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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.1e+102) (- (+ (* x (log y)) (log t)) z) (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.1e+102) {
		tmp = ((x * log(y)) + log(t)) - z;
	} 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 (y <= 3.1d+102) then
        tmp = ((x * log(y)) + log(t)) - z
    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 (y <= 3.1e+102) {
		tmp = ((x * Math.log(y)) + Math.log(t)) - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.1e+102:
		tmp = ((x * math.log(y)) + math.log(t)) - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.1e+102)
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - z);
	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 (y <= 3.1e+102)
		tmp = ((x * log(y)) + log(t)) - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.1e+102], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.09999999999999987e102

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 95.5%

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

   if 3.09999999999999987e102 < y

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= x -2.4e+119)
     t_2
     (if (<= x 4.8e+42)
       (- (log t) (+ y z))
       (if (<= x 2.1e+126) t_2 (- t_1 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (x <= -2.4e+119) {
		tmp = t_2;
	} else if (x <= 4.8e+42) {
		tmp = log(t) - (y + z);
	} else if (x <= 2.1e+126) {
		tmp = t_2;
	} else {
		tmp = t_1 - 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (x <= (-2.4d+119)) then
        tmp = t_2
    else if (x <= 4.8d+42) then
        tmp = log(t) - (y + z)
    else if (x <= 2.1d+126) then
        tmp = t_2
    else
        tmp = t_1 - 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 t_2 = t_1 - y;
	double tmp;
	if (x <= -2.4e+119) {
		tmp = t_2;
	} else if (x <= 4.8e+42) {
		tmp = Math.log(t) - (y + z);
	} else if (x <= 2.1e+126) {
		tmp = t_2;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if x <= -2.4e+119:
		tmp = t_2
	elif x <= 4.8e+42:
		tmp = math.log(t) - (y + z)
	elif x <= 2.1e+126:
		tmp = t_2
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (x <= -2.4e+119)
		tmp = t_2;
	elseif (x <= 4.8e+42)
		tmp = Float64(log(t) - Float64(y + z));
	elseif (x <= 2.1e+126)
		tmp = t_2;
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (x <= -2.4e+119)
		tmp = t_2;
	elseif (x <= 4.8e+42)
		tmp = log(t) - (y + z);
	elseif (x <= 2.1e+126)
		tmp = t_2;
	else
		tmp = t_1 - z;
	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 - y), $MachinePrecision]}, If[LessEqual[x, -2.4e+119], t$95$2, If[LessEqual[x, 4.8e+42], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+126], t$95$2, N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e119 or 4.7999999999999997e42 < x < 2.0999999999999999e126

   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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.9%

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

   if -2.4e119 < x < 4.7999999999999997e42

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 95.9%

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

   if 2.0999999999999999e126 < x

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l- 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 95.9%

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

Alternative 4: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+119} \lor \neg \left(x \leq 1.12 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e+119) (not (<= x 1.12e+42)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e+119) || !(x <= 1.12e+42)) {
		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 <= (-9.5d+119)) .or. (.not. (x <= 1.12d+42))) 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 <= -9.5e+119) || !(x <= 1.12e+42)) {
		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 <= -9.5e+119) or not (x <= 1.12e+42):
		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 <= -9.5e+119) || !(x <= 1.12e+42))
		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 <= -9.5e+119) || ~((x <= 1.12e+42)))
		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, -9.5e+119], N[Not[LessEqual[x, 1.12e+42]], $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 < -9.4999999999999994e119 or 1.12e42 < 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. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 88.1%

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

   if -9.4999999999999994e119 < x < 1.12e42

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 95.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+119} \lor \neg \left(x \leq 1.12 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+121} \lor \neg \left(x \leq 6 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.55e+121) (not (<= x 6e+142)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.55e+121) || !(x <= 6e+142)) {
		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 <= (-3.55d+121)) .or. (.not. (x <= 6d+142))) 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 <= -3.55e+121) || !(x <= 6e+142)) {
		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 <= -3.55e+121) or not (x <= 6e+142):
		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 <= -3.55e+121) || !(x <= 6e+142))
		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 <= -3.55e+121) || ~((x <= 6e+142)))
		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, -3.55e+121], N[Not[LessEqual[x, 6e+142]], $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 < -3.55000000000000012e121 or 5.99999999999999949e142 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 58.3%

