Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 7.0s

Alternatives: 9

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 1 - \mathsf{fma}\left(x \cdot 0.12, x, x \cdot 0.253\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (fma (* x 0.12) x (* x 0.253))))

C

double code(double x) {
	return 1.0 - fma((x * 0.12), x, (x * 0.253));
}

Julia

function code(x)
	return Float64(1.0 - fma(Float64(x * 0.12), x, Float64(x * 0.253)))
end

Wolfram

code[x_] := N[(1.0 - N[(N[(x * 0.12), $MachinePrecision] * x + N[(x * 0.253), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto 1 - x \cdot \color{blue}{\left(x \cdot 0.12 + 0.253\right)} \]

   2. distribute-rgt-in 99.9%

      \[\leadsto 1 - \color{blue}{\left(\left(x \cdot 0.12\right) \cdot x + 0.253 \cdot x\right)} \]

   3. fma-define 99.9%

      \[\leadsto 1 - \color{blue}{\mathsf{fma}\left(x \cdot 0.12, x, 0.253 \cdot x\right)} \]

   4. *-commutative 99.9%

      \[\leadsto 1 - \mathsf{fma}\left(x \cdot 0.12, x, \color{blue}{x \cdot 0.253}\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto 1 - \color{blue}{\mathsf{fma}\left(x \cdot 0.12, x, x \cdot 0.253\right)} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12 - 0.253\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1 - x \cdot 0.253\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-0.12 - \frac{0.253}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -4.0)
   (* x (- (* x -0.12) 0.253))
   (if (<= x 2.0) (- 1.0 (* x 0.253)) (* (* x x) (- -0.12 (/ 0.253 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * ((x * -0.12) - 0.253);
	} else if (x <= 2.0) {
		tmp = 1.0 - (x * 0.253);
	} else {
		tmp = (x * x) * (-0.12 - (0.253 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-4.0d0)) then
        tmp = x * ((x * (-0.12d0)) - 0.253d0)
    else if (x <= 2.0d0) then
        tmp = 1.0d0 - (x * 0.253d0)
    else
        tmp = (x * x) * ((-0.12d0) - (0.253d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * ((x * -0.12) - 0.253);
	} else if (x <= 2.0) {
		tmp = 1.0 - (x * 0.253);
	} else {
		tmp = (x * x) * (-0.12 - (0.253 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -4.0:
		tmp = x * ((x * -0.12) - 0.253)
	elif x <= 2.0:
		tmp = 1.0 - (x * 0.253)
	else:
		tmp = (x * x) * (-0.12 - (0.253 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -4.0)
		tmp = Float64(x * Float64(Float64(x * -0.12) - 0.253));
	elseif (x <= 2.0)
		tmp = Float64(1.0 - Float64(x * 0.253));
	else
		tmp = Float64(Float64(x * x) * Float64(-0.12 - Float64(0.253 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -4.0)
		tmp = x * ((x * -0.12) - 0.253);
	elseif (x <= 2.0)
		tmp = 1.0 - (x * 0.253);
	else
		tmp = (x * x) * (-0.12 - (0.253 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -4.0], N[(x * N[(N[(x * -0.12), $MachinePrecision] - 0.253), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(1.0 - N[(x * 0.253), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(-0.12 - N[(0.253 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.0%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.0%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.0%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.0%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 97.1%

      \[\leadsto \color{blue}{x \cdot \left(-0.12 \cdot x - 0.253\right)} \]

   if -4 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.9%

      \[\leadsto 1 - \color{blue}{0.253 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   5. Simplified 99.9%

      \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   if 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 98.3%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 98.3%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 98.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]

   7. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]
   8. Step-by-step derivation

      1. div-inv 98.3%

         \[\leadsto \left(x \cdot x\right) \cdot \left(-0.12 + \left(-\color{blue}{0.253 \cdot \frac{1}{x}}\right)\right) \]

