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

Percentage Accurate: 99.9% → 99.9%

Time: 10.5s

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, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - \left(y + z\right)\\ t_2 := \log t + x \cdot \log y\\ t_3 := t_2 - z\\ \mathbf{if}\;y \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) (+ y z)))
        (t_2 (+ (log t) (* x (log y))))
        (t_3 (- t_2 z)))
   (if (<= y 2.5e+21)
     t_3
     (if (<= y 4.4e+49)
       t_1
       (if (<= y 6.5e+77) t_3 (if (<= y 2.2e+175) t_1 (- t_2 y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - (y + z);
	double t_2 = log(t) + (x * log(y));
	double t_3 = t_2 - z;
	double tmp;
	if (y <= 2.5e+21) {
		tmp = t_3;
	} else if (y <= 4.4e+49) {
		tmp = t_1;
	} else if (y <= 6.5e+77) {
		tmp = t_3;
	} else if (y <= 2.2e+175) {
		tmp = t_1;
	} else {
		tmp = t_2 - 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log(t) - (y + z)
    t_2 = log(t) + (x * log(y))
    t_3 = t_2 - z
    if (y <= 2.5d+21) then
        tmp = t_3
    else if (y <= 4.4d+49) then
        tmp = t_1
    else if (y <= 6.5d+77) then
        tmp = t_3
    else if (y <= 2.2d+175) then
        tmp = t_1
    else
        tmp = t_2 - 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) - (y + z);
	double t_2 = Math.log(t) + (x * Math.log(y));
	double t_3 = t_2 - z;
	double tmp;
	if (y <= 2.5e+21) {
		tmp = t_3;
	} else if (y <= 4.4e+49) {
		tmp = t_1;
	} else if (y <= 6.5e+77) {
		tmp = t_3;
	} else if (y <= 2.2e+175) {
		tmp = t_1;
	} else {
		tmp = t_2 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - (y + z)
	t_2 = math.log(t) + (x * math.log(y))
	t_3 = t_2 - z
	tmp = 0
	if y <= 2.5e+21:
		tmp = t_3
	elif y <= 4.4e+49:
		tmp = t_1
	elif y <= 6.5e+77:
		tmp = t_3
	elif y <= 2.2e+175:
		tmp = t_1
	else:
		tmp = t_2 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - Float64(y + z))
	t_2 = Float64(log(t) + Float64(x * log(y)))
	t_3 = Float64(t_2 - z)
	tmp = 0.0
	if (y <= 2.5e+21)
		tmp = t_3;
	elseif (y <= 4.4e+49)
		tmp = t_1;
	elseif (y <= 6.5e+77)
		tmp = t_3;
	elseif (y <= 2.2e+175)
		tmp = t_1;
	else
		tmp = Float64(t_2 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - (y + z);
	t_2 = log(t) + (x * log(y));
	t_3 = t_2 - z;
	tmp = 0.0;
	if (y <= 2.5e+21)
		tmp = t_3;
	elseif (y <= 4.4e+49)
		tmp = t_1;
	elseif (y <= 6.5e+77)
		tmp = t_3;
	elseif (y <= 2.2e+175)
		tmp = t_1;
	else
		tmp = t_2 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - z), $MachinePrecision]}, If[LessEqual[y, 2.5e+21], t$95$3, If[LessEqual[y, 4.4e+49], t$95$1, If[LessEqual[y, 6.5e+77], t$95$3, If[LessEqual[y, 2.2e+175], t$95$1, N[(t$95$2 - y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.5e21 or 4.4000000000000001e49 < y < 6.5e77

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 98.8%

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

   if 2.5e21 < y < 4.4000000000000001e49 or 6.5e77 < y < 2.1999999999999999e175

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.9%

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

   if 2.1999999999999999e175 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+49}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+77}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]