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

      1. associate--l+ 58.3%

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

      2. associate-/l* 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in x around inf 83.5%

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

   if -3.55000000000000012e121 < x < 5.99999999999999949e142

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+121} \lor \neg \left(x \leq 6 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -210 \lor \neg \left(z \leq 7.2 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -210.0) (not (<= z 7.2e-9)))
   (* z (- -1.0 (/ y z)))
   (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -210.0) || !(z <= 7.2e-9)) {
		tmp = z * (-1.0 - (y / 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 <= (-210.0d0)) .or. (.not. (z <= 7.2d-9))) then
        tmp = z * ((-1.0d0) - (y / 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 <= -210.0) || !(z <= 7.2e-9)) {
		tmp = z * (-1.0 - (y / z));
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -210.0) or not (z <= 7.2e-9):
		tmp = z * (-1.0 - (y / z))
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -210.0) || !(z <= 7.2e-9))
		tmp = Float64(z * Float64(-1.0 - Float64(y / 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 <= -210.0) || ~((z <= 7.2e-9)))
		tmp = z * (-1.0 - (y / z));
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -210.0], N[Not[LessEqual[z, 7.2e-9]], $MachinePrecision]], N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -210 or 7.2e-9 < z

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 66.0%

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

   6. Taylor expanded in z around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. *-commutative 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. +-commutative 66.2%

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

      5. mul-1-neg 66.2%

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

      6. unsub-neg 66.2%

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

      7. associate-+r- 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in z around -inf 89.0%

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

       1. associate-*r* 89.0%

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

       2. mul-1-neg 89.0%

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

       3. mul-1-neg 89.0%

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

       4. unsub-neg 89.0%

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

       5. associate--l+ 89.0%

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

       6. div-sub 89.0%

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

       7. *-commutative 89.0%

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

       8. associate-/l* 88.7%

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

   11. Simplified 88.7%

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

   12. Taylor expanded in y around inf 84.6%

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

       1. associate-*r/ 84.6%

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

       2. neg-mul-1 84.6%

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

   14. Simplified 84.6%

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

   if -210 < z < 7.2e-9

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \log y - \left(y + \left(z - \log t\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 99.3%

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

      2. pow3 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x around 0 63.7%

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

      1. associate--r+ 63.7%

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

   9. Simplified 63.7%

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

   10. Taylor expanded in z around 0 63.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210 \lor \neg \left(z \leq 7.2 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+120} \lor \neg \left(x \leq 1.5 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.15e+120) (not (<= x 1.5e+92)))
   (* x (log y))
   (* z (- -1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e+120) || !(x <= 1.5e+92)) {
		tmp = x * log(y);
	} else {
		tmp = z * (-1.0 - (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 <= (-1.15d+120)) .or. (.not. (x <= 1.5d+92))) then
        tmp = x * log(y)
    else
        tmp = z * ((-1.0d0) - (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 <= -1.15e+120) || !(x <= 1.5e+92)) {
		tmp = x * Math.log(y);
	} else {
		tmp = z * (-1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.15e+120) or not (x <= 1.5e+92):
		tmp = x * math.log(y)
	else:
		tmp = z * (-1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.15e+120) || !(x <= 1.5e+92))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(z * Float64(-1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.15e+120) || ~((x <= 1.5e+92)))
		tmp = x * log(y);
	else
		tmp = z * (-1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.15e+120], N[Not[LessEqual[x, 1.5e+92]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999996e120 or 1.50000000000000007e92 < 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. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 54.9%