      2. unsub-neg 98.3%

         \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{\left(-0.12 - 0.253 \cdot \frac{1}{x}\right)} \]

      3. div-inv 98.3%

         \[\leadsto \left(x \cdot x\right) \cdot \left(-0.12 - \color{blue}{\frac{0.253}{x}}\right) \]

   9. Applied egg-rr 98.3%

      \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{\left(-0.12 - \frac{0.253}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12 - 0.253\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1 - x \cdot 0.253\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-0.12 - \frac{0.253}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(x \cdot -0.12 - 0.253\right)\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot 0.253\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -4.0) (not (<= x 2.0)))
   (* x (- (* x -0.12) 0.253))
   (- 1.0 (* x 0.253))))

C

double code(double x) {
	double tmp;
	if ((x <= -4.0) || !(x <= 2.0)) {
		tmp = x * ((x * -0.12) - 0.253);
	} else {
		tmp = 1.0 - (x * 0.253);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-4.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * ((x * (-0.12d0)) - 0.253d0)
    else
        tmp = 1.0d0 - (x * 0.253d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -4.0) || !(x <= 2.0)) {
		tmp = x * ((x * -0.12) - 0.253);
	} else {
		tmp = 1.0 - (x * 0.253);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -4.0) or not (x <= 2.0):
		tmp = x * ((x * -0.12) - 0.253)
	else:
		tmp = 1.0 - (x * 0.253)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -4.0) || !(x <= 2.0))
		tmp = Float64(x * Float64(Float64(x * -0.12) - 0.253));
	else
		tmp = Float64(1.0 - Float64(x * 0.253));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -4.0) || ~((x <= 2.0)))
		tmp = x * ((x * -0.12) - 0.253);
	else
		tmp = 1.0 - (x * 0.253);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -4.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * N[(N[(x * -0.12), $MachinePrecision] - 0.253), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x * 0.253), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4 or 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.6%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.6%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.6%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.6%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.6%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.6%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.6%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.6%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 97.7%

      \[\leadsto \color{blue}{x \cdot \left(-0.12 \cdot x - 0.253\right)} \]

   if -4 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.9%

      \[\leadsto 1 - \color{blue}{0.253 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   5. Simplified 99.9%

      \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(x \cdot -0.12 - 0.253\right)\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot 0.253\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -4.0) (not (<= x 2.0))) (* x (* x -0.12)) 1.0))

C

double code(double x) {
	double tmp;
	if ((x <= -4.0) || !(x <= 2.0)) {
		tmp = x * (x * -0.12);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-4.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * (x * (-0.12d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -4.0) || !(x <= 2.0)) {
		tmp = x * (x * -0.12);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -4.0) or not (x <= 2.0):
		tmp = x * (x * -0.12)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -4.0) || !(x <= 2.0))
		tmp = Float64(x * Float64(x * -0.12));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -4.0) || ~((x <= 2.0)))
		tmp = x * (x * -0.12);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -4.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * N[(x * -0.12), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4 or 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.6%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.6%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.6%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.6%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.6%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.6%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.6%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.6%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 97.7%

      \[\leadsto \color{blue}{x \cdot \left(-0.12 \cdot x - 0.253\right)} \]

   7. Taylor expanded in x around inf 96.4%

      \[\leadsto x \cdot \color{blue}{\left(-0.12 \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 96.4%

         \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   9. Simplified 96.4%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   if -4 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1 - x \cdot 0.253\\ \mathbf{else}:\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -4.0)
   (* x (* x -0.12))
   (if (<= x 2.0) (- 1.0 (* x 0.253)) (* -0.12 (* x x)))))

