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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 9

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. Final simplification 99.9%

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

Alternative 2: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+114} \lor \neg \left(z \leq 1.65 \cdot 10^{+111}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e+114) (not (<= z 1.65e+111)))
   (- (log t) (+ y z))
   (+ (- (* x (log y)) y) (log t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+114) || !(z <= 1.65e+111)) {
		tmp = log(t) - (y + z);
	} else {
		tmp = ((x * log(y)) - y) + log(t);
	}
	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 <= (-1.25d+114)) .or. (.not. (z <= 1.65d+111))) then
        tmp = log(t) - (y + z)
    else
        tmp = ((x * log(y)) - y) + log(t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+114) || !(z <= 1.65e+111)) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = ((x * Math.log(y)) - y) + Math.log(t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e+114) or not (z <= 1.65e+111):
		tmp = math.log(t) - (y + z)
	else:
		tmp = ((x * math.log(y)) - y) + math.log(t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e+114) || !(z <= 1.65e+111))
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(Float64(x * log(y)) - y) + log(t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e+114) || ~((z <= 1.65e+111)))
		tmp = log(t) - (y + z);
	else
		tmp = ((x * log(y)) - y) + log(t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e+114], N[Not[LessEqual[z, 1.65e+111]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e114 or 1.6500000000000001e111 < z

   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%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} + \log t \]
   3. Step-by-step derivation

      1. mul-1-neg 87.9%

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

      2. +-commutative 87.9%

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

      3. distribute-neg-in 87.9%

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

      4. sub-neg 87.9%

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

   4. Simplified 87.9%

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

   if -1.25e114 < z < 1.6500000000000001e111

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.2%

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

      2. pow3 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in z around 0 94.9%

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

      1. pow-base-1 94.9%

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

      2. *-lft-identity 94.9%

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

   6. Simplified 94.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+114} \lor \neg \left(z \leq 1.65 \cdot 10^{+111}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \end{array} \]

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 9.6 \cdot 10^{+14}:\\ \;\;\;\;\log t + \left(t_1 - z\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\left(t_1 - y\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 9.6e+14)
     (+ (log t) (- t_1 z))
     (if (<= y 4.8e+141) (+ (- t_1 y) (log t)) (- (log t) (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 9.6e+14) {
		tmp = log(t) + (t_1 - z);
	} else if (y <= 4.8e+141) {
		tmp = (t_1 - y) + log(t);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 9.6d+14) then
        tmp = log(t) + (t_1 - z)
    else if (y <= 4.8d+141) then
        tmp = (t_1 - y) + log(t)
    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 t_1 = x * Math.log(y);
	double tmp;
	if (y <= 9.6e+14) {
		tmp = Math.log(t) + (t_1 - z);
	} else if (y <= 4.8e+141) {
		tmp = (t_1 - y) + Math.log(t);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 9.6e+14:
		tmp = math.log(t) + (t_1 - z)
	elif y <= 4.8e+141:
		tmp = (t_1 - y) + math.log(t)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 9.6e+14)
		tmp = Float64(log(t) + Float64(t_1 - z));
	elseif (y <= 4.8e+141)
		tmp = Float64(Float64(t_1 - y) + log(t));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 9.6e+14)
		tmp = log(t) + (t_1 - z);
	elseif (y <= 4.8e+141)
		tmp = (t_1 - y) + log(t);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 9.6e+14], N[(N[Log[t], $MachinePrecision] + N[(t$95$1 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+141], N[(N[(t$95$1 - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 9.6e14

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.8%

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

   if 9.6e14 < y < 4.79999999999999995e141

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.4%

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

      2. pow3 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in z around 0 84.1%

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

      1. pow-base-1 84.1%

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

      2. *-lft-identity 84.1%

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

   6. Simplified 84.1%

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

   if 4.79999999999999995e141 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} + \log t \]
   3. Step-by-step derivation

