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

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -8500000000000:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -8500000000000.0)
     (- t_1 z)
     (if (<= z 2.9e+55) (- (+ (log t) t_1) y) (- (- z) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -8500000000000.0) {
		tmp = t_1 - z;
	} else if (z <= 2.9e+55) {
		tmp = (log(t) + t_1) - y;
	} else {
		tmp = -z - 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 = x * log(y)
    if (z <= (-8500000000000.0d0)) then
        tmp = t_1 - z
    else if (z <= 2.9d+55) then
        tmp = (log(t) + t_1) - y
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -8500000000000.0) {
		tmp = t_1 - z;
	} else if (z <= 2.9e+55) {
		tmp = (Math.log(t) + t_1) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -8500000000000.0:
		tmp = t_1 - z
	elif z <= 2.9e+55:
		tmp = (math.log(t) + t_1) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -8500000000000.0)
		tmp = Float64(t_1 - z);
	elseif (z <= 2.9e+55)
		tmp = Float64(Float64(log(t) + t_1) - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -8500000000000.0)
		tmp = t_1 - z;
	elseif (z <= 2.9e+55)
		tmp = (log(t) + t_1) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8500000000000.0], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[z, 2.9e+55], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e12

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 99.6%

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

      5. associate-*r* 99.6%

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

      6. fma-def 99.6%

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

      7. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in y around 0 85.0%

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

      1. pow-base-1 85.0%

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

      2. associate-*r* 85.0%

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

      3. *-lft-identity 85.0%

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

   7. Simplified 85.0%

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

   if -8.5e12 < z < 2.8999999999999999e55

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 97.6%

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

   if 2.8999999999999999e55 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 100.0%

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

      5. associate-*r* 99.9%

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

      6. fma-def 99.9%

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

      7. pow2 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in x around 0 91.2%

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

      1. mul-1-neg 91.2%

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

      2. +-commutative 91.2%

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

      3. distribute-neg-in 91.2%

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

      4. sub-neg 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8500000000000:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 3: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;z \leq -5000000000000:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t_1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= z -5000000000000.0)
     (- t_1 z)
     (if (<= z 1.5e+55) (- t_1 y) (- (- z) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (z <= -5000000000000.0) {
		tmp = t_1 - z;
	} else if (z <= 1.5e+55) {
		tmp = t_1 - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) + (x * log(y))
    if (z <= (-5000000000000.0d0)) then
        tmp = t_1 - z
    else if (z <= 1.5d+55) then
        tmp = t_1 - y
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) + (x * Math.log(y));
	double tmp;
	if (z <= -5000000000000.0) {
		tmp = t_1 - z;
	} else if (z <= 1.5e+55) {
		tmp = t_1 - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if z <= -5000000000000.0:
		tmp = t_1 - z
	elif z <= 1.5e+55:
		tmp = t_1 - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (z <= -5000000000000.0)
		tmp = Float64(t_1 - z);
	elseif (z <= 1.5e+55)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (z <= -5000000000000.0)
		tmp = t_1 - z;
	elseif (z <= 1.5e+55)
		tmp = t_1 - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5000000000000.0], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[z, 1.5e+55], N[(t$95$1 - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.4%

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

   if -5e12 < z < 1.50000000000000008e55

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 97.6%

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

   if 1.50000000000000008e55 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 100.0%

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

      5. associate-*r* 99.9%

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

      6. fma-def 99.9%

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

      7. pow2 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in x around 0 91.2%

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

      1. mul-1-neg 91.2%

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

      2. +-commutative 91.2%

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

      3. distribute-neg-in 91.2%

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

      4. sub-neg 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000000000000:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 4: 87.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+143} \lor \neg \left(x \leq -2.5 \cdot 10^{+96}\right) \land \left(x \leq -1.45 \cdot 10^{+40} \lor \neg \left(x \leq 2.5 \cdot 10^{+125}\right)\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e+143)
         (and (not (<= x -2.5e+96))
              (or (<= x -1.45e+40) (not (<= x 2.5e+125)))))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+143) || (!(x <= -2.5e+96) && ((x <= -1.45e+40) || !(x <= 2.5e+125)))) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.8d+143)) .or. (.not. (x <= (-2.5d+96))) .and. (x <= (-1.45d+40)) .or. (.not. (x <= 2.5d+125))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+143) || (!(x <= -2.5e+96) && ((x <= -1.45e+40) || !(x <= 2.5e+125)))) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e+143) or (not (x <= -2.5e+96) and ((x <= -1.45e+40) or not (x <= 2.5e+125))):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e+143) || (!(x <= -2.5e+96) && ((x <= -1.45e+40) || !(x <= 2.5e+125))))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e+143) || (~((x <= -2.5e+96)) && ((x <= -1.45e+40) || ~((x <= 2.5e+125)))))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e+143], And[N[Not[LessEqual[x, -2.5e+96]], $MachinePrecision], Or[LessEqual[x, -1.45e+40], N[Not[LessEqual[x, 2.5e+125]], $MachinePrecision]]]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8e143 or -2.5000000000000002e96 < x < -1.45000000000000009e40 or 2.49999999999999981e125 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. associate--l+ 99.7%

