Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 4.6s

Alternatives: 4

Speedup: 1.0×

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left({x}^{3}, -0.12900613773279798, x \cdot 0.954929658551372\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma (pow x 3.0) -0.12900613773279798 (* x 0.954929658551372)))

C

double code(double x) {
	return fma(pow(x, 3.0), -0.12900613773279798, (x * 0.954929658551372));
}

Julia

function code(x)
	return fma((x ^ 3.0), -0.12900613773279798, Float64(x * 0.954929658551372))
end

Wolfram

code[x_] := N[(N[Power[x, 3.0], $MachinePrecision] * -0.12900613773279798 + N[(x * 0.954929658551372), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. sub-neg 99.7%

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

   2. +-commutative 99.7%

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

   3. *-commutative 99.7%

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

   4. distribute-rgt-neg-in 99.7%

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

   5. fma-def 99.7%

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

   6. unpow3 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{3}}, -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left({x}^{3}, \color{blue}{-0.12900613773279798}, 0.954929658551372 \cdot x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{3}, -0.12900613773279798, 0.954929658551372 \cdot x\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left({x}^{3}, -0.12900613773279798, x \cdot 0.954929658551372\right) \]

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.954929658551372 - {x}^{3} \cdot 0.12900613773279798 \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (* x 0.954929658551372) (* (pow x 3.0) 0.12900613773279798)))

C

double code(double x) {
	return (x * 0.954929658551372) - (pow(x, 3.0) * 0.12900613773279798);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 0.954929658551372d0) - ((x ** 3.0d0) * 0.12900613773279798d0)
end function

Java

public static double code(double x) {
	return (x * 0.954929658551372) - (Math.pow(x, 3.0) * 0.12900613773279798);
}

Python

def code(x):
	return (x * 0.954929658551372) - (math.pow(x, 3.0) * 0.12900613773279798)

Julia

function code(x)
	return Float64(Float64(x * 0.954929658551372) - Float64((x ^ 3.0) * 0.12900613773279798))
end

MATLAB

function tmp = code(x)
	tmp = (x * 0.954929658551372) - ((x ^ 3.0) * 0.12900613773279798);
end

Wolfram

code[x_] := N[(N[(x * 0.954929658551372), $MachinePrecision] - N[(N[Power[x, 3.0], $MachinePrecision] * 0.12900613773279798), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

2. Taylor expanded in x around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

2. Final simplification 99.7%

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

Alternative 4: 49.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.954929658551372 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return x * 0.954929658551372

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. sub-neg 99.7%

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

   2. +-commutative 99.7%

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

   3. *-commutative 99.7%

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

   4. distribute-rgt-neg-in 99.7%

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

   5. fma-def 99.7%

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

   6. unpow3 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{3}}, -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left({x}^{3}, \color{blue}{-0.12900613773279798}, 0.954929658551372 \cdot x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{3}, -0.12900613773279798, 0.954929658551372 \cdot x\right)} \]

4. Taylor expanded in x around 0 55.6%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 55.6%

      \[\leadsto \color{blue}{x \cdot 0.954929658551372} \]

6. Simplified 55.6%

   \[\leadsto \color{blue}{x \cdot 0.954929658551372} \]

7. Final simplification 55.6%

   \[\leadsto x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023309 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))