Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 99.8% → 99.8%

Time: 9.2s

Alternatives: 9

Speedup: 1.4×

• 23.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(3 - x \cdot 12\right) - -9 \cdot \left(x \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (- 3.0 (* x 12.0)) (* -9.0 (* x x))))

C

double code(double x) {
	return (3.0 - (x * 12.0)) - (-9.0 * (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (3.0d0 - (x * 12.0d0)) - ((-9.0d0) * (x * x))
end function

Java

public static double code(double x) {
	return (3.0 - (x * 12.0)) - (-9.0 * (x * x));
}

Python

def code(x):
	return (3.0 - (x * 12.0)) - (-9.0 * (x * x))

Julia

function code(x)
	return Float64(Float64(3.0 - Float64(x * 12.0)) - Float64(-9.0 * Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = (3.0 - (x * 12.0)) - (-9.0 * (x * x));
end

Wolfram

code[x_] := N[(N[(3.0 - N[(x * 12.0), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;\left(\frac{x}{0.1111111111111111} + -12\right) \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 - x \cdot 12\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.58)
   (* (+ (/ x 0.1111111111111111) -12.0) x)
   (if (<= x 1.0) (- 3.0 (* x 12.0)) (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = ((x / 0.1111111111111111) + -12.0) * x;
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.58d0)) then
        tmp = ((x / 0.1111111111111111d0) + (-12.0d0)) * x
    else if (x <= 1.0d0) then
        tmp = 3.0d0 - (x * 12.0d0)
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = ((x / 0.1111111111111111) + -12.0) * x;
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.58:
		tmp = ((x / 0.1111111111111111) + -12.0) * x
	elif x <= 1.0:
		tmp = 3.0 - (x * 12.0)
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = Float64(Float64(Float64(x / 0.1111111111111111) + -12.0) * x);
	elseif (x <= 1.0)
		tmp = Float64(3.0 - Float64(x * 12.0));
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.58)
		tmp = ((x / 0.1111111111111111) + -12.0) * x;
	elseif (x <= 1.0)
		tmp = 3.0 - (x * 12.0);
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.58], N[(N[(N[(x / 0.1111111111111111), $MachinePrecision] + -12.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.0], N[(3.0 - N[(x * 12.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.57999999999999996

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -0.57999999999999996 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;x \cdot \left(-12 - x \cdot -9\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 - x \cdot 12\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.58)
   (* x (- -12.0 (* x -9.0)))
   (if (<= x 1.0) (- 3.0 (* x 12.0)) (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = x * (-12.0 - (x * -9.0));
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.58d0)) then
        tmp = x * ((-12.0d0) - (x * (-9.0d0)))
    else if (x <= 1.0d0) then
        tmp = 3.0d0 - (x * 12.0d0)
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = x * (-12.0 - (x * -9.0));
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.58:
		tmp = x * (-12.0 - (x * -9.0))
	elif x <= 1.0:
		tmp = 3.0 - (x * 12.0)
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = Float64(x * Float64(-12.0 - Float64(x * -9.0)));
	elseif (x <= 1.0)
		tmp = Float64(3.0 - Float64(x * 12.0));
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.58)
		tmp = x * (-12.0 - (x * -9.0));
	elseif (x <= 1.0)
		tmp = 3.0 - (x * 12.0);
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.58], N[(x * N[(-12.0 - N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(3.0 - N[(x * 12.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.57999999999999996

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.57999999999999996 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;\left(x \cdot x\right) \cdot 9\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 - x \cdot 12\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.55)
   (* (* x x) 9.0)
   (if (<= x 1.0) (- 3.0 (* x 12.0)) (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = (x * x) * 9.0;
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.55d0)) then
        tmp = (x * x) * 9.0d0
    else if (x <= 1.0d0) then
        tmp = 3.0d0 - (x * 12.0d0)
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = (x * x) * 9.0;
	} else if (x <= 1.0) {
		tmp = 3.0 - (x * 12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.55:
		tmp = (x * x) * 9.0
	elif x <= 1.0:
		tmp = 3.0 - (x * 12.0)
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.55)
		tmp = Float64(Float64(x * x) * 9.0);
	elseif (x <= 1.0)
		tmp = Float64(3.0 - Float64(x * 12.0));
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.55)
		tmp = (x * x) * 9.0;
	elseif (x <= 1.0)
		tmp = 3.0 - (x * 12.0);
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.55], N[(N[(x * x), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[x, 1.0], N[(3.0 - N[(x * 12.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000004

