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

Percentage Accurate: 99.9% → 99.9%

Time: 10.2s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \log y, \log t - \left(y + z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma x (log y) (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	return fma(x, log(y), (log(t) - (y + z)));
}

Julia

function code(x, y, z, t)
	return fma(x, log(y), Float64(log(t) - Float64(y + z)))
end

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \color{blue}{\log t + \left(\left(x \cdot \log y - y\right) - z\right)} \]

   2. associate--l- 99.8%

      \[\leadsto \log t + \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} \]

   3. associate-+r- 99.8%

      \[\leadsto \color{blue}{\left(\log t + x \cdot \log y\right) - \left(y + z\right)} \]

   4. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \log y + \log t\right)} - \left(y + z\right) \]

   5. associate--l+ 99.8%

      \[\leadsto \color{blue}{x \cdot \log y + \left(\log t - \left(y + z\right)\right)} \]

   6. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t - \left(y + z\right)\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t - \left(y + z\right)\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x, \log y, \log t - \left(y + z\right)\right) \]

Alternative 2: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+70} \lor \neg \left(x \leq 1.9 \cdot 10^{+133}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.8e+70) (not (<= x 1.9e+133)))
   (- (+ (log t) (* x (log y))) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e+70) || !(x <= 1.9e+133)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.8d+70)) .or. (.not. (x <= 1.9d+133))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e+70) || !(x <= 1.9e+133)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.8e+70) or not (x <= 1.9e+133):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.8e+70) || !(x <= 1.9e+133))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.8e+70) || ~((x <= 1.9e+133)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.8e+70], N[Not[LessEqual[x, 1.9e+133]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999974e70 or 1.9000000000000001e133 < x

   1. Initial program 99.5%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around 0 85.7%

      \[\leadsto \color{blue}{\left(\log y \cdot x + \log t\right) - y} \]

   if -4.79999999999999974e70 < x < 1.9000000000000001e133

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 93.5%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+70} \lor \neg \left(x \leq 1.9 \cdot 10^{+133}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 3: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{+140}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.1e+140) (- (+ (log t) (* x (log y))) z) (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.1e+140) {
		tmp = (log(t) + (x * log(y))) - z;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.1d+140) then
        tmp = (log(t) + (x * log(y))) - z
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.1e+140) {
		tmp = (Math.log(t) + (x * Math.log(y))) - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.1e+140:
		tmp = (math.log(t) + (x * math.log(y))) - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.1e+140)
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - z);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.1e+140)
		tmp = (log(t) + (x * log(y))) - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.1e+140], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.1000000000000002e140

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in y around 0 91.9%

      \[\leadsto \color{blue}{\left(\log y \cdot x + \log t\right) - z} \]

   if 2.1000000000000002e140 < y

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 94.3%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{+140}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

2. Final simplification 99.8%

   \[\leadsto \log t + \left(\left(x \cdot \log y - y\right) - z\right) \]

Alternative 5: 48.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-70}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -5400000.0)
     (- z)
     (if (<= z -1.42e-70)
       (- y)
       (if (<= z -6.8e-186)
         t_1
         (if (<= z -4.5e-231)
           (- y)
           (if (<= z -4.3e-285) t_1 (if (<= z 1.595e+35) (- y) (- z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= -1.42e-70) {
		tmp = -y;
	} else if (z <= -6.8e-186) {
		tmp = t_1;
	} else if (z <= -4.5e-231) {
		tmp = -y;
	} else if (z <= -4.3e-285) {
		tmp = t_1;
	} else if (z <= 1.595e+35) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (z <= (-5400000.0d0)) then
        tmp = -z
    else if (z <= (-1.42d-70)) then
        tmp = -y
    else if (z <= (-6.8d-186)) then
        tmp = t_1
    else if (z <= (-4.5d-231)) then
        tmp = -y
    else if (z <= (-4.3d-285)) then
        tmp = t_1
    else if (z <= 1.595d+35) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= -1.42e-70) {
		tmp = -y;
	} else if (z <= -6.8e-186) {
		tmp = t_1;
	} else if (z <= -4.5e-231) {
		tmp = -y;
	} else if (z <= -4.3e-285) {
		tmp = t_1;
	} else if (z <= 1.595e+35) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -5400000.0:
		tmp = -z
	elif z <= -1.42e-70:
		tmp = -y
	elif z <= -6.8e-186:
		tmp = t_1
	elif z <= -4.5e-231:
		tmp = -y
	elif z <= -4.3e-285:
		tmp = t_1
	elif z <= 1.595e+35:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -5400000.0)
		tmp = Float64(-z);
	elseif (z <= -1.42e-70)
		tmp = Float64(-y);
	elseif (z <= -6.8e-186)
		tmp = t_1;
	elseif (z <= -4.5e-231)
		tmp = Float64(-y);
	elseif (z <= -4.3e-285)
		tmp = t_1;
	elseif (z <= 1.595e+35)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -5400000.0)
		tmp = -z;
	elseif (z <= -1.42e-70)
		tmp = -y;
	elseif (z <= -6.8e-186)
		tmp = t_1;
	elseif (z <= -4.5e-231)
		tmp = -y;
	elseif (z <= -4.3e-285)
		tmp = t_1;
	elseif (z <= 1.595e+35)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5400000.0], (-z), If[LessEqual[z, -1.42e-70], (-y), If[LessEqual[z, -6.8e-186], t$95$1, If[LessEqual[z, -4.5e-231], (-y), If[LessEqual[z, -4.3e-285], t$95$1, If[LessEqual[z, 1.595e+35], (-y), (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e6 or 1.595e35 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 67.1%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 67.1%