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

      4. add-cube-cbrt 98.7%

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

      5. associate-*r* 98.7%

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

      6. fma-def 98.7%

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

      7. pow2 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. pow-base-1 87.0%

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

      2. *-commutative 87.0%

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

      3. *-lft-identity 87.0%

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

      4. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   if -3.8e143 < x < -2.5000000000000002e96 or -1.45000000000000009e40 < x < 2.49999999999999981e125

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+143} \lor \neg \left(x \leq -2.5 \cdot 10^{+96}\right) \land \left(x \leq -1.45 \cdot 10^{+40} \lor \neg \left(x \leq 2.5 \cdot 10^{+125}\right)\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 5: 89.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t_1 - z\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+41}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 z)))
   (if (<= x -9.5e+20)
     t_2
     (if (<= x 9.8e+41)
       (- (log t) (+ y z))
       (if (<= x 1.25e+93) t_2 (if (<= x 2.2e+125) (- (- z) y) (- t_1 y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -9.5e+20) {
		tmp = t_2;
	} else if (x <= 9.8e+41) {
		tmp = log(t) - (y + z);
	} else if (x <= 1.25e+93) {
		tmp = t_2;
	} else if (x <= 2.2e+125) {
		tmp = -z - y;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - z
    if (x <= (-9.5d+20)) then
        tmp = t_2
    else if (x <= 9.8d+41) then
        tmp = log(t) - (y + z)
    else if (x <= 1.25d+93) then
        tmp = t_2
    else if (x <= 2.2d+125) then
        tmp = -z - y
    else
        tmp = t_1 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - z;
	double tmp;
	if (x <= -9.5e+20) {
		tmp = t_2;
	} else if (x <= 9.8e+41) {
		tmp = Math.log(t) - (y + z);
	} else if (x <= 1.25e+93) {
		tmp = t_2;
	} else if (x <= 2.2e+125) {
		tmp = -z - y;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - z
	tmp = 0
	if x <= -9.5e+20:
		tmp = t_2
	elif x <= 9.8e+41:
		tmp = math.log(t) - (y + z)
	elif x <= 1.25e+93:
		tmp = t_2
	elif x <= 2.2e+125:
		tmp = -z - y
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - z)
	tmp = 0.0
	if (x <= -9.5e+20)
		tmp = t_2;
	elseif (x <= 9.8e+41)
		tmp = Float64(log(t) - Float64(y + z));
	elseif (x <= 1.25e+93)
		tmp = t_2;
	elseif (x <= 2.2e+125)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - z;
	tmp = 0.0;
	if (x <= -9.5e+20)
		tmp = t_2;
	elseif (x <= 9.8e+41)
		tmp = log(t) - (y + z);
	elseif (x <= 1.25e+93)
		tmp = t_2;
	elseif (x <= 2.2e+125)
		tmp = -z - y;
	else
		tmp = t_1 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, If[LessEqual[x, -9.5e+20], t$95$2, If[LessEqual[x, 9.8e+41], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+93], t$95$2, If[LessEqual[x, 2.2e+125], N[((-z) - y), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.5e20 or 9.7999999999999998e41 < x < 1.25e93

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. add-cube-cbrt 99.2%

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

      5. associate-*r* 99.1%

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

      6. fma-def 99.2%

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

      7. pow2 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. pow-base-1 84.6%

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

      2. associate-*r* 84.6%

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

      3. *-lft-identity 84.6%

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

   7. Simplified 84.6%

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

   if -9.5e20 < x < 9.7999999999999998e41

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.7%

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

   if 1.25e93 < x < 2.19999999999999991e125

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 100.0%

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

      5. associate-*r* 100.0%

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

      6. fma-def 100.0%

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

      7. pow2 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in x around 0 87.6%

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

      1. mul-1-neg 87.6%

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

      2. +-commutative 87.6%

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

      3. distribute-neg-in 87.6%

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

      4. sub-neg 87.6%

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

   7. Simplified 87.6%

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

   if 2.19999999999999991e125 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. add-cube-cbrt 98.4%

