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

Percentage Accurate: 99.9% → 99.9%

Time: 11.1s

Alternatives: 13

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate--l- 99.8%

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

   3. associate-+r- 99.8%

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

   4. +-commutative 99.8%

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

   5. associate--l+ 99.9%

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

   6. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(x, \log y, \log t - \left(z + y\right)\right) \]

Alternative 2: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310 \lor \neg \left(x \leq 2.2 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -310.0) (not (<= x 2.2e+67)))
   (- (+ (log t) (* x (log y))) y)
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -310.0) || !(x <= 2.2e+67)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = log(t) - (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) :: tmp
    if ((x <= (-310.0d0)) .or. (.not. (x <= 2.2d+67))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -310.0) || !(x <= 2.2e+67)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -310.0) or not (x <= 2.2e+67):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -310.0) || !(x <= 2.2e+67))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -310.0) || ~((x <= 2.2e+67)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -310.0], N[Not[LessEqual[x, 2.2e+67]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -310 or 2.2e67 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 87.7%

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

   if -310 < x < 2.2e67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310 \lor \neg \left(x \leq 2.2 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]

Alternative 3: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;t_1 - y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= x -0.28)
     (- t_1 y)
     (if (<= x 1.42e+116) (- (log t) (+ z y)) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (x <= -0.28) {
		tmp = t_1 - y;
	} else if (x <= 1.42e+116) {
		tmp = log(t) - (z + y);
	} 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) :: tmp
    t_1 = log(t) + (x * log(y))
    if (x <= (-0.28d0)) then
        tmp = t_1 - y
    else if (x <= 1.42d+116) then
        tmp = log(t) - (z + y)
    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 = Math.log(t) + (x * Math.log(y));
	double tmp;
	if (x <= -0.28) {
		tmp = t_1 - y;
	} else if (x <= 1.42e+116) {
		tmp = Math.log(t) - (z + y);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if x <= -0.28:
		tmp = t_1 - y
	elif x <= 1.42e+116:
		tmp = math.log(t) - (z + y)
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (x <= -0.28)
		tmp = Float64(t_1 - y);
	elseif (x <= 1.42e+116)
		tmp = Float64(log(t) - Float64(z + y));
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (x <= -0.28)
		tmp = t_1 - y;
	elseif (x <= 1.42e+116)
		tmp = log(t) - (z + y);
	else
		tmp = t_1 - z;
	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[x, -0.28], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 1.42e+116], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.28000000000000003

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 89.0%

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

   if -0.28000000000000003 < x < 1.4199999999999999e116

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.0%

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

   if 1.4199999999999999e116 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 92.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \end{array} \]

Alternative 4: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22000 \lor \neg \left(x \leq 2.7 \cdot 10^{+118}\right):\\ \;\;\;\;\log t + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -22000.0) (not (<= x 2.7e+118)))
   (+ (log t) (* x (log y)))
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -22000.0) || !(x <= 2.7e+118)) {
		tmp = log(t) + (x * log(y));
	} else {
		tmp = log(t) - (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) :: tmp
    if ((x <= (-22000.0d0)) .or. (.not. (x <= 2.7d+118))) then
        tmp = log(t) + (x * log(y))
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -22000.0) || !(x <= 2.7e+118)) {
		tmp = Math.log(t) + (x * Math.log(y));
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -22000.0) or not (x <= 2.7e+118):
		tmp = math.log(t) + (x * math.log(y))
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -22000.0) || !(x <= 2.7e+118))
		tmp = Float64(log(t) + Float64(x * log(y)));
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -22000.0) || ~((x <= 2.7e+118)))
		tmp = log(t) + (x * log(y));
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -22000.0], N[Not[LessEqual[x, 2.7e+118]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -22000 or 2.7e118 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 87.7%