      \[\leadsto \color{blue}{-z} \]

   if -5.4e6 < z < -1.42000000000000002e-70 or -6.7999999999999999e-186 < z < -4.4999999999999998e-231 or -4.30000000000000011e-285 < z < 1.595e35

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in y around inf 53.7%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto \color{blue}{-y} \]

   4. Simplified 53.7%

      \[\leadsto \color{blue}{-y} \]

   if -1.42000000000000002e-70 < z < -6.7999999999999999e-186 or -4.4999999999999998e-231 < z < -4.30000000000000011e-285

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Step-by-step derivation

      1. associate--l- 99.6%

         \[\leadsto \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} + \log t \]

      2. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot \log y - \left(\left(y + z\right) - \log t\right)} \]

      3. add-cube-cbrt 99.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right) \cdot \sqrt[3]{\log y}\right)} - \left(\left(y + z\right) - \log t\right) \]

      4. associate-*r* 99.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right)\right) \cdot \sqrt[3]{\log y}} - \left(\left(y + z\right) - \log t\right) \]

      5. fma-neg 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right), \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

      6. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{{\left(\sqrt[3]{\log y}\right)}^{2}}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right) \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot {\left(\sqrt[3]{\log y}\right)}^{2}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

   4. Taylor expanded in x around inf 54.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 54.5%

         \[\leadsto \color{blue}{1} \cdot \left(\log y \cdot x\right) \]

      2. *-lft-identity 54.5%

         \[\leadsto \color{blue}{\log y \cdot x} \]

   6. Simplified 54.5%

      \[\leadsto \color{blue}{\log y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-70}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 82.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+218} \lor \neg \left(x \leq -5.2 \cdot 10^{+175}\right) \land \left(x \leq -1.22 \cdot 10^{+89} \lor \neg \left(x \leq 2.2 \cdot 10^{+130}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.16e+218)
         (and (not (<= x -5.2e+175))
              (or (<= x -1.22e+89) (not (<= x 2.2e+130)))))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.16e+218) || (!(x <= -5.2e+175) && ((x <= -1.22e+89) || !(x <= 2.2e+130)))) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.16d+218)) .or. (.not. (x <= (-5.2d+175))) .and. (x <= (-1.22d+89)) .or. (.not. (x <= 2.2d+130))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.16e+218) || (!(x <= -5.2e+175) && ((x <= -1.22e+89) || !(x <= 2.2e+130)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.16e+218) or (not (x <= -5.2e+175) and ((x <= -1.22e+89) or not (x <= 2.2e+130))):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.16e+218) || (!(x <= -5.2e+175) && ((x <= -1.22e+89) || !(x <= 2.2e+130))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.16e+218) || (~((x <= -5.2e+175)) && ((x <= -1.22e+89) || ~((x <= 2.2e+130)))))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.16e+218], And[N[Not[LessEqual[x, -5.2e+175]], $MachinePrecision], Or[LessEqual[x, -1.22e+89], N[Not[LessEqual[x, 2.2e+130]], $MachinePrecision]]]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15999999999999994e218 or -5.2000000000000001e175 < x < -1.22e89 or 2.19999999999999993e130 < x

   1. Initial program 99.5%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Step-by-step derivation

      1. associate--l- 99.5%

         \[\leadsto \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} + \log t \]

      2. associate-+l- 99.5%

         \[\leadsto \color{blue}{x \cdot \log y - \left(\left(y + z\right) - \log t\right)} \]