Alternative 3: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+14} \lor \neg \left(x \leq 6.5 \cdot 10^{+69}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -2 + \left(y + \log t\right)\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e+14) (not (<= x 6.5e+69)))
   (- (+ (log t) (* x (log y))) y)
   (- (+ (* y -2.0) (+ y (log t))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e+14) || !(x <= 6.5e+69)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = ((y * -2.0) + (y + log(t))) - 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 <= (-1.5d+14)) .or. (.not. (x <= 6.5d+69))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = ((y * (-2.0d0)) + (y + log(t))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e+14) || !(x <= 6.5e+69)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = ((y * -2.0) + (y + Math.log(t))) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5e+14) or not (x <= 6.5e+69):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = ((y * -2.0) + (y + math.log(t))) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5e+14) || !(x <= 6.5e+69))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(Float64(Float64(y * -2.0) + Float64(y + log(t))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.5e+14) || ~((x <= 6.5e+69)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = ((y * -2.0) + (y + log(t))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5e+14], N[Not[LessEqual[x, 6.5e+69]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[(y * -2.0), $MachinePrecision] + N[(y + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e14 or 6.5000000000000001e69 < 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 86.0%

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

   if -1.5e14 < x < 6.5000000000000001e69

   1. Initial program 100.0%

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

      1. flip-- 63.2%

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

      2. clear-num 63.1%

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

      3. associate-+l- 63.1%

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

      4. pow2 63.1%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 63.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around 0 97.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+14} \lor \neg \left(x \leq 6.5 \cdot 10^{+69}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -2 + \left(y + \log t\right)\right) - z\\ \end{array} \]

Alternative 4: 48.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-104}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-226}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-260}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+99}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.22e+26)
     t_1
     (if (<= x -1.8e-104)
       (- z)
       (if (<= x -1.8e-226)
         (- y)
         (if (<= x 3.05e-260) (- z) (if (<= x 3e+99) (- y) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.22e+26) {
		tmp = t_1;
	} else if (x <= -1.8e-104) {
		tmp = -z;
	} else if (x <= -1.8e-226) {
		tmp = -y;
	} else if (x <= 3.05e-260) {
		tmp = -z;
	} else if (x <= 3e+99) {
		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 <= (-1.22d+26)) then
        tmp = t_1
    else if (x <= (-1.8d-104)) then
        tmp = -z
    else if (x <= (-1.8d-226)) then
        tmp = -y
    else if (x <= 3.05d-260) then
        tmp = -z
    else if (x <= 3d+99) 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 <= -1.22e+26) {
		tmp = t_1;
	} else if (x <= -1.8e-104) {
		tmp = -z;
	} else if (x <= -1.8e-226) {
		tmp = -y;
	} else if (x <= 3.05e-260) {
		tmp = -z;
	} else if (x <= 3e+99) {
		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 <= -1.22e+26:
		tmp = t_1
	elif x <= -1.8e-104:
		tmp = -z
	elif x <= -1.8e-226:
		tmp = -y
	elif x <= 3.05e-260:
		tmp = -z
	elif x <= 3e+99:
		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 <= -1.22e+26)
		tmp = t_1;
	elseif (x <= -1.8e-104)
		tmp = Float64(-z);
	elseif (x <= -1.8e-226)
		tmp = Float64(-y);
	elseif (x <= 3.05e-260)
		tmp = Float64(-z);
	elseif (x <= 3e+99)
		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 <= -1.22e+26)
		tmp = t_1;
	elseif (x <= -1.8e-104)
		tmp = -z;
	elseif (x <= -1.8e-226)
		tmp = -y;
	elseif (x <= 3.05e-260)
		tmp = -z;
	elseif (x <= 3e+99)
		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, -1.22e+26], t$95$1, If[LessEqual[x, -1.8e-104], (-z), If[LessEqual[x, -1.8e-226], (-y), If[LessEqual[x, 3.05e-260], (-z), If[LessEqual[x, 3e+99], (-y), t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2200000000000001e26 or 3.00000000000000014e99 < x

   1. Initial program 99.7%

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

      1. flip-- 18.5%

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

      2. clear-num 18.5%

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

      3. associate-+l- 18.5%

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

      4. pow2 18.5%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 18.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around inf 65.8%

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

   if -1.2200000000000001e26 < x < -1.7999999999999999e-104 or -1.79999999999999997e-226 < x < 3.0500000000000001e-260

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 50.3%

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

      1. neg-mul-1 50.3%

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

   4. Simplified 50.3%

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

   if -1.7999999999999999e-104 < x < -1.79999999999999997e-226 or 3.0500000000000001e-260 < x < 3.00000000000000014e99

   1. Initial program 100.0%

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

      1. flip-- 61.9%

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

      2. clear-num 61.8%

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

      3. associate-+l- 61.8%

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

      4. pow2 61.9%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 61.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in y around inf 49.7%