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

   3. Taylor expanded in y around 0 77.8%

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

   if -22000 < x < 2.7e118

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22000 \lor \neg \left(x \leq 2.7 \cdot 10^{+118}\right):\\ \;\;\;\;\log t + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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- 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 7: 47.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 44:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -7.5e-5)
     t_1
     (if (<= x 44.0)
       (- y)
       (if (<= x 2.85e+76) (- z) (if (<= x 1.42e+116) (- y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 44.0) {
		tmp = -y;
	} else if (x <= 2.85e+76) {
		tmp = -z;
	} else if (x <= 1.42e+116) {
		tmp = -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-7.5d-5)) then
        tmp = t_1
    else if (x <= 44.0d0) then
        tmp = -y
    else if (x <= 2.85d+76) then
        tmp = -z
    else if (x <= 1.42d+116) then
        tmp = -y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 44.0) {
		tmp = -y;
	} else if (x <= 2.85e+76) {
		tmp = -z;
	} else if (x <= 1.42e+116) {
		tmp = -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -7.5e-5:
		tmp = t_1
	elif x <= 44.0:
		tmp = -y
	elif x <= 2.85e+76:
		tmp = -z
	elif x <= 1.42e+116:
		tmp = -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 44.0)
		tmp = Float64(-y);
	elseif (x <= 2.85e+76)
		tmp = Float64(-z);
	elseif (x <= 1.42e+116)
		tmp = Float64(-y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 44.0)
		tmp = -y;
	elseif (x <= 2.85e+76)
		tmp = -z;
	elseif (x <= 1.42e+116)
		tmp = -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-5], t$95$1, If[LessEqual[x, 44.0], (-y), If[LessEqual[x, 2.85e+76], (-z), If[LessEqual[x, 1.42e+116], (-y), t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999934e-5 or 1.4199999999999999e116 < 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%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 77.0%

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

   if -7.49999999999999934e-5 < x < 44 or 2.85000000000000002e76 < x < 1.4199999999999999e116

   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%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 48.8%

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

      1. mul-1-neg 48.8%

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

   6. Simplified 48.8%

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

   if 44 < x < 2.85000000000000002e76

   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%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. neg-mul-1 56.9%

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

   6. Simplified 56.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 44:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 8: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 90:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -7.5e-5)
     t_1
     (if (<= x 90.0)
       t_2
       (if (<= x 4.2e+76) (- z) (if (<= x 1.42e+116) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 90.0) {
		tmp = t_2;
	} else if (x <= 4.2e+76) {
		tmp = -z;
	} else if (x <= 1.42e+116) {
		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 = log(t) - y
    if (x <= (-7.5d-5)) then
        tmp = t_1
    else if (x <= 90.0d0) then
        tmp = t_2
    else if (x <= 4.2d+76) then
        tmp = -z
    else if (x <= 1.42d+116) 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 = Math.log(t) - y;
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 90.0) {
		tmp = t_2;
	} else if (x <= 4.2e+76) {
		tmp = -z;
	} else if (x <= 1.42e+116) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -7.5e-5:
		tmp = t_1
	elif x <= 90.0:
		tmp = t_2
	elif x <= 4.2e+76:
		tmp = -z
	elif x <= 1.42e+116:
		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(log(t) - y)
	tmp = 0.0
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 90.0)
		tmp = t_2;
	elseif (x <= 4.2e+76)
		tmp = Float64(-z);
	elseif (x <= 1.42e+116)
		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 = log(t) - y;
	tmp = 0.0;
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 90.0)
		tmp = t_2;
	elseif (x <= 4.2e+76)
		tmp = -z;
	elseif (x <= 1.42e+116)
		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[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -7.5e-5], t$95$1, If[LessEqual[x, 90.0], t$95$2, If[LessEqual[x, 4.2e+76], (-z), If[LessEqual[x, 1.42e+116], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999934e-5 or 1.4199999999999999e116 < 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%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 77.0%

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

   if -7.49999999999999934e-5 < x < 90 or 4.20000000000000013e76 < x < 1.4199999999999999e116

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.3%

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

      1. neg-mul-1 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in y around 0 75.3%

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

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{\log t + -1 \cdot y} \]

      2. mul-1-neg 75.3%

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

      3. sub-neg 75.3%

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

   7. Simplified 75.3%

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

   if 90 < x < 4.20000000000000013e76

   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%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. neg-mul-1 56.9%

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

   6. Simplified 56.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 90:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+116}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 9: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -7.5e-5)
     t_1
     (if (<= x 1.5e-7)
       t_2
       (if (<= x 4.6e+77) (- (log t) z) (if (<= x 3.2e+116) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 1.5e-7) {
		tmp = t_2;
	} else if (x <= 4.6e+77) {
		tmp = log(t) - z;
	} else if (x <= 3.2e+116) {
		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 = log(t) - y
    if (x <= (-7.5d-5)) then
        tmp = t_1
    else if (x <= 1.5d-7) then
        tmp = t_2
    else if (x <= 4.6d+77) then
        tmp = log(t) - z
    else if (x <= 3.2d+116) 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 = Math.log(t) - y;
	double tmp;
	if (x <= -7.5e-5) {
		tmp = t_1;
	} else if (x <= 1.5e-7) {
		tmp = t_2;
	} else if (x <= 4.6e+77) {
		tmp = Math.log(t) - z;
	} else if (x <= 3.2e+116) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -7.5e-5:
		tmp = t_1
	elif x <= 1.5e-7:
		tmp = t_2
	elif x <= 4.6e+77:
		tmp = math.log(t) - z
	elif x <= 3.2e+116:
		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(log(t) - y)
	tmp = 0.0
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 1.5e-7)
		tmp = t_2;
	elseif (x <= 4.6e+77)
		tmp = Float64(log(t) - z);
	elseif (x <= 3.2e+116)
		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 = log(t) - y;
	tmp = 0.0;
	if (x <= -7.5e-5)
		tmp = t_1;
	elseif (x <= 1.5e-7)
		tmp = t_2;
	elseif (x <= 4.6e+77)
		tmp = log(t) - z;
	elseif (x <= 3.2e+116)
		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[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -7.5e-5], t$95$1, If[LessEqual[x, 1.5e-7], t$95$2, If[LessEqual[x, 4.6e+77], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 3.2e+116], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999934e-5 or 3.2e116 < 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%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 77.0%

