Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 10.6s

Alternatives: 5

Speedup: 1.2×

• 34.8% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. associate-*l* 99.9%

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

4. Applied egg-rr 99.9%

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

Alternative 2: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.7)
   (* 0.954929658551372 x)
   (* x (* (* x x) -0.12900613773279798))))

C

double code(double x) {
	double tmp;
	if (x <= 2.7) {
		tmp = 0.954929658551372 * x;
	} else {
		tmp = x * ((x * x) * -0.12900613773279798);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 2.7d0) then
        tmp = 0.954929658551372d0 * x
    else
        tmp = x * ((x * x) * (-0.12900613773279798d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.7) {
		tmp = 0.954929658551372 * x;
	} else {
		tmp = x * ((x * x) * -0.12900613773279798);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.7:
		tmp = 0.954929658551372 * x
	else:
		tmp = x * ((x * x) * -0.12900613773279798)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.7)
		tmp = Float64(0.954929658551372 * x);
	else
		tmp = Float64(x * Float64(Float64(x * x) * -0.12900613773279798));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.7)
		tmp = 0.954929658551372 * x;
	else
		tmp = x * ((x * x) * -0.12900613773279798);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.7], N[(0.954929658551372 * x), $MachinePrecision], N[(x * N[(N[(x * x), $MachinePrecision] * -0.12900613773279798), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7000000000000002

   1. Initial program 99.9%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   if 2.7000000000000002 < x

   1. Initial program 99.8%

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

      1. associate-*r* 99.8%

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

      2. distribute-rgt-out-- 99.8%

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

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 98.5%

      \[\leadsto x \cdot \color{blue}{\left(-0.12900613773279798 \cdot {x}^{2}\right)} \]
   8. Step-by-step derivation

      1. unpow2 98.5%

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

   9. Simplified 98.5%

      \[\leadsto x \cdot \color{blue}{\left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.7:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right) \]
4. Add Preprocessing

Alternative 4: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*r* 99.8%

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

   2. distribute-rgt-out-- 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

   \[\leadsto x \cdot \left(0.954929658551372 - \left(x \cdot x\right) \cdot 0.12900613773279798\right) \]
6. Add Preprocessing

Alternative 5: 48.2% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return 0.954929658551372 * x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 52.0%

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

   1. *-commutative 52.0%

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

5. Simplified 52.0%

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

6. Final simplification 52.0%

   \[\leadsto 0.954929658551372 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024097 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))