      3. add-cube-cbrt 98.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right) \cdot \sqrt[3]{\log y}\right)} - \left(\left(y + z\right) - \log t\right) \]

      4. associate-*r* 98.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right)\right) \cdot \sqrt[3]{\log y}} - \left(\left(y + z\right) - \log t\right) \]

      5. fma-neg 98.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right), \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

      6. pow2 98.6%

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{{\left(\sqrt[3]{\log y}\right)}^{2}}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right) \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot {\left(\sqrt[3]{\log y}\right)}^{2}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

   4. Taylor expanded in x around inf 80.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 80.3%

         \[\leadsto \color{blue}{1} \cdot \left(\log y \cdot x\right) \]

      2. *-lft-identity 80.3%

         \[\leadsto \color{blue}{\log y \cdot x} \]

   6. Simplified 80.3%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -1.15999999999999994e218 < x < -5.2000000000000001e175 or -1.22e89 < x < 2.19999999999999993e130

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 92.1%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+218} \lor \neg \left(x \leq -5.2 \cdot 10^{+175}\right) \land \left(x \leq -1.22 \cdot 10^{+89} \lor \neg \left(x \leq 2.2 \cdot 10^{+130}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 7: 59.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)))
   (if (<= z -5400000.0)
     (- z)
     (if (<= z -3.8e-231)
       t_1
       (if (<= z -6.4e-277) (* x (log y)) (if (<= z 1.595e+35) t_1 (- z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= -3.8e-231) {
		tmp = t_1;
	} else if (z <= -6.4e-277) {
		tmp = x * log(y);
	} else if (z <= 1.595e+35) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - y
    if (z <= (-5400000.0d0)) then
        tmp = -z
    else if (z <= (-3.8d-231)) then
        tmp = t_1
    else if (z <= (-6.4d-277)) then
        tmp = x * log(y)
    else if (z <= 1.595d+35) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - y;
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= -3.8e-231) {
		tmp = t_1;
	} else if (z <= -6.4e-277) {
		tmp = x * Math.log(y);
	} else if (z <= 1.595e+35) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	tmp = 0
	if z <= -5400000.0:
		tmp = -z
	elif z <= -3.8e-231:
		tmp = t_1
	elif z <= -6.4e-277:
		tmp = x * math.log(y)
	elif z <= 1.595e+35:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	tmp = 0.0
	if (z <= -5400000.0)
		tmp = Float64(-z);
	elseif (z <= -3.8e-231)
		tmp = t_1;
	elseif (z <= -6.4e-277)
		tmp = Float64(x * log(y));
	elseif (z <= 1.595e+35)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	tmp = 0.0;
	if (z <= -5400000.0)
		tmp = -z;
	elseif (z <= -3.8e-231)
		tmp = t_1;
	elseif (z <= -6.4e-277)
		tmp = x * log(y);
	elseif (z <= 1.595e+35)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[z, -5400000.0], (-z), If[LessEqual[z, -3.8e-231], t$95$1, If[LessEqual[z, -6.4e-277], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.595e+35], t$95$1, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e6 or 1.595e35 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 67.1%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 67.1%

      \[\leadsto \color{blue}{-z} \]

   if -5.4e6 < z < -3.80000000000000013e-231 or -6.3999999999999996e-277 < z < 1.595e35

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around 0 97.6%

      \[\leadsto \color{blue}{\left(\log y \cdot x + \log t\right) - y} \]

   3. Taylor expanded in x around 0 67.0%

      \[\leadsto \color{blue}{\log t} - y \]

   if -3.80000000000000013e-231 < z < -6.3999999999999996e-277

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Step-by-step derivation

      1. associate--l- 99.6%

         \[\leadsto \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} + \log t \]

      2. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot \log y - \left(\left(y + z\right) - \log t\right)} \]

      3. add-cube-cbrt 98.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right) \cdot \sqrt[3]{\log y}\right)} - \left(\left(y + z\right) - \log t\right) \]

      4. associate-*r* 98.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right)\right) \cdot \sqrt[3]{\log y}} - \left(\left(y + z\right) - \log t\right) \]

      5. fma-neg 98.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right), \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

      6. pow2 98.3%

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{{\left(\sqrt[3]{\log y}\right)}^{2}}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right) \]

   3. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot {\left(\sqrt[3]{\log y}\right)}^{2}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

   4. Taylor expanded in x around inf 82.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 82.8%

         \[\leadsto \color{blue}{1} \cdot \left(\log y \cdot x\right) \]

      2. *-lft-identity 82.8%

         \[\leadsto \color{blue}{\log y \cdot x} \]