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

      1. mul-1-neg 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-104}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-226}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-260}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+99}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 5: 60.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \log t - z\\ \mathbf{if}\;x \leq -9 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (* x (log y))) (t_3 (- (log t) z)))
   (if (<= x -9e+25)
     t_2
     (if (<= x -7.5e-104)
       t_3
       (if (<= x -1.8e-226)
         t_1
         (if (<= x 9.8e-262) t_3 (if (<= x 6.5e+99) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = x * log(y);
	double t_3 = log(t) - z;
	double tmp;
	if (x <= -9e+25) {
		tmp = t_2;
	} else if (x <= -7.5e-104) {
		tmp = t_3;
	} else if (x <= -1.8e-226) {
		tmp = t_1;
	} else if (x <= 9.8e-262) {
		tmp = t_3;
	} else if (x <= 6.5e+99) {
		tmp = t_1;
	} 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) - y
    t_2 = x * log(y)
    t_3 = log(t) - z
    if (x <= (-9d+25)) then
        tmp = t_2
    else if (x <= (-7.5d-104)) then
        tmp = t_3
    else if (x <= (-1.8d-226)) then
        tmp = t_1
    else if (x <= 9.8d-262) then
        tmp = t_3
    else if (x <= 6.5d+99) then
        tmp = t_1
    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) - y;
	double t_2 = x * Math.log(y);
	double t_3 = Math.log(t) - z;
	double tmp;
	if (x <= -9e+25) {
		tmp = t_2;
	} else if (x <= -7.5e-104) {
		tmp = t_3;
	} else if (x <= -1.8e-226) {
		tmp = t_1;
	} else if (x <= 9.8e-262) {
		tmp = t_3;
	} else if (x <= 6.5e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = x * math.log(y)
	t_3 = math.log(t) - z
	tmp = 0
	if x <= -9e+25:
		tmp = t_2
	elif x <= -7.5e-104:
		tmp = t_3
	elif x <= -1.8e-226:
		tmp = t_1
	elif x <= 9.8e-262:
		tmp = t_3
	elif x <= 6.5e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(x * log(y))
	t_3 = Float64(log(t) - z)
	tmp = 0.0
	if (x <= -9e+25)
		tmp = t_2;
	elseif (x <= -7.5e-104)
		tmp = t_3;
	elseif (x <= -1.8e-226)
		tmp = t_1;
	elseif (x <= 9.8e-262)
		tmp = t_3;
	elseif (x <= 6.5e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = x * log(y);
	t_3 = log(t) - z;
	tmp = 0.0;
	if (x <= -9e+25)
		tmp = t_2;
	elseif (x <= -7.5e-104)
		tmp = t_3;
	elseif (x <= -1.8e-226)
		tmp = t_1;
	elseif (x <= 9.8e-262)
		tmp = t_3;
	elseif (x <= 6.5e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -9e+25], t$95$2, If[LessEqual[x, -7.5e-104], t$95$3, If[LessEqual[x, -1.8e-226], t$95$1, If[LessEqual[x, 9.8e-262], t$95$3, If[LessEqual[x, 6.5e+99], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000006e25 or 6.5000000000000004e99 < x

   1. Initial program 99.7%

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

      1. flip-- 18.5%

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

      2. clear-num 18.5%

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

      3. associate-+l- 18.5%

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

      4. pow2 18.5%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 18.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around inf 65.8%

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

   if -9.0000000000000006e25 < x < -7.5e-104 or -1.79999999999999997e-226 < x < 9.8000000000000005e-262

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.4%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -7.5e-104 < x < -1.79999999999999997e-226 or 9.8000000000000005e-262 < x < 6.5000000000000004e99

   1. Initial program 100.0%

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

      1. flip-- 62.3%

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

      2. clear-num 62.3%

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

      3. associate-+l- 62.3%

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

      4. pow2 62.3%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in z around 0 49.7%

      \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(\log y \cdot x - y\right)}^{2}}}} + \log t \]

