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

Percentage Accurate: 99.9% → 99.9%

Time: 9.4s

Alternatives: 11

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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l- 99.9%

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

   3. associate-+r- 99.9%

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

   4. +-commutative 99.9%

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

   5. associate--l+ 99.9%

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

   6. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+135} \lor \neg \left(x \leq 9.6 \cdot 10^{+83}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e+135) (not (<= x 9.6e+83)))
   (- (+ (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 <= -2.6e+135) || !(x <= 9.6e+83)) {
		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 <= (-2.6d+135)) .or. (.not. (x <= 9.6d+83))) 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 <= -2.6e+135) || !(x <= 9.6e+83)) {
		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 <= -2.6e+135) or not (x <= 9.6e+83):
		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 <= -2.6e+135) || !(x <= 9.6e+83))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.6e+135) || ~((x <= 9.6e+83)))
		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, -2.6e+135], N[Not[LessEqual[x, 9.6e+83]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e135 or 9.59999999999999965e83 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 86.9%

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

   if -2.6e135 < x < 9.59999999999999965e83

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.9%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 95.9%

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

   4. Simplified 95.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+135} \lor \neg \left(x \leq 9.6 \cdot 10^{+83}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]

Alternative 3: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= x -2.3e+62)
     (- t_1 z)
     (if (<= x 1.15e+84) (- (- (log t) y) z) (- t_1 y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (x <= -2.3e+62) {
		tmp = t_1 - z;
	} else if (x <= 1.15e+84) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = t_1 - 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) + (x * log(y))
    if (x <= (-2.3d+62)) then
        tmp = t_1 - z
    else if (x <= 1.15d+84) then
        tmp = (log(t) - y) - z
    else
        tmp = t_1 - 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) + (x * Math.log(y));
	double tmp;
	if (x <= -2.3e+62) {
		tmp = t_1 - z;
	} else if (x <= 1.15e+84) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if x <= -2.3e+62:
		tmp = t_1 - z
	elif x <= 1.15e+84:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (x <= -2.3e+62)
		tmp = Float64(t_1 - z);
	elseif (x <= 1.15e+84)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (x <= -2.3e+62)
		tmp = t_1 - z;
	elseif (x <= 1.15e+84)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+62], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[x, 1.15e+84], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.29999999999999984e62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.3%

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

   if -2.29999999999999984e62 < x < 1.1499999999999999e84

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.0%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 97.0%

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

   4. Simplified 97.0%

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

   if 1.1499999999999999e84 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 89.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((log(t) + (x * log(y))) - z) - 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 = ((log(t) + (x * log(y))) - z) - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0 99.9%

