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

Percentage Accurate: 99.9% → 99.9%

Time: 12.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+47} \lor \neg \left(z \leq 1.25 \cdot 10^{+149}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.65e+47) (not (<= z 1.25e+149)))
   (- (log t) (+ y z))
   (- (+ (* x (log y)) (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.65e+47) || !(z <= 1.25e+149)) {
		tmp = log(t) - (y + z);
	} else {
		tmp = ((x * log(y)) + 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 <= (-2.65d+47)) .or. (.not. (z <= 1.25d+149))) then
        tmp = log(t) - (y + z)
    else
        tmp = ((x * log(y)) + 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 <= -2.65e+47) || !(z <= 1.25e+149)) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = ((x * Math.log(y)) + Math.log(t)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.65e+47) or not (z <= 1.25e+149):
		tmp = math.log(t) - (y + z)
	else:
		tmp = ((x * math.log(y)) + math.log(t)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.65e+47) || !(z <= 1.25e+149))
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.65e+47) || ~((z <= 1.25e+149)))
		tmp = log(t) - (y + z);
	else
		tmp = ((x * log(y)) + log(t)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.65e+47], N[Not[LessEqual[z, 1.25e+149]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e47 or 1.24999999999999998e149 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.1%

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

   if -2.65e47 < z < 1.24999999999999998e149

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 96.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+47} \lor \neg \left(z \leq 1.25 \cdot 10^{+149}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.9e+27) (- (+ (* 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 <= 1.9e+27) {
		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 <= 1.9d+27) 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 <= 1.9e+27) {
		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 <= 1.9e+27:
		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 <= 1.9e+27)
		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 <= 1.9e+27)
		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, 1.9e+27], 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 < 1.90000000000000011e27

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.2%

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

   if 1.90000000000000011e27 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.5%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{-298}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.3e-298)
   (log t)
   (if (<= y 2e-94)
     (- z)
     (if (<= y 1.75e-9) (* x (log y)) (if (<= y 2.3e+44) (- z) (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.3e-298) {
		tmp = log(t);
	} else if (y <= 2e-94) {
		tmp = -z;
	} else if (y <= 1.75e-9) {
		tmp = x * log(y);
	} else if (y <= 2.3e+44) {
		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 <= 3.3d-298) then
        tmp = log(t)
    else if (y <= 2d-94) then
        tmp = -z
    else if (y <= 1.75d-9) then
        tmp = x * log(y)
    else if (y <= 2.3d+44) 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 <= 3.3e-298) {
		tmp = Math.log(t);
	} else if (y <= 2e-94) {
		tmp = -z;
	} else if (y <= 1.75e-9) {
		tmp = x * Math.log(y);
	} else if (y <= 2.3e+44) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.3e-298:
		tmp = math.log(t)
	elif y <= 2e-94:
		tmp = -z
	elif y <= 1.75e-9:
		tmp = x * math.log(y)
	elif y <= 2.3e+44:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.3e-298)
		tmp = log(t);
	elseif (y <= 2e-94)
		tmp = Float64(-z);
	elseif (y <= 1.75e-9)
		tmp = Float64(x * log(y));
	elseif (y <= 2.3e+44)
		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 <= 3.3e-298)
		tmp = log(t);
	elseif (y <= 2e-94)
		tmp = -z;
	elseif (y <= 1.75e-9)
		tmp = x * log(y);
	elseif (y <= 2.3e+44)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.3e-298], N[Log[t], $MachinePrecision], If[LessEqual[y, 2e-94], (-z), If[LessEqual[y, 1.75e-9], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+44], (-z), (-y)]]]]

Derivation

1. Split input into 4 regimes

2. if y < 3.3000000000000002e-298

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in x around inf 99.7%

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

   9. Taylor expanded in x around 0 90.0%

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

   if 3.3000000000000002e-298 < y < 1.9999999999999999e-94 or 1.75e-9 < y < 2.30000000000000004e44

