Rosa's Benchmark

Average Error: 0.2 → 0.2

Time: 3.4s

Precision: binary64

Math

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

↓

\[x \cdot \left(0.954929658551372 + -0.12900613773279798 \cdot {x}^{2}\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

↓

(FPCore (x)
 :precision binary64
 (* x (+ 0.954929658551372 (* -0.12900613773279798 (pow x 2.0)))))

C

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

↓

double code(double x) {
	return x * (0.954929658551372 + (-0.12900613773279798 * pow(x, 2.0)));
}

Fortran

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 = x * (0.954929658551372d0 + ((-0.12900613773279798d0) * (x ** 2.0d0)))
end function

Java

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

↓

public static double code(double x) {
	return x * (0.954929658551372 + (-0.12900613773279798 * Math.pow(x, 2.0)));
}

Python

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

↓

def code(x):
	return x * (0.954929658551372 + (-0.12900613773279798 * math.pow(x, 2.0)))

Julia

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

↓

function code(x)
	return Float64(x * Float64(0.954929658551372 + Float64(-0.12900613773279798 * (x ^ 2.0))))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = x * (0.954929658551372 + (-0.12900613773279798 * (x ^ 2.0)));
end

Wolfram

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

↓

code[x_] := N[(x * N[(0.954929658551372 + N[(-0.12900613773279798 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Taylor expanded in x around 0 0.2

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

3. Simplified 0.2

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

4. Taylor expanded in x around inf 0.2

   \[\leadsto x \cdot \color{blue}{\left(0.954929658551372 + -0.12900613773279798 \cdot {x}^{2}\right)} \]

5. Final simplification 0.2

   \[\leadsto x \cdot \left(0.954929658551372 + -0.12900613773279798 \cdot {x}^{2}\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))