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

3. Final simplification 99.9%

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

Alternative 6: 48.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-227}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-254}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-197}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.7e+135)
     t_1
     (if (<= x -2.5e-58)
       (- y)
       (if (<= x -6.9e-227)
         (- z)
         (if (<= x -6.6e-254)
           (- y)
           (if (<= x 1.32e-197) (- z) (if (<= x 3.3e+48) (- y) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.7e+135) {
		tmp = t_1;
	} else if (x <= -2.5e-58) {
		tmp = -y;
	} else if (x <= -6.9e-227) {
		tmp = -z;
	} else if (x <= -6.6e-254) {
		tmp = -y;
	} else if (x <= 1.32e-197) {
		tmp = -z;
	} else if (x <= 3.3e+48) {
		tmp = -y;
	} else {
		tmp = t_1;
	}
	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 (x <= (-2.7d+135)) then
        tmp = t_1
    else if (x <= (-2.5d-58)) then
        tmp = -y
    else if (x <= (-6.9d-227)) then
        tmp = -z
    else if (x <= (-6.6d-254)) then
        tmp = -y
    else if (x <= 1.32d-197) then
        tmp = -z
    else if (x <= 3.3d+48) then
        tmp = -y
    else
        tmp = t_1
    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 (x <= -2.7e+135) {
		tmp = t_1;
	} else if (x <= -2.5e-58) {
		tmp = -y;
	} else if (x <= -6.9e-227) {
		tmp = -z;
	} else if (x <= -6.6e-254) {
		tmp = -y;
	} else if (x <= 1.32e-197) {
		tmp = -z;
	} else if (x <= 3.3e+48) {
		tmp = -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.7e+135:
		tmp = t_1
	elif x <= -2.5e-58:
		tmp = -y
	elif x <= -6.9e-227:
		tmp = -z
	elif x <= -6.6e-254:
		tmp = -y
	elif x <= 1.32e-197:
		tmp = -z
	elif x <= 3.3e+48:
		tmp = -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.7e+135)
		tmp = t_1;
	elseif (x <= -2.5e-58)
		tmp = Float64(-y);
	elseif (x <= -6.9e-227)
		tmp = Float64(-z);
	elseif (x <= -6.6e-254)
		tmp = Float64(-y);
	elseif (x <= 1.32e-197)
		tmp = Float64(-z);
	elseif (x <= 3.3e+48)
		tmp = Float64(-y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.7e+135)
		tmp = t_1;
	elseif (x <= -2.5e-58)
		tmp = -y;
	elseif (x <= -6.9e-227)
		tmp = -z;
	elseif (x <= -6.6e-254)
		tmp = -y;
	elseif (x <= 1.32e-197)
		tmp = -z;
	elseif (x <= 3.3e+48)
		tmp = -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+135], t$95$1, If[LessEqual[x, -2.5e-58], (-y), If[LessEqual[x, -6.9e-227], (-z), If[LessEqual[x, -6.6e-254], (-y), If[LessEqual[x, 1.32e-197], (-z), If[LessEqual[x, 3.3e+48], (-y), t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999985e135 or 3.30000000000000023e48 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -2.69999999999999985e135 < x < -2.49999999999999989e-58 or -6.89999999999999989e-227 < x < -6.60000000000000033e-254 or 1.32e-197 < x < 3.30000000000000023e48

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. neg-mul-1 57.3%

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

   5. Simplified 57.3%

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

   if -2.49999999999999989e-58 < x < -6.89999999999999989e-227 or -6.60000000000000033e-254 < x < 1.32e-197

