdot x\right) \]

  8. Simplified32.3

    \[\leadsto 1 - \left(\color{blue}{\left(x \cdot \sqrt{0.12}\right)} \cdot \left(\sqrt{0.12} \cdot {\left(\sqrt{x}\right)}^{2}\right) + 0.253 \cdot x\right) \]

  9. Simplified0.2

    \[\leadsto 1 - \left(\left(x \cdot \sqrt{0.12}\right) \cdot \color{blue}{\left(x \cdot \sqrt{0.12}\right)} + 0.253 \cdot x\right) \]

  10. Applied associate-*l*_binary640.1

    \[\leadsto 1 - \left(\color{blue}{x \cdot \left(\sqrt{0.12} \cdot \left(x \cdot \sqrt{0.12}\right)\right)} + 0.253 \cdot x\right) \]

  11. Simplified0.1

    \[\leadsto 1 - \left(x \cdot \color{blue}{\left(0.12 \cdot x\right)} + 0.253 \cdot x\right) \]

  12. Final simplification0.1

    \[\leadsto 1 - \left(x \cdot \left(x \cdot 0.12\right) + x \cdot 0.253\right) \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))