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

Percentage Accurate: 99.9% → 99.9%

Time: 15.7s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 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 99.9%

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

Alternative 2: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - \left(y + z\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+22}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) (+ y z))))
   (if (<= z -8.2e+86)
     t_1
     (if (<= z 1.25e+22) (+ (- (* x (log y)) y) (log t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - (y + z);
	double tmp;
	if (z <= -8.2e+86) {
		tmp = t_1;
	} else if (z <= 1.25e+22) {
		tmp = ((x * log(y)) - y) + log(t);
	} 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 = log(t) - (y + z)
    if (z <= (-8.2d+86)) then
        tmp = t_1
    else if (z <= 1.25d+22) then
        tmp = ((x * log(y)) - y) + log(t)
    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 = Math.log(t) - (y + z);
	double tmp;
	if (z <= -8.2e+86) {
		tmp = t_1;
	} else if (z <= 1.25e+22) {
		tmp = ((x * Math.log(y)) - y) + Math.log(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - (y + z)
	tmp = 0
	if z <= -8.2e+86:
		tmp = t_1
	elif z <= 1.25e+22:
		tmp = ((x * math.log(y)) - y) + math.log(t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - Float64(y + z))
	tmp = 0.0
	if (z <= -8.2e+86)
		tmp = t_1;
	elseif (z <= 1.25e+22)
		tmp = Float64(Float64(Float64(x * log(y)) - y) + log(t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - (y + z);
	tmp = 0.0;
	if (z <= -8.2e+86)
		tmp = t_1;
	elseif (z <= 1.25e+22)
		tmp = ((x * log(y)) - y) + log(t);
	else
		tmp = t_1;
	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]}, If[LessEqual[z, -8.2e+86], t$95$1, If[LessEqual[z, 1.25e+22], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e86 or 1.2499999999999999e22 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.1999999999999998e86 < z < 1.2499999999999999e22

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.105:\\ \;\;\;\;\left(x \cdot \log y - z\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(-1 - \frac{z}{y}\right) - \left(0 - \log y \cdot \frac{x}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.105)
   (+ (- (* x (log y)) z) (log t))
   (* y (- (- -1.0 (/ z y)) (- 0.0 (* (log y) (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.105) {
		tmp = ((x * log(y)) - z) + log(t);
	} else {
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (log(y) * (x / 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 <= 0.105d0) then
        tmp = ((x * log(y)) - z) + log(t)
    else
        tmp = y * (((-1.0d0) - (z / y)) - (0.0d0 - (log(y) * (x / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.105) {
		tmp = ((x * Math.log(y)) - z) + Math.log(t);
	} else {
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (Math.log(y) * (x / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 0.105:
		tmp = ((x * math.log(y)) - z) + math.log(t)
	else:
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (math.log(y) * (x / y))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.105)
		tmp = Float64(Float64(Float64(x * log(y)) - z) + log(t));
	else
		tmp = Float64(y * Float64(Float64(-1.0 - Float64(z / y)) - Float64(0.0 - Float64(log(y) * Float64(x / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 0.105)
		tmp = ((x * log(y)) - z) + log(t);
	else
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (log(y) * (x / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.105], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(0.0 - N[(N[Log[y], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.104999999999999996

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 0.104999999999999996 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 4: 86.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+23}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \left(\left(-1 - \frac{z}{y}\right) - \left(0 - \log y \cdot \frac{x}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -6.4e+140)
     t_1
     (if (<= x 1.38e+23)
       (- (log t) (+ y z))
       (if (<= x 3.3e+199)
         (* y (- (- -1.0 (/ z y)) (- 0.0 (* (log y) (/ x y)))))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -6.4e+140) {
		tmp = t_1;
	} else if (x <= 1.38e+23) {
		tmp = log(t) - (y + z);
	} else if (x <= 3.3e+199) {
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (log(y) * (x / 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 <= (-6.4d+140)) then
        tmp = t_1
    else if (x <= 1.38d+23) then
        tmp = log(t) - (y + z)
    else if (x <= 3.3d+199) then
        tmp = y * (((-1.0d0) - (z / y)) - (0.0d0 - (log(y) * (x / 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 <= -6.4e+140) {
		tmp = t_1;
	} else if (x <= 1.38e+23) {
		tmp = Math.log(t) - (y + z);
	} else if (x <= 3.3e+199) {
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (Math.log(y) * (x / y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -6.4e+140:
		tmp = t_1
	elif x <= 1.38e+23:
		tmp = math.log(t) - (y + z)
	elif x <= 3.3e+199:
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (math.log(y) * (x / 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 <= -6.4e+140)
		tmp = t_1;
	elseif (x <= 1.38e+23)
		tmp = Float64(log(t) - Float64(y + z));
	elseif (x <= 3.3e+199)
		tmp = Float64(y * Float64(Float64(-1.0 - Float64(z / y)) - Float64(0.0 - Float64(log(y) * Float64(x / 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 <= -6.4e+140)
		tmp = t_1;
	elseif (x <= 1.38e+23)
		tmp = log(t) - (y + z);
	elseif (x <= 3.3e+199)
		tmp = y * ((-1.0 - (z / y)) - (0.0 - (log(y) * (x / 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, -6.4e+140], t$95$1, If[LessEqual[x, 1.38e+23], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+199], N[(y * N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(0.0 - N[(N[Log[y], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.40000000000000021e140 or 3.2999999999999998e199 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.40000000000000021e140 < x < 1.38e23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.38e23 < x < 3.2999999999999998e199

