Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.8%

Time: 16.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- x (- (* (+ y 0.5) (log y)) y)) z))

C

double code(double x, double y, double z) {
	return (x - (((y + 0.5) * log(y)) - y)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - (((y + 0.5d0) * log(y)) - y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x - (((y + 0.5) * Math.log(y)) - y)) - z;
}

Python

def code(x, y, z):
	return (x - (((y + 0.5) * math.log(y)) - y)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x - Float64(Float64(Float64(y + 0.5) * log(y)) - y)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - (((y + 0.5) * log(y)) - y)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x - N[(N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right) - z\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;\left(y + \left(x - z\right)\right) \cdot \frac{y + \left(z + x\right)}{z + x}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-202}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+95}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y (- 1.0 (log y))) z)))
   (if (<= x -4.8e+69)
     (* (+ y (- x z)) (/ (+ y (+ z x)) (+ z x)))
     (if (<= x -1.3e-147)
       t_0
       (if (<= x -1.9e-202)
         (- (* (log y) -0.5) z)
         (if (<= x 4.8e+95) t_0 (- x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - log(y))) - z;
	double tmp;
	if (x <= -4.8e+69) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (x <= -1.3e-147) {
		tmp = t_0;
	} else if (x <= -1.9e-202) {
		tmp = (log(y) * -0.5) - z;
	} else if (x <= 4.8e+95) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - log(y))) - z
    if (x <= (-4.8d+69)) then
        tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
    else if (x <= (-1.3d-147)) then
        tmp = t_0
    else if (x <= (-1.9d-202)) then
        tmp = (log(y) * (-0.5d0)) - z
    else if (x <= 4.8d+95) then
        tmp = t_0
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - Math.log(y))) - z;
	double tmp;
	if (x <= -4.8e+69) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (x <= -1.3e-147) {
		tmp = t_0;
	} else if (x <= -1.9e-202) {
		tmp = (Math.log(y) * -0.5) - z;
	} else if (x <= 4.8e+95) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (1.0 - math.log(y))) - z
	tmp = 0
	if x <= -4.8e+69:
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
	elif x <= -1.3e-147:
		tmp = t_0
	elif x <= -1.9e-202:
		tmp = (math.log(y) * -0.5) - z
	elif x <= 4.8e+95:
		tmp = t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(1.0 - log(y))) - z)
	tmp = 0.0
	if (x <= -4.8e+69)
		tmp = Float64(Float64(y + Float64(x - z)) * Float64(Float64(y + Float64(z + x)) / Float64(z + x)));
	elseif (x <= -1.3e-147)
		tmp = t_0;
	elseif (x <= -1.9e-202)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	elseif (x <= 4.8e+95)
		tmp = t_0;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (1.0 - log(y))) - z;
	tmp = 0.0;
	if (x <= -4.8e+69)
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	elseif (x <= -1.3e-147)
		tmp = t_0;
	elseif (x <= -1.9e-202)
		tmp = (log(y) * -0.5) - z;
	elseif (x <= 4.8e+95)
		tmp = t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -4.8e+69], N[(N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] / N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-147], t$95$0, If[LessEqual[x, -1.9e-202], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 4.8e+95], t$95$0, N[(x - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.8000000000000003e69

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -4.8000000000000003e69 < x < -1.2999999999999999e-147 or -1.90000000000000007e-202 < x < 4.8000000000000001e95

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.2999999999999999e-147 < x < -1.90000000000000007e-202

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 4.8000000000000001e95 < x

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96:\\ \;\;\;\;\left(y + \left(x - z\right)\right) \cdot \frac{y + \left(z + x\right)}{z + x}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -96.0)
   (* (+ y (- x z)) (/ (+ y (+ z x)) (+ z x)))
   (if (<= z 5.5e-42)
     (+ x (* (log y) -0.5))
     (if (<= z 2.65e+45) (* y (- 1.0 (log y))) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -96.0) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (z <= 5.5e-42) {
		tmp = x + (log(y) * -0.5);
	} else if (z <= 2.65e+45) {
		tmp = y * (1.0 - log(y));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-96.0d0)) then
        tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
    else if (z <= 5.5d-42) then
        tmp = x + (log(y) * (-0.5d0))
    else if (z <= 2.65d+45) then
        tmp = y * (1.0d0 - log(y))
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -96.0) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (z <= 5.5e-42) {
		tmp = x + (Math.log(y) * -0.5);
	} else if (z <= 2.65e+45) {
		tmp = y * (1.0 - Math.log(y));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -96.0:
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
	elif z <= 5.5e-42:
		tmp = x + (math.log(y) * -0.5)
	elif z <= 2.65e+45:
		tmp = y * (1.0 - math.log(y))
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -96.0)
		tmp = Float64(Float64(y + Float64(x - z)) * Float64(Float64(y + Float64(z + x)) / Float64(z + x)));
	elseif (z <= 5.5e-42)
		tmp = Float64(x + Float64(log(y) * -0.5));
	elseif (z <= 2.65e+45)
		tmp = Float64(y * Float64(1.0 - log(y)));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -96.0)
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	elseif (z <= 5.5e-42)
		tmp = x + (log(y) * -0.5);
	elseif (z <= 2.65e+45)
		tmp = y * (1.0 - log(y));
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -96.0], N[(N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] / N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-42], N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+45], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -96