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

      5. associate-*r* 98.5%

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

      6. fma-def 98.5%

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

      7. pow2 98.5%

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

   3. Applied egg-rr 98.5%

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

   4. Taylor expanded in z around inf 98.5%

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

   5. Taylor expanded in z around 0 91.5%

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

      1. pow-base-1 91.5%

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

      2. *-commutative 91.5%

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

      3. *-lft-identity 91.5%

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

      4. *-commutative 91.5%

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

   7. Simplified 91.5%

      \[\leadsto \color{blue}{\log y \cdot x - y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+41}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 6: 69.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-z\right) - y\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- z) y)))
   (if (<= x -1.75e+146)
     t_1
     (if (<= x -5.8e-207)
       t_2
       (if (<= x -2.6e-226) (log t) (if (<= x 1.26e+150) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -z - y;
	double tmp;
	if (x <= -1.75e+146) {
		tmp = t_1;
	} else if (x <= -5.8e-207) {
		tmp = t_2;
	} else if (x <= -2.6e-226) {
		tmp = log(t);
	} else if (x <= 1.26e+150) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = -z - y
    if (x <= (-1.75d+146)) then
        tmp = t_1
    else if (x <= (-5.8d-207)) then
        tmp = t_2
    else if (x <= (-2.6d-226)) then
        tmp = log(t)
    else if (x <= 1.26d+150) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = -z - y;
	double tmp;
	if (x <= -1.75e+146) {
		tmp = t_1;
	} else if (x <= -5.8e-207) {
		tmp = t_2;
	} else if (x <= -2.6e-226) {
		tmp = Math.log(t);
	} else if (x <= 1.26e+150) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -z - y
	tmp = 0
	if x <= -1.75e+146:
		tmp = t_1
	elif x <= -5.8e-207:
		tmp = t_2
	elif x <= -2.6e-226:
		tmp = math.log(t)
	elif x <= 1.26e+150:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (x <= -1.75e+146)
		tmp = t_1;
	elseif (x <= -5.8e-207)
		tmp = t_2;
	elseif (x <= -2.6e-226)
		tmp = log(t);
	elseif (x <= 1.26e+150)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = -z - y;
	tmp = 0.0;
	if (x <= -1.75e+146)
		tmp = t_1;
	elseif (x <= -5.8e-207)
		tmp = t_2;
	elseif (x <= -2.6e-226)
		tmp = log(t);
	elseif (x <= 1.26e+150)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[x, -1.75e+146], t$95$1, If[LessEqual[x, -5.8e-207], t$95$2, If[LessEqual[x, -2.6e-226], N[Log[t], $MachinePrecision], If[LessEqual[x, 1.26e+150], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e146 or 1.26e150 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. associate--l+ 99.7%

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

      4. add-cube-cbrt 98.7%

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

      5. associate-*r* 98.7%

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

      6. fma-def 98.7%

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

      7. pow2 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. pow-base-1 75.2%

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

      2. associate-*r* 75.2%

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

      3. *-lft-identity 75.2%

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

   7. Simplified 75.2%

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

   if -1.7500000000000001e146 < x < -5.80000000000000022e-207 or -2.5999999999999998e-226 < x < 1.26e150

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 99.8%

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

      5. associate-*r* 99.8%

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

      6. fma-def 99.8%

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

      7. pow2 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 86.7%

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

   5. Taylor expanded in x around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. distribute-neg-in 75.5%

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

      4. sub-neg 75.5%

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

   7. Simplified 75.5%

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

   if -5.80000000000000022e-207 < x < -2.5999999999999998e-226

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. add-log-exp 99.7%

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

      3. sum-log 100.0%

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

      4. associate--l- 100.0%

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

      5. exp-diff 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around 0 86.9%

      \[\leadsto \color{blue}{\log \left(\frac{t}{e^{y}}\right)} \]
   6. Step-by-step derivation

      1. log-div 86.9%

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

      2. rem-log-exp 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around 0 86.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-207}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+150}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 7: 67.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) - y\\ \mathbf{if}\;z \leq -6900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- z) y)))
   (if (<= z -6900000000.0)
     t_1
     (if (<= z 4.2e-52)
       (- (log t) y)
       (if (<= z 1.25e+55) (* x (log y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double tmp;
	if (z <= -6900000000.0) {
		tmp = t_1;
	} else if (z <= 4.2e-52) {
		tmp = log(t) - y;
	} else if (z <= 1.25e+55) {
		tmp = x * log(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 = -z - y
    if (z <= (-6900000000.0d0)) then
        tmp = t_1
    else if (z <= 4.2d-52) then
        tmp = log(t) - y
    else if (z <= 1.25d+55) then
        tmp = x * log(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 = -z - y;
	double tmp;
	if (z <= -6900000000.0) {
		tmp = t_1;
	} else if (z <= 4.2e-52) {
		tmp = Math.log(t) - y;
	} else if (z <= 1.25e+55) {
		tmp = x * Math.log(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z - y
	tmp = 0
	if z <= -6900000000.0:
		tmp = t_1
	elif z <= 4.2e-52:
		tmp = math.log(t) - y
	elif z <= 1.25e+55:
		tmp = x * math.log(y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (z <= -6900000000.0)
		tmp = t_1;
	elseif (z <= 4.2e-52)
		tmp = Float64(log(t) - y);
	elseif (z <= 1.25e+55)
		tmp = Float64(x * log(y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z - y;
	tmp = 0.0;
	if (z <= -6900000000.0)
		tmp = t_1;
	elseif (z <= 4.2e-52)
		tmp = log(t) - y;
	elseif (z <= 1.25e+55)
		tmp = x * log(y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[z, -6900000000.0], t$95$1, If[LessEqual[z, 4.2e-52], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[z, 1.25e+55], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9e9 or 1.25000000000000011e55 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. add-cube-cbrt 99.8%