      1. mul-1-neg 94.0%

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

      2. +-commutative 94.0%

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

      3. distribute-neg-in 94.0%

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

      4. sub-neg 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{+14}:\\ \;\;\;\;\log t + \left(x \cdot \log y - z\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 4: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+79} \lor \neg \left(x \leq 2.3 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.2e+79) (not (<= x 2.3e+101)))
   (+ (* x (log y)) (log t))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.2e+79) || !(x <= 2.3e+101)) {
		tmp = (x * log(y)) + log(t);
	} 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 <= (-6.2d+79)) .or. (.not. (x <= 2.3d+101))) then
        tmp = (x * log(y)) + log(t)
    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 <= -6.2e+79) || !(x <= 2.3e+101)) {
		tmp = (x * Math.log(y)) + Math.log(t);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.2e+79) or not (x <= 2.3e+101):
		tmp = (x * math.log(y)) + math.log(t)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.2e+79) || !(x <= 2.3e+101))
		tmp = Float64(Float64(x * log(y)) + log(t));
	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 <= -6.2e+79) || ~((x <= 2.3e+101)))
		tmp = (x * log(y)) + log(t);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.2e+79], N[Not[LessEqual[x, 2.3e+101]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999998e79 or 2.3000000000000001e101 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 91.6%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -6.1999999999999998e79 < x < 2.3000000000000001e101

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} + \log t \]
   3. Step-by-step derivation

      1. mul-1-neg 95.1%

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

      2. +-commutative 95.1%

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

      3. distribute-neg-in 95.1%

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

      4. sub-neg 95.1%

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

   4. Simplified 95.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+79} \lor \neg \left(x \leq 2.3 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 5: 60.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+100} \lor \neg \left(z \leq 2.7 \cdot 10^{+99}\right):\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+100) (not (<= z 2.7e+99))) (- (log t) z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+100) || !(z <= 2.7e+99)) {
		tmp = log(t) - z;
	} else {
		tmp = log(t) - 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 ((z <= (-7.5d+100)) .or. (.not. (z <= 2.7d+99))) then
        tmp = log(t) - z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+100) || !(z <= 2.7e+99)) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+100) or not (z <= 2.7e+99):
		tmp = math.log(t) - z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+100) || !(z <= 2.7e+99))
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+100) || ~((z <= 2.7e+99)))
		tmp = log(t) - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+100], N[Not[LessEqual[z, 2.7e+99]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999983e100 or 2.69999999999999989e99 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. neg-mul-1 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in z around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   if -7.49999999999999983e100 < z < 2.69999999999999989e99

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.2%

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

      2. pow3 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in y around inf 58.6%

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

      1. neg-mul-1 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. sub-neg 58.6%

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

   9. Simplified 58.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+100} \lor \neg \left(z \leq 2.7 \cdot 10^{+99}\right):\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 6: 70.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 68.9%

   \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} + \log t \]
3. Step-by-step derivation

   1. mul-1-neg 68.9%

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

   2. +-commutative 68.9%

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

   3. distribute-neg-in 68.9%

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

   4. sub-neg 68.9%

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

4. Simplified 68.9%

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

5. Final simplification 68.9%

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

Alternative 7: 42.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 105:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 105.0) (log t) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 105.0) {
		tmp = log(t);
	} 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 <= 105.0d0) then
        tmp = log(t)
    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 <= 105.0) {
		tmp = Math.log(t);
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 105.0:
		tmp = math.log(t)
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 105.0)
		tmp = log(t);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 105.0)
		tmp = log(t);
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 105.0], N[Log[t], $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 105

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 57.3%

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

      1. neg-mul-1 57.3%

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

   4. Simplified 57.3%

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

   5. Taylor expanded in z around 0 26.1%

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

   if 105 < y

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. neg-mul-1 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in y around inf 62.9%

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

      1. mul-1-neg 62.9%

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

   9. Simplified 62.9%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 105:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 8: 43.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] - y), $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. add-cube-cbrt 99.4%

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

   2. pow3 99.4%

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

3. Applied egg-rr 99.4%

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

4. Taylor expanded in y around inf 43.2%

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

   1. neg-mul-1 43.2%

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

6. Simplified 43.2%

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

7. Taylor expanded in y around 0 43.2%

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

   1. mul-1-neg 43.2%

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

   2. sub-neg 43.2%

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

9. Simplified 43.2%

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

10. Final simplification 43.2%

    \[\leadsto \log t - y \]

Alternative 9: 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 99.9%

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

   1. add-cube-cbrt 99.4%

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

   2. pow3 99.4%

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

3. Applied egg-rr 99.4%

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

4. Taylor expanded in y around inf 43.2%

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

   1. neg-mul-1 43.2%

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

6. Simplified 43.2%

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

7. Taylor expanded in y around inf 29.4%

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

   1. mul-1-neg 29.4%

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

9. Simplified 29.4%

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

10. Final simplification 29.4%

    \[\leadsto -y \]

Reproduce

herbie shell --seed 2023298 
(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)))