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in z around inf 53.5%

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

      1. mul-1-neg 53.5%

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

   5. Simplified 53.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-227}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-254}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-197}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 7: 59.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-204}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -8e+135)
     t_1
     (if (<= x -8e-254)
       t_2
       (if (<= x -2.8e-272)
         (- z)
         (if (<= x 1.4e-291)
           t_2
           (if (<= x 7e-204) (- z) (if (<= x 6.8e+35) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -8e+135) {
		tmp = t_1;
	} else if (x <= -8e-254) {
		tmp = t_2;
	} else if (x <= -2.8e-272) {
		tmp = -z;
	} else if (x <= 1.4e-291) {
		tmp = t_2;
	} else if (x <= 7e-204) {
		tmp = -z;
	} else if (x <= 6.8e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = log(t) - y
    if (x <= (-8d+135)) then
        tmp = t_1
    else if (x <= (-8d-254)) then
        tmp = t_2
    else if (x <= (-2.8d-272)) then
        tmp = -z
    else if (x <= 1.4d-291) then
        tmp = t_2
    else if (x <= 7d-204) then
        tmp = -z
    else if (x <= 6.8d+35) then
        tmp = t_2
    else
        tmp = t_1
    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 t_2 = Math.log(t) - y;
	double tmp;
	if (x <= -8e+135) {
		tmp = t_1;
	} else if (x <= -8e-254) {
		tmp = t_2;
	} else if (x <= -2.8e-272) {
		tmp = -z;
	} else if (x <= 1.4e-291) {
		tmp = t_2;
	} else if (x <= 7e-204) {
		tmp = -z;
	} else if (x <= 6.8e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -8e+135:
		tmp = t_1
	elif x <= -8e-254:
		tmp = t_2
	elif x <= -2.8e-272:
		tmp = -z
	elif x <= 1.4e-291:
		tmp = t_2
	elif x <= 7e-204:
		tmp = -z
	elif x <= 6.8e+35:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -8e+135)
		tmp = t_1;
	elseif (x <= -8e-254)
		tmp = t_2;
	elseif (x <= -2.8e-272)
		tmp = Float64(-z);
	elseif (x <= 1.4e-291)
		tmp = t_2;
	elseif (x <= 7e-204)
		tmp = Float64(-z);
	elseif (x <= 6.8e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = log(t) - y;
	tmp = 0.0;
	if (x <= -8e+135)
		tmp = t_1;
	elseif (x <= -8e-254)
		tmp = t_2;
	elseif (x <= -2.8e-272)
		tmp = -z;
	elseif (x <= 1.4e-291)
		tmp = t_2;
	elseif (x <= 7e-204)
		tmp = -z;
	elseif (x <= 6.8e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -8e+135], t$95$1, If[LessEqual[x, -8e-254], t$95$2, If[LessEqual[x, -2.8e-272], (-z), If[LessEqual[x, 1.4e-291], t$95$2, If[LessEqual[x, 7e-204], (-z), If[LessEqual[x, 6.8e+35], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999969e135 or 6.8000000000000002e35 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -7.99999999999999969e135 < x < -7.9999999999999993e-254 or -2.79999999999999994e-272 < x < 1.4e-291 or 7.00000000000000054e-204 < x < 6.8000000000000002e35

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 70.7%

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

   3. Taylor expanded in x around 0 68.1%

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

   if -7.9999999999999993e-254 < x < -2.79999999999999994e-272 or 1.4e-291 < x < 7.00000000000000054e-204

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in z around inf 69.0%

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

      1. mul-1-neg 69.0%

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

   5. Simplified 69.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-254}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-204}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+35}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 8: 60.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (* x (log y))) (t_3 (- (log t) y)))
   (if (<= x -4.9e+135)
     t_2
     (if (<= x -2.5e-60)
       t_3
       (if (<= x -9e-227)
         t_1
         (if (<= x -4.6e-254)
           t_3
           (if (<= x 2.6e-203) t_1 (if (<= x 2.75e+47) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = x * log(y);
	double t_3 = log(t) - y;
	double tmp;
	if (x <= -4.9e+135) {
		tmp = t_2;
	} else if (x <= -2.5e-60) {
		tmp = t_3;
	} else if (x <= -9e-227) {
		tmp = t_1;
	} else if (x <= -4.6e-254) {
		tmp = t_3;
	} else if (x <= 2.6e-203) {
		tmp = t_1;
	} else if (x <= 2.75e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log(t) - z
    t_2 = x * log(y)
    t_3 = log(t) - y
    if (x <= (-4.9d+135)) then
        tmp = t_2
    else if (x <= (-2.5d-60)) then
        tmp = t_3
    else if (x <= (-9d-227)) then
        tmp = t_1
    else if (x <= (-4.6d-254)) then
        tmp = t_3
    else if (x <= 2.6d-203) then
        tmp = t_1
    else if (x <= 2.75d+47) then
        tmp = t_3
    else
        tmp = t_2
    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 t_2 = x * Math.log(y);
	double t_3 = Math.log(t) - y;
	double tmp;
	if (x <= -4.9e+135) {
		tmp = t_2;
	} else if (x <= -2.5e-60) {
		tmp = t_3;
	} else if (x <= -9e-227) {
		tmp = t_1;
	} else if (x <= -4.6e-254) {
		tmp = t_3;
	} else if (x <= 2.6e-203) {
		tmp = t_1;
	} else if (x <= 2.75e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = x * math.log(y)
	t_3 = math.log(t) - y
	tmp = 0
	if x <= -4.9e+135:
		tmp = t_2
	elif x <= -2.5e-60:
		tmp = t_3
	elif x <= -9e-227:
		tmp = t_1
	elif x <= -4.6e-254:
		tmp = t_3
	elif x <= 2.6e-203:
		tmp = t_1
	elif x <= 2.75e+47:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(x * log(y))
	t_3 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -4.9e+135)
		tmp = t_2;
	elseif (x <= -2.5e-60)
		tmp = t_3;
	elseif (x <= -9e-227)
		tmp = t_1;
	elseif (x <= -4.6e-254)
		tmp = t_3;
	elseif (x <= 2.6e-203)
		tmp = t_1;
	elseif (x <= 2.75e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = x * log(y);
	t_3 = log(t) - y;
	tmp = 0.0;
	if (x <= -4.9e+135)
		tmp = t_2;
	elseif (x <= -2.5e-60)
		tmp = t_3;
	elseif (x <= -9e-227)
		tmp = t_1;
	elseif (x <= -4.6e-254)
		tmp = t_3;
	elseif (x <= 2.6e-203)
		tmp = t_1;
	elseif (x <= 2.75e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -4.9e+135], t$95$2, If[LessEqual[x, -2.5e-60], t$95$3, If[LessEqual[x, -9e-227], t$95$1, If[LessEqual[x, -4.6e-254], t$95$3, If[LessEqual[x, 2.6e-203], t$95$1, If[LessEqual[x, 2.75e+47], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9000000000000001e135 or 2.7499999999999999e47 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -4.9000000000000001e135 < x < -2.5000000000000001e-60 or -8.99999999999999986e-227 < x < -4.5999999999999997e-254 or 2.59999999999999975e-203 < x < 2.7499999999999999e47