C

double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * (x * -0.12);
	} else if (x <= 2.0) {
		tmp = 1.0 - (x * 0.253);
	} else {
		tmp = -0.12 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-4.0d0)) then
        tmp = x * (x * (-0.12d0))
    else if (x <= 2.0d0) then
        tmp = 1.0d0 - (x * 0.253d0)
    else
        tmp = (-0.12d0) * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * (x * -0.12);
	} else if (x <= 2.0) {
		tmp = 1.0 - (x * 0.253);
	} else {
		tmp = -0.12 * (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -4.0:
		tmp = x * (x * -0.12)
	elif x <= 2.0:
		tmp = 1.0 - (x * 0.253)
	else:
		tmp = -0.12 * (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -4.0)
		tmp = Float64(x * Float64(x * -0.12));
	elseif (x <= 2.0)
		tmp = Float64(1.0 - Float64(x * 0.253));
	else
		tmp = Float64(-0.12 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -4.0)
		tmp = x * (x * -0.12);
	elseif (x <= 2.0)
		tmp = 1.0 - (x * 0.253);
	else
		tmp = -0.12 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -4.0], N[(x * N[(x * -0.12), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(1.0 - N[(x * 0.253), $MachinePrecision]), $MachinePrecision], N[(-0.12 * N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.0%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.0%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.0%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.0%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 97.1%

      \[\leadsto \color{blue}{x \cdot \left(-0.12 \cdot x - 0.253\right)} \]

   7. Taylor expanded in x around inf 95.8%

      \[\leadsto x \cdot \color{blue}{\left(-0.12 \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   9. Simplified 95.8%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   if -4 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.9%

      \[\leadsto 1 - \color{blue}{0.253 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   5. Simplified 99.9%

      \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   if 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 98.3%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 98.3%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 98.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]

   7. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]

   8. Taylor expanded in x around inf 97.2%

      \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{-0.12} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1 - x \cdot 0.253\\ \mathbf{else}:\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -4.0) (* x (* x -0.12)) (if (<= x 2.0) 1.0 (* -0.12 (* x x)))))

C

double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * (x * -0.12);
	} else if (x <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -0.12 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-4.0d0)) then
        tmp = x * (x * (-0.12d0))
    else if (x <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = (-0.12d0) * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * (x * -0.12);
	} else if (x <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -0.12 * (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -4.0:
		tmp = x * (x * -0.12)
	elif x <= 2.0:
		tmp = 1.0
	else:
		tmp = -0.12 * (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -4.0)
		tmp = Float64(x * Float64(x * -0.12));
	elseif (x <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(-0.12 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -4.0)
		tmp = x * (x * -0.12);
	elseif (x <= 2.0)
		tmp = 1.0;
	else
		tmp = -0.12 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -4.0], N[(x * N[(x * -0.12), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], 1.0, N[(-0.12 * N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.0%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.0%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.0%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.0%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 97.1%

      \[\leadsto \color{blue}{x \cdot \left(-0.12 \cdot x - 0.253\right)} \]

   7. Taylor expanded in x around inf 95.8%

      \[\leadsto x \cdot \color{blue}{\left(-0.12 \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   9. Simplified 95.8%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot -0.12\right)} \]

   if -4 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{1} \]

   if 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 98.3%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 98.3%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 98.3%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 98.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]

   7. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right) \]

   8. Taylor expanded in x around inf 97.2%

      \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{-0.12} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(x \cdot 0.12 + 0.253\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ (* x 0.12) 0.253))))

C

double code(double x) {
	return 1.0 - (x * ((x * 0.12) + 0.253));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * ((x * 0.12d0) + 0.253d0))
end function

Java

public static double code(double x) {
	return 1.0 - (x * ((x * 0.12) + 0.253));
}

Python

def code(x):
	return 1.0 - (x * ((x * 0.12) + 0.253))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(Float64(x * 0.12) + 0.253)))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * ((x * 0.12) + 0.253));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(N[(x * 0.12), $MachinePrecision] + 0.253), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto 1 - x \cdot \left(x \cdot 0.12 + 0.253\right) \]
4. Add Preprocessing

Alternative 8: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot 0.253\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x -4.0) (* x 0.253) 1.0))