   5. Taylor expanded in y around inf 72.0%

      \[\leadsto \color{blue}{-1 \cdot y} + \log t \]
   6. Step-by-step derivation

      1. neg-mul-1 72.0%

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

   7. Simplified 72.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-104}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-226}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 6: 83.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+186} \lor \neg \left(x \leq 3.3 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -2 + \left(y + \log t\right)\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.72e+186) (not (<= x 3.3e+169)))
   (* x (log y))
   (- (+ (* y -2.0) (+ y (log t))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.72e+186) || !(x <= 3.3e+169)) {
		tmp = x * log(y);
	} else {
		tmp = ((y * -2.0) + (y + log(t))) - 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 <= (-1.72d+186)) .or. (.not. (x <= 3.3d+169))) then
        tmp = x * log(y)
    else
        tmp = ((y * (-2.0d0)) + (y + log(t))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.72e+186) || !(x <= 3.3e+169)) {
		tmp = x * Math.log(y);
	} else {
		tmp = ((y * -2.0) + (y + Math.log(t))) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.72e+186) or not (x <= 3.3e+169):
		tmp = x * math.log(y)
	else:
		tmp = ((y * -2.0) + (y + math.log(t))) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.72e+186) || !(x <= 3.3e+169))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(Float64(y * -2.0) + Float64(y + log(t))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.72e+186) || ~((x <= 3.3e+169)))
		tmp = x * log(y);
	else
		tmp = ((y * -2.0) + (y + log(t))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.72e+186], N[Not[LessEqual[x, 3.3e+169]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -2.0), $MachinePrecision] + N[(y + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.72e186 or 3.2999999999999997e169 < x

   1. Initial program 99.6%

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

      1. flip-- 5.9%

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

      2. clear-num 5.9%

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

      3. associate-+l- 5.9%

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

      4. pow2 5.9%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 5.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.6%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around inf 86.4%

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

   if -1.72e186 < x < 3.2999999999999997e169

   1. Initial program 99.9%

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

      1. flip-- 53.3%

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

      2. clear-num 53.3%

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

      3. associate-+l- 53.3%

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

      4. pow2 53.3%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 53.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around 0 84.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+186} \lor \neg \left(x \leq 3.3 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -2 + \left(y + \log t\right)\right) - z\\ \end{array} \]

Alternative 7: 59.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 1.15 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 1.15e-275)
     t_1
     (if (<= y 5e-229) (* x (log y)) (if (<= y 1.2e+27) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 1.15e-275) {
		tmp = t_1;
	} else if (y <= 5e-229) {
		tmp = x * log(y);
	} else if (y <= 1.2e+27) {
		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 <= 1.15d-275) then
        tmp = t_1
    else if (y <= 5d-229) then
        tmp = x * log(y)
    else if (y <= 1.2d+27) 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 <= 1.15e-275) {
		tmp = t_1;
	} else if (y <= 5e-229) {
		tmp = x * Math.log(y);
	} else if (y <= 1.2e+27) {
		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 <= 1.15e-275:
		tmp = t_1
	elif y <= 5e-229:
		tmp = x * math.log(y)
	elif y <= 1.2e+27:
		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 <= 1.15e-275)
		tmp = t_1;
	elseif (y <= 5e-229)
		tmp = Float64(x * log(y));
	elseif (y <= 1.2e+27)
		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 <= 1.15e-275)
		tmp = t_1;
	elseif (y <= 5e-229)
		tmp = x * log(y);
	elseif (y <= 1.2e+27)
		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, 1.15e-275], t$95$1, If[LessEqual[y, 5e-229], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+27], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.14999999999999995e-275 or 5.00000000000000016e-229 < y < 1.19999999999999999e27

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 97.8%

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

   3. Taylor expanded in x around 0 62.3%

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

   if 1.14999999999999995e-275 < y < 5.00000000000000016e-229

   1. Initial program 99.7%

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

      1. flip-- 46.2%

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

      2. clear-num 46.2%

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

      3. associate-+l- 46.2%

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

      4. pow2 46.2%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 46.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around inf 61.1%

