Average Error: 0.2 → 0.2
Time: 2.0s
Precision: binary64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
↓
\[0.954929658551372 \cdot x - x \cdot \left(x \cdot \left(x \cdot 0.12900613773279798\right)\right) \]
(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))
↓
(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* x (* x (* x 0.12900613773279798)))))
double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}
↓
double code(double x) {
	return (0.954929658551372 * x) - (x * (x * (x * 0.12900613773279798)));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.954929658551372d0 * x) - (0.12900613773279798d0 * ((x * x) * x))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.954929658551372d0 * x) - (x * (x * (x * 0.12900613773279798d0)))
end function

public static double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}
↓
public static double code(double x) {
	return (0.954929658551372 * x) - (x * (x * (x * 0.12900613773279798)));
}

def code(x):
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x))
↓
def code(x):
	return (0.954929658551372 * x) - (x * (x * (x * 0.12900613773279798)))

function code(x)
	return Float64(Float64(0.954929658551372 * x) - Float64(0.12900613773279798 * Float64(Float64(x * x) * x)))
end
↓
function code(x)
	return Float64(Float64(0.954929658551372 * x) - Float64(x * Float64(x * Float64(x * 0.12900613773279798))))
end

function tmp = code(x)
	tmp = (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
end
↓
function tmp = code(x)
	tmp = (0.954929658551372 * x) - (x * (x * (x * 0.12900613773279798)));
end

code[x_] := N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(x * N[(x * N[(x * 0.12900613773279798), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.954929658551372 \cdot x - x \cdot \left(x \cdot \left(x \cdot 0.12900613773279798\right)\right)

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right)} \]

  3. Taylor expanded in x around 0 0.2

    \[\leadsto \color{blue}{0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}} \]

  4. Applied cube-mult_binary640.2

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{\left(x \cdot \left(x \cdot x\right)\right)} \]

  5. Applied associate-*r*_binary640.2

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot x\right) \cdot \left(x \cdot x\right)} \]

  6. Applied associate-*r*_binary640.2

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(\left(0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x} \]

  7. Final simplification0.2

    \[\leadsto 0.954929658551372 \cdot x - x \cdot \left(x \cdot \left(x \cdot 0.12900613773279798\right)\right) \]

Reproduce

herbie shell --seed 2022129 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))