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

   if -7.49999999999999934e-5 < x < 1.4999999999999999e-7 or 4.5999999999999999e77 < x < 3.2e116

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.8%

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

      1. neg-mul-1 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

         \[\leadsto \color{blue}{\log t + -1 \cdot y} \]

      2. mul-1-neg 75.8%

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

      3. sub-neg 75.8%

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

   7. Simplified 75.8%

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

   if 1.4999999999999999e-7 < x < 4.5999999999999999e77

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 56.2%

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

      1. neg-mul-1 56.2%

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

   4. Simplified 56.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+116}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 10: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22000 \lor \neg \left(x \leq 2.25 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -22000.0) (not (<= x 2.25e+116)))
   (* x (log y))
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -22000.0) || !(x <= 2.25e+116)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (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) :: tmp
    if ((x <= (-22000.0d0)) .or. (.not. (x <= 2.25d+116))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -22000.0) || !(x <= 2.25e+116)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -22000.0) or not (x <= 2.25e+116):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -22000.0) || !(x <= 2.25e+116))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -22000.0) || ~((x <= 2.25e+116)))
		tmp = x * log(y);
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -22000.0], N[Not[LessEqual[x, 2.25e+116]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -22000 or 2.25000000000000008e116 < 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%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 77.7%

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

   if -22000 < x < 2.25000000000000008e116

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22000 \lor \neg \left(x \leq 2.25 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]

Alternative 11: 44.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-90}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.8e-90) (log t) (if (<= y 7.6e+16) (- z) (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.8e-90) {
		tmp = log(t);
	} else if (y <= 7.6e+16) {
		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 <= 2.8d-90) then
        tmp = log(t)
    else if (y <= 7.6d+16) 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 <= 2.8e-90) {
		tmp = Math.log(t);
	} else if (y <= 7.6e+16) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.8e-90:
		tmp = math.log(t)
	elif y <= 7.6e+16:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.8e-90)
		tmp = log(t);
	elseif (y <= 7.6e+16)
		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 <= 2.8e-90)
		tmp = log(t);
	elseif (y <= 7.6e+16)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.8e-90], N[Log[t], $MachinePrecision], If[LessEqual[y, 7.6e+16], (-z), (-y)]]

Derivation

1. Split input into 3 regimes

2. if y < 2.7999999999999999e-90

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 34.3%

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

      1. neg-mul-1 34.3%

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

   4. Simplified 34.3%

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

   5. Taylor expanded in y around 0 34.3%

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

   if 2.7999999999999999e-90 < y < 7.6e16

   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%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 34.1%

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

      1. neg-mul-1 34.1%

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

   6. Simplified 34.1%

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

   if 7.6e16 < 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%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around inf 60.6%

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

      1. mul-1-neg 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-90}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 12: 48.2% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -230:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -230.0) (- z) (if (<= z 3.4e+135) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -230.0) {
		tmp = -z;
	} else if (z <= 3.4e+135) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-230.0d0)) then
        tmp = -z
    else if (z <= 3.4d+135) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -230.0) {
		tmp = -z;
	} else if (z <= 3.4e+135) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -230.0:
		tmp = -z
	elif z <= 3.4e+135:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -230.0)
		tmp = Float64(-z);
	elseif (z <= 3.4e+135)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -230.0)
		tmp = -z;
	elseif (z <= 3.4e+135)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -230.0], (-z), If[LessEqual[z, 3.4e+135], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -230 or 3.4000000000000001e135 < 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%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 55.3%

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

      1. neg-mul-1 55.3%

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

   6. Simplified 55.3%

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

   if -230 < z < 3.4000000000000001e135

   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%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 40.7%

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

      1. mul-1-neg 40.7%

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

   6. Simplified 40.7%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -230:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 13: 30.3% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.9%

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

3. Applied egg-rr 99.9%

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

4. Taylor expanded in y around inf 31.7%

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

   1. mul-1-neg 31.7%

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

6. Simplified 31.7%

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

7. Final simplification 31.7%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023200 
(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)))