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

   if 1.19999999999999999e27 < y

   1. Initial program 99.9%

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

      1. flip-- 27.0%

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

      2. clear-num 27.0%

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

      3. associate-+l- 27.0%

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

      4. pow2 27.0%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 27.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-275}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 8: 83.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{+186} \lor \neg \left(x \leq 6.2 \cdot 10^{+168}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.3e+186) (not (<= x 6.2e+168)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.3e+186) || !(x <= 6.2e+168)) {
		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 <= (-8.3d+186)) .or. (.not. (x <= 6.2d+168))) 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 <= -8.3e+186) || !(x <= 6.2e+168)) {
		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 <= -8.3e+186) or not (x <= 6.2e+168):
		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 <= -8.3e+186) || !(x <= 6.2e+168))
		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 <= -8.3e+186) || ~((x <= 6.2e+168)))
		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, -8.3e+186], N[Not[LessEqual[x, 6.2e+168]], $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 < -8.3000000000000003e186 or 6.19999999999999993e168 < x

   1. Initial program 99.6%

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

      1. flip-- 5.9%

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

      2. clear-num 5.9%

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

      3. associate-+l- 5.9%

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

      4. pow2 5.9%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 5.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.6%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in x around inf 86.4%

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

   if -8.3000000000000003e186 < x < 6.19999999999999993e168

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{+186} \lor \neg \left(x \leq 6.2 \cdot 10^{+168}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 9: 46.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-175}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-38}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3e-175)
   (- z)
   (if (<= y 1.5e-38) (log t) (if (<= y 1.4e+27) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3e-175) {
		tmp = -z;
	} else if (y <= 1.5e-38) {
		tmp = log(t);
	} else if (y <= 1.4e+27) {
		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 <= 3d-175) then
        tmp = -z
    else if (y <= 1.5d-38) then
        tmp = log(t)
    else if (y <= 1.4d+27) 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 <= 3e-175) {
		tmp = -z;
	} else if (y <= 1.5e-38) {
		tmp = Math.log(t);
	} else if (y <= 1.4e+27) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3e-175:
		tmp = -z
	elif y <= 1.5e-38:
		tmp = math.log(t)
	elif y <= 1.4e+27:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3e-175)
		tmp = Float64(-z);
	elseif (y <= 1.5e-38)
		tmp = log(t);
	elseif (y <= 1.4e+27)
		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 <= 3e-175)
		tmp = -z;
	elseif (y <= 1.5e-38)
		tmp = log(t);
	elseif (y <= 1.4e+27)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3e-175], (-z), If[LessEqual[y, 1.5e-38], N[Log[t], $MachinePrecision], If[LessEqual[y, 1.4e+27], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 3e-175 or 1.49999999999999994e-38 < y < 1.4e27

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 43.0%

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

      1. neg-mul-1 43.0%

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

   4. Simplified 43.0%

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

   if 3e-175 < y < 1.49999999999999994e-38

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in x around 0 59.6%

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

   4. Taylor expanded in z around 0 38.6%

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

   if 1.4e27 < y

   1. Initial program 99.9%

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

      1. flip-- 27.0%

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

      2. clear-num 27.0%

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

      3. associate-+l- 27.0%

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

      4. pow2 27.0%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 27.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-175}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-38}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 48.8% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.3e+27) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e+27) {
		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 <= 1.3d+27) 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 <= 1.3e+27) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.3e+27:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.3e+27)
		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 <= 1.3e+27)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.3e+27], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.30000000000000004e27

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 33.9%

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

      1. neg-mul-1 33.9%

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

   4. Simplified 33.9%

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

   if 1.30000000000000004e27 < y

   1. Initial program 99.9%

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

      1. flip-- 27.0%

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

      2. clear-num 27.0%

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

      3. associate-+l- 27.0%

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

      4. pow2 27.0%

         \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

   3. Applied egg-rr 27.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

   4. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

   5. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 11: 30.4% 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 99.8%

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

   1. flip-- 42.9%

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

   2. clear-num 42.9%

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

   3. associate-+l- 42.9%

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

   4. pow2 42.9%

      \[\leadsto \frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{\color{blue}{{\left(x \cdot \log y - y\right)}^{2}} - z \cdot z}} + \log t \]

3. Applied egg-rr 42.9%

   \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot \log y - \left(y - z\right)}{{\left(x \cdot \log y - y\right)}^{2} - z \cdot z}}} + \log t \]

4. Taylor expanded in x around inf 99.8%

   \[\leadsto \color{blue}{\left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right)} + \log t \]

5. Taylor expanded in y around inf 31.2%

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

   1. mul-1-neg 31.2%

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

7. Simplified 31.2%

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

8. Final simplification 31.2%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023195 
(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)))