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 5: 59.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-123}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)))
   (if (<= z -4.4e+88)
     (- z)
     (if (<= z 3.3e-158)
       t_1
       (if (<= z 1e-123) (* x (log y)) (if (<= z 1.55e+66) t_1 (- z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double tmp;
	if (z <= -4.4e+88) {
		tmp = -z;
	} else if (z <= 3.3e-158) {
		tmp = t_1;
	} else if (z <= 1e-123) {
		tmp = x * log(y);
	} else if (z <= 1.55e+66) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - y
    if (z <= (-4.4d+88)) then
        tmp = -z
    else if (z <= 3.3d-158) then
        tmp = t_1
    else if (z <= 1d-123) then
        tmp = x * log(y)
    else if (z <= 1.55d+66) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - y;
	double tmp;
	if (z <= -4.4e+88) {
		tmp = -z;
	} else if (z <= 3.3e-158) {
		tmp = t_1;
	} else if (z <= 1e-123) {
		tmp = x * Math.log(y);
	} else if (z <= 1.55e+66) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	tmp = 0
	if z <= -4.4e+88:
		tmp = -z
	elif z <= 3.3e-158:
		tmp = t_1
	elif z <= 1e-123:
		tmp = x * math.log(y)
	elif z <= 1.55e+66:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	tmp = 0.0
	if (z <= -4.4e+88)
		tmp = Float64(-z);
	elseif (z <= 3.3e-158)
		tmp = t_1;
	elseif (z <= 1e-123)
		tmp = Float64(x * log(y));
	elseif (z <= 1.55e+66)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	tmp = 0.0;
	if (z <= -4.4e+88)
		tmp = -z;
	elseif (z <= 3.3e-158)
		tmp = t_1;
	elseif (z <= 1e-123)
		tmp = x * log(y);
	elseif (z <= 1.55e+66)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[z, -4.4e+88], (-z), If[LessEqual[z, 3.3e-158], t$95$1, If[LessEqual[z, 1e-123], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+66], t$95$1, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000017e88 or 1.55000000000000009e66 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.40000000000000017e88 < z < 3.3000000000000002e-158 or 1.0000000000000001e-123 < z < 1.55000000000000009e66

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.3000000000000002e-158 < z < 1.0000000000000001e-123

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 6: 47.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+89}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-234}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 10^{-123}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+55}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+89)
   (- z)
   (if (<= z 2e-234)
     (- y)
     (if (<= z 1e-123) (* x (log y)) (if (<= z 1.9e+55) (- y) (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+89) {
		tmp = -z;
	} else if (z <= 2e-234) {
		tmp = -y;
	} else if (z <= 1e-123) {
		tmp = x * log(y);
	} else if (z <= 1.9e+55) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+89)) then
        tmp = -z
    else if (z <= 2d-234) then
        tmp = -y
    else if (z <= 1d-123) then
        tmp = x * log(y)
    else if (z <= 1.9d+55) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+89) {
		tmp = -z;
	} else if (z <= 2e-234) {
		tmp = -y;
	} else if (z <= 1e-123) {
		tmp = x * Math.log(y);
	} else if (z <= 1.9e+55) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+89:
		tmp = -z
	elif z <= 2e-234:
		tmp = -y
	elif z <= 1e-123:
		tmp = x * math.log(y)
	elif z <= 1.9e+55:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+89)
		tmp = Float64(-z);
	elseif (z <= 2e-234)
		tmp = Float64(-y);
	elseif (z <= 1e-123)
		tmp = Float64(x * log(y));
	elseif (z <= 1.9e+55)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+89)
		tmp = -z;
	elseif (z <= 2e-234)
		tmp = -y;
	elseif (z <= 1e-123)
		tmp = x * log(y);
	elseif (z <= 1.9e+55)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+89], (-z), If[LessEqual[z, 2e-234], (-y), If[LessEqual[z, 1e-123], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+55], (-y), (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999995e88 or 1.9e55 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -9.99999999999999995e88 < z < 1.9999999999999999e-234 or 1.0000000000000001e-123 < z < 1.9e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.9999999999999999e-234 < z < 1.0000000000000001e-123