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.8%

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

   3. Taylor expanded in x around 0 71.9%

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

   if -2.5000000000000001e-60 < x < -8.99999999999999986e-227 or -4.5999999999999997e-254 < x < 2.59999999999999975e-203

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.0%

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

   3. Taylor expanded in x around 0 77.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-60}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-227}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-254}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-203}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+47}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 9: 84.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+136} \lor \neg \left(x \leq 1.15 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e+136) (not (<= x 1.15e+89)))
   (* x (log y))
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+136) || !(x <= 1.15e+89)) {
		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 <= (-4d+136)) .or. (.not. (x <= 1.15d+89))) 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 <= -4e+136) || !(x <= 1.15e+89)) {
		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 <= -4e+136) or not (x <= 1.15e+89):
		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 <= -4e+136) || !(x <= 1.15e+89))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e+136) || ~((x <= 1.15e+89)))
		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, -4e+136], N[Not[LessEqual[x, 1.15e+89]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000023e136 or 1.1499999999999999e89 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 76.1%

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

   if -4.00000000000000023e136 < x < 1.1499999999999999e89

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.4%

      \[\leadsto \color{blue}{\log t - \left(y + z\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 95.4%

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

   4. Simplified 95.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+136} \lor \neg \left(x \leq 1.15 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]

Alternative 10: 46.8% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+107}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 5.4e+107) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.4e+107) {
		tmp = -z;
	} 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) :: tmp
    if (y <= 5.4d+107) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.4e+107) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.4e+107:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.4e+107)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 5.4e+107)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.4e+107], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.4000000000000003e107

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in z around inf 36.7%

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

      1. mul-1-neg 36.7%

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

   5. Simplified 36.7%

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

   if 5.4000000000000003e107 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around inf 74.2%

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

      1. neg-mul-1 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+107}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 11: 29.4% 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 99.9%

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

2. Taylor expanded in z around 0 99.9%

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

3. Taylor expanded in y around inf 31.2%

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

   1. neg-mul-1 31.2%

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

5. Simplified 31.2%

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

6. Final simplification 31.2%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023230 
(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)))