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -96 < z < 5.5e-42

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 5.5e-42 < z < 2.64999999999999996e45

   1. Initial program 99.5%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.64999999999999996e45 < z

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 4: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;\left(y + \left(x - z\right)\right) \cdot \frac{y + \left(z + x\right)}{z + x}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+139}:\\ \;\;\;\;x + \left(y - \log y \cdot \left(y + 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.6e+69)
   (* (+ y (- x z)) (/ (+ y (+ z x)) (+ z x)))
   (if (<= z 1.65e+139) (+ x (- y (* (log y) (+ y 0.5)))) (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+69) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (z <= 1.65e+139) {
		tmp = x + (y - (log(y) * (y + 0.5)));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.6d+69)) then
        tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
    else if (z <= 1.65d+139) then
        tmp = x + (y - (log(y) * (y + 0.5d0)))
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+69) {
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	} else if (z <= 1.65e+139) {
		tmp = x + (y - (Math.log(y) * (y + 0.5)));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.6e+69:
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x))
	elif z <= 1.65e+139:
		tmp = x + (y - (math.log(y) * (y + 0.5)))
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.6e+69)
		tmp = Float64(Float64(y + Float64(x - z)) * Float64(Float64(y + Float64(z + x)) / Float64(z + x)));
	elseif (z <= 1.65e+139)
		tmp = Float64(x + Float64(y - Float64(log(y) * Float64(y + 0.5))));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.6e+69)
		tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
	elseif (z <= 1.65e+139)
		tmp = x + (y - (log(y) * (y + 0.5)));
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.6e+69], N[(N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] / N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+139], N[(x + N[(y - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.59999999999999986e69

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if -8.59999999999999986e69 < z < 1.6500000000000001e139

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if 1.6500000000000001e139 < z

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   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: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x - \left(y \cdot \log y - y\right)\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.5e-7)
   (- (- x (* 0.5 (log y))) z)
   (- (- x (- (* y (log y)) y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-7) {
		tmp = (x - (0.5 * log(y))) - z;
	} else {
		tmp = (x - ((y * log(y)) - y)) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 8.5d-7) then
        tmp = (x - (0.5d0 * log(y))) - z
    else
        tmp = (x - ((y * log(y)) - y)) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-7) {
		tmp = (x - (0.5 * Math.log(y))) - z;
	} else {
		tmp = (x - ((y * Math.log(y)) - y)) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.5e-7:
		tmp = (x - (0.5 * math.log(y))) - z
	else:
		tmp = (x - ((y * math.log(y)) - y)) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.5e-7)
		tmp = Float64(Float64(x - Float64(0.5 * log(y))) - z);
	else
		tmp = Float64(Float64(x - Float64(Float64(y * log(y)) - y)) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8.5e-7)
		tmp = (x - (0.5 * log(y))) - z;
	else
		tmp = (x - ((y * log(y)) - y)) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.5e-7], N[(N[(x - N[(0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x - N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.50000000000000014e-7

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.50000000000000014e-7 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 6: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y \cdot \log y\right) + y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.5e-7)
   (- (- x (* 0.5 (log y))) z)
   (- (+ (- x (* y (log y))) y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-7) {
		tmp = (x - (0.5 * log(y))) - z;
	} else {
		tmp = ((x - (y * log(y))) + y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 8.5d-7) then
        tmp = (x - (0.5d0 * log(y))) - z
    else
        tmp = ((x - (y * log(y))) + y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-7) {
		tmp = (x - (0.5 * Math.log(y))) - z;
	} else {
		tmp = ((x - (y * Math.log(y))) + y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.5e-7:
		tmp = (x - (0.5 * math.log(y))) - z
	else:
		tmp = ((x - (y * math.log(y))) + y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.5e-7)
		tmp = Float64(Float64(x - Float64(0.5 * log(y))) - z);
	else
		tmp = Float64(Float64(Float64(x - Float64(y * log(y))) + y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8.5e-7)
		tmp = (x - (0.5 * log(y))) - z;
	else
		tmp = ((x - (y * log(y))) + y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.5e-7], N[(N[(x - N[(0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.50000000000000014e-7