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

      5. associate-*r* 99.8%

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

      6. fma-def 99.8%

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

      7. pow2 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 99.5%

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

   5. Taylor expanded in x around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. +-commutative 84.9%

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

      3. distribute-neg-in 84.9%

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

      4. sub-neg 84.9%

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

   7. Simplified 84.9%

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

   if -6.9e9 < z < 4.1999999999999997e-52

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-log-exp 30.4%

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

      3. sum-log 30.5%

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

      4. associate--l- 30.5%

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

      5. exp-diff 29.4%

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

      6. *-commutative 29.4%

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

      7. exp-to-pow 29.4%

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

   3. Applied egg-rr 29.4%

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

   4. Taylor expanded in x around 0 28.8%

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

   5. Taylor expanded in z around 0 28.1%

      \[\leadsto \color{blue}{\log \left(\frac{t}{e^{y}}\right)} \]
   6. Step-by-step derivation

      1. log-div 28.0%

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

      2. rem-log-exp 66.7%

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

   7. Simplified 66.7%

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

   if 4.1999999999999997e-52 < z < 1.25000000000000011e55

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. add-cube-cbrt 99.0%

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

      5. associate-*r* 98.9%

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

      6. fma-def 98.9%

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

      7. pow2 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in z around inf 90.1%

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

   5. Taylor expanded in x around inf 61.9%

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

      1. pow-base-1 61.9%

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

      2. associate-*r* 61.9%

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

      3. *-lft-identity 61.9%

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

   7. Simplified 61.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6900000000:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 8: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+146} \lor \neg \left(x \leq 8.6 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e+146) (not (<= x 8.6e+145)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e+146) || !(x <= 8.6e+145)) {
		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 <= (-5.8d+146)) .or. (.not. (x <= 8.6d+145))) 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 <= -5.8e+146) || !(x <= 8.6e+145)) {
		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 <= -5.8e+146) or not (x <= 8.6e+145):
		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 <= -5.8e+146) || !(x <= 8.6e+145))
		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 <= -5.8e+146) || ~((x <= 8.6e+145)))
		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, -5.8e+146], N[Not[LessEqual[x, 8.6e+145]], $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 < -5.7999999999999997e146 or 8.59999999999999996e145 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. associate--l+ 99.7%

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

      4. add-cube-cbrt 98.7%

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

      5. associate-*r* 98.7%

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

      6. fma-def 98.7%

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

      7. pow2 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. pow-base-1 75.2%

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

      2. associate-*r* 75.2%

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

      3. *-lft-identity 75.2%

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

   7. Simplified 75.2%

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

   if -5.7999999999999997e146 < x < 8.59999999999999996e145

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+146} \lor \neg \left(x \leq 8.6 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 9: 47.6% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.5e+69) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.5e+69) {
		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 <= 1.5d+69) 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 <= 1.5e+69) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.5e+69:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.5e+69)
		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 <= 1.5e+69)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.5e+69], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.49999999999999992e69

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 45.8%

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

      1. mul-1-neg 45.8%

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

   4. Simplified 45.8%

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

   if 1.49999999999999992e69 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 64.5%

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

      1. neg-mul-1 64.5%

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

   4. Simplified 64.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 57.3% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-z) - 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. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. associate--l+ 99.9%

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

   4. add-cube-cbrt 99.5%

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

   5. associate-*r* 99.5%

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

   6. fma-def 99.5%

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

   7. pow2 99.5%

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

3. Applied egg-rr 99.5%

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

4. Taylor expanded in z around inf 88.0%

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

5. Taylor expanded in x around 0 62.1%

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

   1. mul-1-neg 62.1%

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

   2. +-commutative 62.1%

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

   3. distribute-neg-in 62.1%

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

   4. sub-neg 62.1%

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

7. Simplified 62.1%

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

8. Final simplification 62.1%

   \[\leadsto \left(-z\right) - y \]

Alternative 11: 29.4% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around inf 27.6%

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

   1. neg-mul-1 27.6%

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

4. Simplified 27.6%

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

5. Final simplification 27.6%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023185 
(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)))