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 7: 46.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-230}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-160}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+87)
   (- z)
   (if (<= z 1.02e-230)
     (- y)
     (if (<= z 3.9e-160) (log t) (if (<= z 4.5e+55) (- y) (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+87) {
		tmp = -z;
	} else if (z <= 1.02e-230) {
		tmp = -y;
	} else if (z <= 3.9e-160) {
		tmp = log(t);
	} else if (z <= 4.5e+55) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d+87)) then
        tmp = -z
    else if (z <= 1.02d-230) then
        tmp = -y
    else if (z <= 3.9d-160) then
        tmp = log(t)
    else if (z <= 4.5d+55) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+87) {
		tmp = -z;
	} else if (z <= 1.02e-230) {
		tmp = -y;
	} else if (z <= 3.9e-160) {
		tmp = Math.log(t);
	} else if (z <= 4.5e+55) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+87:
		tmp = -z
	elif z <= 1.02e-230:
		tmp = -y
	elif z <= 3.9e-160:
		tmp = math.log(t)
	elif z <= 4.5e+55:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+87)
		tmp = Float64(-z);
	elseif (z <= 1.02e-230)
		tmp = Float64(-y);
	elseif (z <= 3.9e-160)
		tmp = log(t);
	elseif (z <= 4.5e+55)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+87)
		tmp = -z;
	elseif (z <= 1.02e-230)
		tmp = -y;
	elseif (z <= 3.9e-160)
		tmp = log(t);
	elseif (z <= 4.5e+55)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+87], (-z), If[LessEqual[z, 1.02e-230], (-y), If[LessEqual[z, 3.9e-160], N[Log[t], $MachinePrecision], If[LessEqual[z, 4.5e+55], (-y), (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999963e87 or 4.49999999999999998e55 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.79999999999999963e87 < z < 1.02e-230 or 3.89999999999999989e-160 < z < 4.49999999999999998e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.02e-230 < z < 3.89999999999999989e-160

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 8: 83.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+172}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.3e+141) t_1 (if (<= x 2.95e+172) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.3e+141) {
		tmp = t_1;
	} else if (x <= 2.95e+172) {
		tmp = log(t) - (y + z);
	} 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 <= (-1.3d+141)) then
        tmp = t_1
    else if (x <= 2.95d+172) then
        tmp = log(t) - (y + z)
    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 <= -1.3e+141) {
		tmp = t_1;
	} else if (x <= 2.95e+172) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.3e+141:
		tmp = t_1
	elif x <= 2.95e+172:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.3e+141)
		tmp = t_1;
	elseif (x <= 2.95e+172)
		tmp = Float64(log(t) - Float64(y + z));
	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 <= -1.3e+141)
		tmp = t_1;
	elseif (x <= 2.95e+172)
		tmp = log(t) - (y + z);
	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, -1.3e+141], t$95$1, If[LessEqual[x, 2.95e+172], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e141 or 2.9499999999999999e172 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.3e141 < x < 2.9499999999999999e172

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 9: 47.5% accurate, 17.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+88}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+53}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+88) (- z) (if (<= z 7.2e+53) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+88) {
		tmp = -z;
	} else if (z <= 7.2e+53) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d+88)) then
        tmp = -z
    else if (z <= 7.2d+53) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+88) {
		tmp = -z;
	} else if (z <= 7.2e+53) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+88:
		tmp = -z
	elif z <= 7.2e+53:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+88)
		tmp = Float64(-z);
	elseif (z <= 7.2e+53)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+88)
		tmp = -z;
	elseif (z <= 7.2e+53)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+88], (-z), If[LessEqual[z, 7.2e+53], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999984e88 or 7.2e53 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -3.99999999999999984e88 < z < 7.2e53

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

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

Alternative 10: 30.2% 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. Add Preprocessing

3. Taylor expanded in y around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))