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 46.0%

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

      1. neg-mul-1 46.0%

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

   5. Simplified 46.0%

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

   if 1.9999999999999999e-94 < y < 1.75e-9

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. associate--l+ 99.7%

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

      4. add-cube-cbrt 98.9%

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

      5. associate-*l* 98.9%

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

      6. fma-define 98.9%

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

      7. pow2 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in x around inf 51.9%

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

   if 2.30000000000000004e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{-298}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 6.5e-60)
     t_1
     (if (<= y 5e-15) (* x (log y)) (if (<= y 3.4e+44) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 6.5e-60) {
		tmp = t_1;
	} else if (y <= 5e-15) {
		tmp = x * log(y);
	} else if (y <= 3.4e+44) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (y <= 6.5d-60) then
        tmp = t_1
    else if (y <= 5d-15) then
        tmp = x * log(y)
    else if (y <= 3.4d+44) then
        tmp = t_1
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double tmp;
	if (y <= 6.5e-60) {
		tmp = t_1;
	} else if (y <= 5e-15) {
		tmp = x * Math.log(y);
	} else if (y <= 3.4e+44) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if y <= 6.5e-60:
		tmp = t_1
	elif y <= 5e-15:
		tmp = x * math.log(y)
	elif y <= 3.4e+44:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (y <= 6.5e-60)
		tmp = t_1;
	elseif (y <= 5e-15)
		tmp = Float64(x * log(y));
	elseif (y <= 3.4e+44)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (y <= 6.5e-60)
		tmp = t_1;
	elseif (y <= 5e-15)
		tmp = x * log(y);
	elseif (y <= 3.4e+44)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 6.5e-60], t$95$1, If[LessEqual[y, 5e-15], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+44], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.49999999999999995e-60 or 4.99999999999999999e-15 < y < 3.4e44

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.6%

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

   4. Taylor expanded in x around 0 68.4%

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

   if 6.49999999999999995e-60 < y < 4.99999999999999999e-15

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. sub-neg 99.5%

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

      3. associate--l+ 99.5%

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

      4. add-cube-cbrt 98.4%

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

      5. associate-*l* 98.5%

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

      6. fma-define 98.5%

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

      7. pow2 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if 3.4e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 1.15e-59)
     t_1
     (if (<= y 5.8e-15) (* x (log y)) (if (<= y 3.4e+44) t_1 (- (log t) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 1.15e-59) {
		tmp = t_1;
	} else if (y <= 5.8e-15) {
		tmp = x * log(y);
	} else if (y <= 3.4e+44) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (y <= 1.15d-59) then
        tmp = t_1
    else if (y <= 5.8d-15) then
        tmp = x * log(y)
    else if (y <= 3.4d+44) then
        tmp = t_1
    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 t_1 = Math.log(t) - z;
	double tmp;
	if (y <= 1.15e-59) {
		tmp = t_1;
	} else if (y <= 5.8e-15) {
		tmp = x * Math.log(y);
	} else if (y <= 3.4e+44) {
		tmp = t_1;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if y <= 1.15e-59:
		tmp = t_1
	elif y <= 5.8e-15:
		tmp = x * math.log(y)
	elif y <= 3.4e+44:
		tmp = t_1
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (y <= 1.15e-59)
		tmp = t_1;
	elseif (y <= 5.8e-15)
		tmp = Float64(x * log(y));
	elseif (y <= 3.4e+44)
		tmp = t_1;
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (y <= 1.15e-59)
		tmp = t_1;
	elseif (y <= 5.8e-15)
		tmp = x * log(y);
	elseif (y <= 3.4e+44)
		tmp = t_1;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 1.15e-59], t$95$1, If[LessEqual[y, 5.8e-15], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+44], t$95$1, N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.1499999999999999e-59 or 5.80000000000000037e-15 < y < 3.4e44

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.6%

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

   4. Taylor expanded in x around 0 68.4%

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

   if 1.1499999999999999e-59 < y < 5.80000000000000037e-15

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. sub-neg 99.5%

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

      3. associate--l+ 99.5%

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

      4. add-cube-cbrt 98.4%

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

      5. associate-*l* 98.5%

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

      6. fma-define 98.5%

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

      7. pow2 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if 3.4e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. associate-/l* 70.6%