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

   7. Simplified 54.9%

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

   8. Taylor expanded in x around inf 75.5%

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

   if -1.14999999999999996e120 < x < 1.50000000000000007e92

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 71.0%

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

   6. Taylor expanded in z around -inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

      3. distribute-rgt-neg-in 49.0%

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

      4. +-commutative 49.0%

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

      5. mul-1-neg 49.0%

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

      6. unsub-neg 49.0%

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

      7. associate-+r- 49.0%

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

   8. Simplified 49.0%

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

   9. Taylor expanded in z around -inf 79.3%

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

       1. associate-*r* 79.3%

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

       2. mul-1-neg 79.3%

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

       3. mul-1-neg 79.3%

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

       4. unsub-neg 79.3%

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

       5. associate--l+ 79.3%

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

       6. div-sub 79.3%

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

       7. *-commutative 79.3%

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

       8. associate-/l* 79.0%

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

   11. Simplified 79.0%

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

   12. Taylor expanded in y around inf 65.8%

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

       1. associate-*r/ 65.8%

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

       2. neg-mul-1 65.8%

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

   14. Simplified 65.8%

       \[\leadsto \left(-z\right) \cdot \left(1 - \color{blue}{\frac{-y}{z}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+120} \lor \neg \left(x \leq 1.5 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-48} \lor \neg \left(z \leq 5.6 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e-48) (not (<= z 5.6e-46))) (* z (- -1.0 (/ y z))) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-48) || !(z <= 5.6e-46)) {
		tmp = z * (-1.0 - (y / 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 ((z <= (-1.05d-48)) .or. (.not. (z <= 5.6d-46))) then
        tmp = z * ((-1.0d0) - (y / 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 ((z <= -1.05e-48) || !(z <= 5.6e-46)) {
		tmp = z * (-1.0 - (y / z));
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e-48) or not (z <= 5.6e-46):
		tmp = z * (-1.0 - (y / z))
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-48) || !(z <= 5.6e-46))
		tmp = Float64(z * Float64(-1.0 - Float64(y / z)));
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-48) || ~((z <= 5.6e-46)))
		tmp = z * (-1.0 - (y / z));
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e-48], N[Not[LessEqual[z, 5.6e-46]], $MachinePrecision]], N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999994e-48 or 5.5999999999999997e-46 < z

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 68.2%

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

   6. Taylor expanded in z around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. +-commutative 67.7%

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

      5. mul-1-neg 67.7%

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

      6. unsub-neg 67.7%

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

      7. associate-+r- 67.7%

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

   8. Simplified 67.7%

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

   9. Taylor expanded in z around -inf 89.0%

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

       1. associate-*r* 89.0%

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

       2. mul-1-neg 89.0%

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

       3. mul-1-neg 89.0%

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

       4. unsub-neg 89.0%

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

       5. associate--l+ 89.0%

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

       6. div-sub 89.0%

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

       7. *-commutative 89.0%

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

       8. associate-/l* 88.7%

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

   11. Simplified 88.7%

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

   12. Taylor expanded in y around inf 82.2%

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

       1. associate-*r/ 82.2%

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

       2. neg-mul-1 82.2%

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

   14. Simplified 82.2%

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

   if -1.04999999999999994e-48 < z < 5.5999999999999997e-46

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 38.6%

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

      1. mul-1-neg 38.6%

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

   7. Simplified 38.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-48} \lor \neg \left(z \leq 5.6 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+102}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.7e+102) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.7e+102) {
		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 <= 2.7d+102) 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 <= 2.7e+102) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.7e+102:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.7e+102)
		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 <= 2.7e+102)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.7e+102], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.7000000000000001e102

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 44.4%

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

      1. mul-1-neg 44.4%

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

   7. Simplified 44.4%

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

   if 2.7000000000000001e102 < y

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 73.0%

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

      1. mul-1-neg 73.0%

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

   7. Simplified 73.0%

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

Alternative 10: 30.2% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. 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. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 29.4%

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

   1. mul-1-neg 29.4%

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

7. Simplified 29.4%

   \[\leadsto \color{blue}{-y} \]
8. Add Preprocessing

Alternative 11: 2.2% accurate, 209.0× 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 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. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 29.4%

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

   1. mul-1-neg 29.4%

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

7. Simplified 29.4%

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

   1. neg-sub0 29.4%

      \[\leadsto \color{blue}{0 - y} \]

   2. sub-neg 29.4%

      \[\leadsto \color{blue}{0 + \left(-y\right)} \]

   3. add-sqr-sqrt 0.0%

      \[\leadsto 0 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}} \]

   4. sqrt-unprod 2.3%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

   5. sqr-neg 2.3%

      \[\leadsto 0 + \sqrt{\color{blue}{y \cdot y}} \]

   6. sqrt-unprod 2.4%

      \[\leadsto 0 + \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

   7. add-sqr-sqrt 2.4%

      \[\leadsto 0 + \color{blue}{y} \]

9. Applied egg-rr 2.4%

   \[\leadsto \color{blue}{0 + y} \]
10. Step-by-step derivation

    1. +-lft-identity 2.4%

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

11. Simplified 2.4%

    \[\leadsto \color{blue}{y} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(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)))