   6. Simplified 82.8%

      \[\leadsto \color{blue}{\log y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 3.4 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 3.4e-189)
     t_1
     (if (<= y 4.8e-182) (* x (log y)) (if (<= y 1.4e+165) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 3.4e-189) {
		tmp = t_1;
	} else if (y <= 4.8e-182) {
		tmp = x * log(y);
	} else if (y <= 1.4e+165) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (y <= 3.4d-189) then
        tmp = t_1
    else if (y <= 4.8d-182) then
        tmp = x * log(y)
    else if (y <= 1.4d+165) then
        tmp = t_1
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double tmp;
	if (y <= 3.4e-189) {
		tmp = t_1;
	} else if (y <= 4.8e-182) {
		tmp = x * Math.log(y);
	} else if (y <= 1.4e+165) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if y <= 3.4e-189:
		tmp = t_1
	elif y <= 4.8e-182:
		tmp = x * math.log(y)
	elif y <= 1.4e+165:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (y <= 3.4e-189)
		tmp = t_1;
	elseif (y <= 4.8e-182)
		tmp = Float64(x * log(y));
	elseif (y <= 1.4e+165)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (y <= 3.4e-189)
		tmp = t_1;
	elseif (y <= 4.8e-182)
		tmp = x * log(y);
	elseif (y <= 1.4e+165)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 3.4e-189], t$95$1, If[LessEqual[y, 4.8e-182], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+165], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.4000000000000001e-189 or 4.7999999999999997e-182 < y < 1.3999999999999999e165

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in y around 0 90.0%

      \[\leadsto \color{blue}{\left(\log y \cdot x + \log t\right) - z} \]

   3. Taylor expanded in x around 0 60.7%

      \[\leadsto \color{blue}{\log t} - z \]

   if 3.4000000000000001e-189 < y < 4.7999999999999997e-182

   1. Initial program 99.1%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Step-by-step derivation

      1. associate--l- 99.1%

         \[\leadsto \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} + \log t \]

      2. associate-+l- 99.1%

         \[\leadsto \color{blue}{x \cdot \log y - \left(\left(y + z\right) - \log t\right)} \]

      3. add-cube-cbrt 98.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right) \cdot \sqrt[3]{\log y}\right)} - \left(\left(y + z\right) - \log t\right) \]

      4. associate-*r* 98.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right)\right) \cdot \sqrt[3]{\log y}} - \left(\left(y + z\right) - \log t\right) \]

      5. fma-neg 98.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(\sqrt[3]{\log y} \cdot \sqrt[3]{\log y}\right), \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

      6. pow2 98.1%

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{{\left(\sqrt[3]{\log y}\right)}^{2}}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right) \]

   3. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot {\left(\sqrt[3]{\log y}\right)}^{2}, \sqrt[3]{\log y}, -\left(\left(y + z\right) - \log t\right)\right)} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 99.1%

         \[\leadsto \color{blue}{1} \cdot \left(\log y \cdot x\right) \]

      2. *-lft-identity 99.1%

         \[\leadsto \color{blue}{\log y \cdot x} \]

   6. Simplified 99.1%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if 1.3999999999999999e165 < y

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in y around inf 88.0%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. mul-1-neg 88.0%

         \[\leadsto \color{blue}{-y} \]

   4. Simplified 88.0%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{-189}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+165}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9: 47.9% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5400000.0) (- z) (if (<= z 1.595e+35) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= 1.595e+35) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5400000.0d0)) then
        tmp = -z
    else if (z <= 1.595d+35) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5400000.0) {
		tmp = -z;
	} else if (z <= 1.595e+35) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5400000.0:
		tmp = -z
	elif z <= 1.595e+35:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5400000.0)
		tmp = Float64(-z);
	elseif (z <= 1.595e+35)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5400000.0)
		tmp = -z;
	elseif (z <= 1.595e+35)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5400000.0], (-z), If[LessEqual[z, 1.595e+35], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e6 or 1.595e35 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 67.1%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 67.1%

      \[\leadsto \color{blue}{-z} \]

   if -5.4e6 < z < 1.595e35

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in y around inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \color{blue}{-y} \]

   4. Simplified 42.9%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5400000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.595 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 30.8% accurate, 104.5× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-y)

Derivation

1. Initial program 99.8%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

2. Taylor expanded in y around inf 28.0%

   \[\leadsto \color{blue}{-1 \cdot y} \]
3. Step-by-step derivation

   1. mul-1-neg 28.0%

      \[\leadsto \color{blue}{-y} \]

4. Simplified 28.0%

   \[\leadsto \color{blue}{-y} \]

5. Final simplification 28.0%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023187 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))