C

double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * 0.253;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-4.0d0)) then
        tmp = x * 0.253d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -4.0) {
		tmp = x * 0.253;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -4.0:
		tmp = x * 0.253
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -4.0)
		tmp = Float64(x * 0.253);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -4.0)
		tmp = x * 0.253;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -4.0], N[(x * 0.253), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.0%

      \[\leadsto \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.0%

         \[\leadsto \color{blue}{-{x}^{2} \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)} \]

      2. distribute-rgt-neg-in 97.0%

         \[\leadsto \color{blue}{{x}^{2} \cdot \left(-\left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

      3. distribute-neg-in 97.0%

         \[\leadsto {x}^{2} \cdot \color{blue}{\left(\left(-0.12\right) + \left(-0.253 \cdot \frac{1}{x}\right)\right)} \]

      4. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(\color{blue}{-0.12} + \left(-0.253 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\color{blue}{\frac{0.253 \cdot 1}{x}}\right)\right) \]

      6. metadata-eval 97.0%

         \[\leadsto {x}^{2} \cdot \left(-0.12 + \left(-\frac{\color{blue}{0.253}}{x}\right)\right) \]

   5. Simplified 97.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(-0.12 + \left(-\frac{0.253}{x}\right)\right)} \]

   6. Taylor expanded in x around 0 0.5%

      \[\leadsto \color{blue}{-0.253 \cdot x} \]
   7. Step-by-step derivation

      1. *-commutative 0.5%

         \[\leadsto \color{blue}{x \cdot -0.253} \]

   8. Simplified 0.5%

      \[\leadsto \color{blue}{x \cdot -0.253} \]
   9. Step-by-step derivation

      1. metadata-eval 0.5%

         \[\leadsto x \cdot \color{blue}{\left(-0.253\right)} \]

      2. distribute-rgt-neg-in 0.5%

         \[\leadsto \color{blue}{-x \cdot 0.253} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto -\color{blue}{\sqrt{x \cdot 0.253} \cdot \sqrt{x \cdot 0.253}} \]

      4. sqrt-unprod 56.6%

         \[\leadsto -\color{blue}{\sqrt{\left(x \cdot 0.253\right) \cdot \left(x \cdot 0.253\right)}} \]

      5. swap-sqr 56.6%

         \[\leadsto -\sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(0.253 \cdot 0.253\right)}} \]

      6. metadata-eval 56.6%

         \[\leadsto -\sqrt{\left(x \cdot x\right) \cdot \color{blue}{0.064009}} \]

      7. metadata-eval 56.6%

         \[\leadsto -\sqrt{\left(x \cdot x\right) \cdot \color{blue}{\left(-0.253 \cdot -0.253\right)}} \]

      8. swap-sqr 56.6%

         \[\leadsto -\sqrt{\color{blue}{\left(x \cdot -0.253\right) \cdot \left(x \cdot -0.253\right)}} \]

      9. sqrt-unprod 7.3%

         \[\leadsto -\color{blue}{\sqrt{x \cdot -0.253} \cdot \sqrt{x \cdot -0.253}} \]

      10. add-sqr-sqrt 7.3%

          \[\leadsto -\color{blue}{x \cdot -0.253} \]

      11. *-commutative 7.3%

          \[\leadsto -\color{blue}{-0.253 \cdot x} \]

   10. Applied egg-rr 7.3%

       \[\leadsto \color{blue}{--0.253 \cdot x} \]

   11. Taylor expanded in x around 0 7.3%

       \[\leadsto \color{blue}{0.253 \cdot x} \]
   12. Step-by-step derivation

       1. *-commutative 7.3%

          \[\leadsto \color{blue}{x \cdot 0.253} \]

   13. Simplified 7.3%

       \[\leadsto \color{blue}{x \cdot 0.253} \]

   if -4 < x

   1. Initial program 99.9%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 67.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 49.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 49.8%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024172 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))