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.50000000000000014e-7 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 7: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{+54}:\\ \;\;\;\;\left(x - 0.5 \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.05e+54) (- (- x (* 0.5 (log y))) z) (- (* y (- 1.0 (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.05e+54) {
		tmp = (x - (0.5 * log(y))) - z;
	} else {
		tmp = (y * (1.0 - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.05d+54) then
        tmp = (x - (0.5d0 * log(y))) - z
    else
        tmp = (y * (1.0d0 - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.05e+54) {
		tmp = (x - (0.5 * Math.log(y))) - z;
	} else {
		tmp = (y * (1.0 - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.05e+54:
		tmp = (x - (0.5 * math.log(y))) - z
	else:
		tmp = (y * (1.0 - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.05e+54)
		tmp = Float64(Float64(x - Float64(0.5 * log(y))) - z);
	else
		tmp = Float64(Float64(y * Float64(1.0 - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.05e+54)
		tmp = (x - (0.5 * log(y))) - z;
	else
		tmp = (y * (1.0 - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.05e+54], N[(N[(x - N[(0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.04999999999999984e54

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.04999999999999984e54 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 9: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+122}:\\ \;\;\;\;\left(x + y\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.35e+122) (- (+ x y) z) (* y (- 1.0 (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.35e+122) {
		tmp = (x + y) - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.35d+122) then
        tmp = (x + y) - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.35e+122) {
		tmp = (x + y) - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.35e+122:
		tmp = (x + y) - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.35e+122)
		tmp = Float64(Float64(x + y) - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.35e+122)
		tmp = (x + y) - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.35e+122], N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3499999999999999e122

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.3499999999999999e122 < y

   1. Initial program 99.5%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 10: 57.7% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \left(y + \left(x - z\right)\right) \cdot \frac{y + \left(z + x\right)}{z + x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* (+ y (- x z)) (/ (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	return (y + (x - z)) * ((y + (z + x)) / (z + x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y + (x - z)) * ((y + (z + x)) / (z + x))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (x - z)) * ((y + (z + x)) / (z + x));
}

Python

def code(x, y, z):
	return (y + (x - z)) * ((y + (z + x)) / (z + x))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(x - z)) * Float64(Float64(y + Float64(z + x)) / Float64(z + x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (x - z)) * ((y + (z + x)) / (z + x));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision] / N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]

12. Applied egg-rr 0

    \[\leadsto expr\]
13. Add Preprocessing

Alternative 11: 47.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+69) x (if (<= x 1.35e+68) (- z) (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+69) {
		tmp = x;
	} else if (x <= 1.35e+68) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.8d+69)) then
        tmp = x
    else if (x <= 1.35d+68) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+69) {
		tmp = x;
	} else if (x <= 1.35e+68) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.8e+69:
		tmp = x
	elif x <= 1.35e+68:
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+69)
		tmp = x;
	elseif (x <= 1.35e+68)
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.8e+69)
		tmp = x;
	elseif (x <= 1.35e+68)
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+69], x, If[LessEqual[x, 1.35e+68], (-z), N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999973e69

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.79999999999999973e69 < x < 1.34999999999999995e68

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 1.34999999999999995e68 < x

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 12: 47.7% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e+69) x (if (<= x 3.2e+68) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+69) {
		tmp = x;
	} else if (x <= 3.2e+68) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d+69)) then
        tmp = x
    else if (x <= 3.2d+68) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+69) {
		tmp = x;
	} else if (x <= 3.2e+68) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e+69:
		tmp = x
	elif x <= 3.2e+68:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e+69)
		tmp = x;
	elseif (x <= 3.2e+68)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e+69)
		tmp = x;
	elseif (x <= 3.2e+68)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e+69], x, If[LessEqual[x, 3.2e+68], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999991e69 or 3.19999999999999994e68 < x

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.39999999999999991e69 < x < 3.19999999999999994e68

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 13: 57.2% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x z))

C

double code(double x, double y, double z) {
	return x - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - z
end function

Java

public static double code(double x, double y, double z) {
	return x - z;
}

Python

def code(x, y, z):
	return x - z

Julia

function code(x, y, z)
	return Float64(x - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - z;
end

Wolfram

code[x_, y_, z_] := N[(x - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 14: 29.6% accurate, 111.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (+ y x) z) (* (+ y 0.5) (log y))))

C

double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * log(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((y + x) - z) - ((y + 0.5d0) * log(y))
end function

Java

public static double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * Math.log(y));
}

Python

def code(x, y, z):
	return ((y + x) - z) - ((y + 0.5) * math.log(y))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y + x) - z) - Float64(Float64(y + 0.5) * log(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y + x) - z) - ((y + 0.5) * log(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y + x), $MachinePrecision] - z), $MachinePrecision] - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))