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.55000000000000004 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;\left(x \cdot x\right) \cdot 9\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.58) (* (* x x) 9.0) (if (<= x 1.7) 3.0 (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = (x * x) * 9.0;
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.58d0)) then
        tmp = (x * x) * 9.0d0
    else if (x <= 1.7d0) then
        tmp = 3.0d0
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = (x * x) * 9.0;
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.58:
		tmp = (x * x) * 9.0
	elif x <= 1.7:
		tmp = 3.0
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = Float64(Float64(x * x) * 9.0);
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.58)
		tmp = (x * x) * 9.0;
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.58], N[(N[(x * x), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[x, 1.7], 3.0, N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.57999999999999996

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -0.57999999999999996 < x < 1.69999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.69999999999999996 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (* x 9.0)))) (if (<= x -0.58) t_0 (if (<= x 1.7) 3.0 t_0))))

C

double code(double x) {
	double t_0 = x * (x * 9.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x * 9.0d0)
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 1.7d0) then
        tmp = 3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * (x * 9.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * (x * 9.0)
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 1.7:
		tmp = 3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(x * 9.0))
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * (x * 9.0);
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 1.7], 3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 1.69999999999999996 < x

   1. Initial program 99.7%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.57999999999999996 < x < 1.69999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 3 - x \cdot \left(12 + x \cdot -9\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 3.0 (* x (+ 12.0 (* x -9.0)))))

C

double code(double x) {
	return 3.0 - (x * (12.0 + (x * -9.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 - (x * (12.0d0 + (x * (-9.0d0))))
end function

Java

public static double code(double x) {
	return 3.0 - (x * (12.0 + (x * -9.0)));
}

Python

def code(x):
	return 3.0 - (x * (12.0 + (x * -9.0)))

Julia

function code(x)
	return Float64(3.0 - Float64(x * Float64(12.0 + Float64(x * -9.0))))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 - (x * (12.0 + (x * -9.0)));
end

Wolfram

code[x_] := N[(3.0 - N[(x * N[(12.0 + N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 8: 97.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ 3 - -9 \cdot \left(x \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 3.0 (* -9.0 (* x x))))

C

double code(double x) {
	return 3.0 - (-9.0 * (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 - ((-9.0d0) * (x * x))
end function

Java

public static double code(double x) {
	return 3.0 - (-9.0 * (x * x));
}

Python

def code(x):
	return 3.0 - (-9.0 * (x * x))

Julia

function code(x)
	return Float64(3.0 - Float64(-9.0 * Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 - (-9.0 * (x * x));
end

Wolfram

code[x_] := N[(3.0 - N[(-9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in x around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]
10. Add Preprocessing

Alternative 9: 51.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 3.0)

C

double code(double x) {
	return 3.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0
end function

Java

public static double code(double x) {
	return 3.0;
}

Python

def code(x):
	return 3.0

Julia

function code(x)
	return 3.0
end

MATLAB

function tmp = code(x)
	tmp = 3.0;
end

Wolfram

code[x_] := 3.0

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x))))

C

double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (((9.0d0 * x) * x) - (12.0d0 * x))
end function

Java

public static double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Python

def code(x):
	return 3.0 + (((9.0 * x) * x) - (12.0 * x))

Julia

function code(x)
	return Float64(3.0 + Float64(Float64(Float64(9.0 * x) * x) - Float64(12.0 * x)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + (((9.0 * x) * x) - (12.0 * x));
end

Wolfram

code[x_] := N[(3.0 + N[(N[(N[(9.0 * x), $MachinePrecision] * x), $MachinePrecision] - N[(12.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024110 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))