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

   5. Simplified 70.6%

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

      1. clear-num 70.6%

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

      2. un-div-inv 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in y around inf 70.4%

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

      1. mul-1-neg 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-298}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-46}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6e-298)
   (log t)
   (if (<= y 2.1e-95)
     (- z)
     (if (<= y 2.4e-46) (log t) (if (<= y 2.5e+44) (- z) (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e-298) {
		tmp = log(t);
	} else if (y <= 2.1e-95) {
		tmp = -z;
	} else if (y <= 2.4e-46) {
		tmp = log(t);
	} else if (y <= 2.5e+44) {
		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 <= 6d-298) then
        tmp = log(t)
    else if (y <= 2.1d-95) then
        tmp = -z
    else if (y <= 2.4d-46) then
        tmp = log(t)
    else if (y <= 2.5d+44) 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 <= 6e-298) {
		tmp = Math.log(t);
	} else if (y <= 2.1e-95) {
		tmp = -z;
	} else if (y <= 2.4e-46) {
		tmp = Math.log(t);
	} else if (y <= 2.5e+44) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6e-298:
		tmp = math.log(t)
	elif y <= 2.1e-95:
		tmp = -z
	elif y <= 2.4e-46:
		tmp = math.log(t)
	elif y <= 2.5e+44:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6e-298)
		tmp = log(t);
	elseif (y <= 2.1e-95)
		tmp = Float64(-z);
	elseif (y <= 2.4e-46)
		tmp = log(t);
	elseif (y <= 2.5e+44)
		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 <= 6e-298)
		tmp = log(t);
	elseif (y <= 2.1e-95)
		tmp = -z;
	elseif (y <= 2.4e-46)
		tmp = log(t);
	elseif (y <= 2.5e+44)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6e-298], N[Log[t], $MachinePrecision], If[LessEqual[y, 2.1e-95], (-z), If[LessEqual[y, 2.4e-46], N[Log[t], $MachinePrecision], If[LessEqual[y, 2.5e+44], (-z), (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.9999999999999999e-298 or 2.1e-95 < y < 2.40000000000000013e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. associate-/l* 91.0%

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

   5. Simplified 91.0%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.1%

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

   7. Applied egg-rr 91.1%

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

   8. Taylor expanded in x around inf 95.3%

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

   9. Taylor expanded in x around 0 62.7%

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

   if 5.9999999999999999e-298 < y < 2.1e-95 or 2.40000000000000013e-46 < y < 2.4999999999999998e44

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 43.8%

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

      1. neg-mul-1 43.8%

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

   5. Simplified 43.8%

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

   if 2.4999999999999998e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-298}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-46}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+200} \lor \neg \left(x \leq 1.85 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e+200) (not (<= x 1.85e+157)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+200) || !(x <= 1.85e+157)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.2d+200)) .or. (.not. (x <= 1.85d+157))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+200) || !(x <= 1.85e+157)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.2e+200) or not (x <= 1.85e+157):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.2e+200) || !(x <= 1.85e+157))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.2e+200) || ~((x <= 1.85e+157)))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.2e+200], N[Not[LessEqual[x, 1.85e+157]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000003e200 or 1.8499999999999999e157 < x

   1. Initial program 99.6%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. Add Preprocessing
   3. 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. sub-neg 99.6%

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

      3. associate--l+ 99.6%

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

      4. add-cube-cbrt 98.4%

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

      5. associate-*l* 98.4%

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

      6. fma-define 98.4%

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

      7. pow2 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around inf 80.1%

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

   if -5.2000000000000003e200 < x < 1.8499999999999999e157

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+200} \lor \neg \left(x \leq 1.85 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.6% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.2e+44) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+44) {
		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 <= 2.2d+44) 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 <= 2.2e+44) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e+44:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e+44)
		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 <= 2.2e+44)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e+44], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.19999999999999996e44

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 38.1%

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

      1. neg-mul-1 38.1%

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

   5. Simplified 38.1%

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

   if 2.19999999999999996e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.1% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 34.0%

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

   1. neg-mul-1 34.0%

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

5. Simplified 34.0%

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

6. Final simplification 34.0%

   \[\leadsto -y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))