Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 8.6s

Alternatives: 5

Speedup: 1.2×

• 32.7% 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. associate-*r* N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \left(\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \left(\left(\left(x \cdot x\right) \cdot \frac{6450306886639899}{50000000000000000}\right) \cdot x\right)\right) \]

   3. associate-*l* N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \left(\left(x \cdot x\right) \cdot \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot x\right)}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \mathsf{*.f64}\left(\left(x \cdot x\right), \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot x\right)}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(\color{blue}{\frac{6450306886639899}{50000000000000000}} \cdot x\right)\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(x \cdot \color{blue}{\frac{6450306886639899}{50000000000000000}}\right)\right)\right) \]

   7. *-lowering-*.f64 99.8%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{238732414637843}{250000000000000}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{*.f64}\left(x, \color{blue}{\frac{6450306886639899}{50000000000000000}}\right)\right)\right) \]

4. Applied egg-rr 99.8%

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

Alternative 2: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.8)
   (* 0.954929658551372 x)
   (* x (* (* x x) -0.12900613773279798))))

C

double code(double x) {
	double tmp;
	if (x <= 2.8) {
		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 <= 2.8d0) 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 <= 2.8) {
		tmp = 0.954929658551372 * x;
	} else {
		tmp = x * ((x * x) * -0.12900613773279798);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.8:
		tmp = 0.954929658551372 * x
	else:
		tmp = x * ((x * x) * -0.12900613773279798)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.8)
		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 <= 2.8)
		tmp = 0.954929658551372 * x;
	else
		tmp = x * ((x * x) * -0.12900613773279798);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.8], 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 < 2.7999999999999998

   1. Initial program 99.8%

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

      1. associate-*r* N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

      2. distribute-rgt-out-- N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{238732414637843}{250000000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 72.9%

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

   if 2.7999999999999998 < x

   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. associate-*r* N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

      2. distribute-rgt-out-- N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot {x}^{2}\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

      3. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 99.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.8)
   (* 0.954929658551372 x)
   (* -0.12900613773279798 (* x (* x x)))))

C

double code(double x) {
	double tmp;
	if (x <= 2.8) {
		tmp = 0.954929658551372 * x;
	} else {
		tmp = -0.12900613773279798 * (x * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 2.8d0) then
        tmp = 0.954929658551372d0 * x
    else
        tmp = (-0.12900613773279798d0) * (x * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.8) {
		tmp = 0.954929658551372 * x;
	} else {
		tmp = -0.12900613773279798 * (x * (x * x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.8:
		tmp = 0.954929658551372 * x
	else:
		tmp = -0.12900613773279798 * (x * (x * x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.8)
		tmp = Float64(0.954929658551372 * x);
	else
		tmp = Float64(-0.12900613773279798 * Float64(x * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.8)
		tmp = 0.954929658551372 * x;
	else
		tmp = -0.12900613773279798 * (x * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.8], N[(0.954929658551372 * x), $MachinePrecision], N[(-0.12900613773279798 * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7999999999999998

   1. Initial program 99.8%

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

      1. associate-*r* N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

      2. distribute-rgt-out-- N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{238732414637843}{250000000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 72.9%

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

   if 2.7999999999999998 < x

   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. associate-*r* N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

      2. distribute-rgt-out-- N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{-6450306886639899}{50000000000000000} \cdot {x}^{3}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \color{blue}{\left({x}^{3}\right)}\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \left(x \cdot {x}^{\color{blue}{2}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

      6. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{-6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 99.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;0.954929658551372 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
5. 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. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

   2. distribute-rgt-out-- N/A

      \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

   6. *-lowering-*.f64 99.8%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

3. Simplified 99.8%

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

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: 49.8% 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. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{x} \]

   2. distribute-rgt-out-- N/A

      \[\leadsto x \cdot \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{238732414637843}{250000000000000} - \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

   6. *-lowering-*.f64 99.8%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{238732414637843}{250000000000000}, \mathsf{*.f64}\left(\frac{6450306886639899}{50000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

3. Simplified 99.8%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{238732414637843}{250000000000000}}\right) \]
6. Step-by-step derivation

7. Simplified 55.7%

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

8. Final simplification 55.7%

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

Reproduce

herbie shell --seed 2024192 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))