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

Percentage Accurate: 99.9% → 99.9%

Time: 10.2s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. 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. Final simplification 99.9%

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

Alternative 2: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5e+90) t_2 (if (<= t_2 5e-8) (- (log t) (+ y z)) (- 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 (t_2 <= -5e+90) {
		tmp = t_2;
	} else if (t_2 <= 5e-8) {
		tmp = log(t) - (y + z);
	} 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 (t_2 <= (-5d+90)) then
        tmp = t_2
    else if (t_2 <= 5d-8) then
        tmp = log(t) - (y + z)
    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 (t_2 <= -5e+90) {
		tmp = t_2;
	} else if (t_2 <= 5e-8) {
		tmp = Math.log(t) - (y + z);
	} 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 t_2 <= -5e+90:
		tmp = t_2
	elif t_2 <= 5e-8:
		tmp = math.log(t) - (y + z)
	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 (t_2 <= -5e+90)
		tmp = t_2;
	elseif (t_2 <= 5e-8)
		tmp = Float64(log(t) - Float64(y + z));
	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 (t_2 <= -5e+90)
		tmp = t_2;
	elseif (t_2 <= 5e-8)
		tmp = log(t) - (y + z);
	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[t$95$2, -5e+90], t$95$2, If[LessEqual[t$95$2, 5e-8], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5.0000000000000004e90

   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 89.3%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999998e-8

   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 96.2%

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

   if 4.9999999999999998e-8 < (-.f64 (*.f64 x (log.f64 y)) y)

   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 97.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+65} \lor \neg \left(z \leq 1.42 \cdot 10^{+109}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(\log t - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.8e+65) (not (<= z 1.42e+109)))
   (- (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 <= -6.8e+65) || !(z <= 1.42e+109)) {
		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 <= (-6.8d+65)) .or. (.not. (z <= 1.42d+109))) 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 <= -6.8e+65) || !(z <= 1.42e+109)) {
		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 <= -6.8e+65) or not (z <= 1.42e+109):
		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 <= -6.8e+65) || !(z <= 1.42e+109))
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) + Float64(log(t) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.8e+65) || ~((z <= 1.42e+109)))
		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, -6.8e+65], N[Not[LessEqual[z, 1.42e+109]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999999e65 or 1.4200000000000001e109 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. 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 86.1%

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

   if -6.7999999999999999e65 < z < 1.4200000000000001e109

   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 z around 0 98.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+65} \lor \neg \left(z \leq 1.42 \cdot 10^{+109}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(\log t - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 340:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\log y \cdot \frac{x}{y} + \left(-1 - \frac{z}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 340.0)
   (- (+ (* x (log y)) (log t)) z)
   (* y (+ (* (log y) (/ x y)) (- -1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 340.0) {
		tmp = ((x * log(y)) + log(t)) - z;
	} else {
		tmp = y * ((log(y) * (x / y)) + (-1.0 - (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 (y <= 340.0d0) then
        tmp = ((x * log(y)) + log(t)) - z
    else
        tmp = y * ((log(y) * (x / y)) + ((-1.0d0) - (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 340.0) {
		tmp = ((x * Math.log(y)) + Math.log(t)) - z;
	} else {
		tmp = y * ((Math.log(y) * (x / y)) + (-1.0 - (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 340.0:
		tmp = ((x * math.log(y)) + math.log(t)) - z
	else:
		tmp = y * ((math.log(y) * (x / y)) + (-1.0 - (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 340.0)
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - z);
	else
		tmp = Float64(y * Float64(Float64(log(y) * Float64(x / y)) + Float64(-1.0 - Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 340.0)
		tmp = ((x * log(y)) + log(t)) - z;
	else
		tmp = y * ((log(y) * (x / y)) + (-1.0 - (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 340.0], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(y * N[(N[(N[Log[y], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 340

   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 99.1%

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

   if 340 < 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 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-neg-frac 98.7%

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

   10. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 340:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\log y \cdot \frac{x}{y} + \left(-1 - \frac{z}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 6: 49.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -225000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-283}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -225000000.0)
     t_1
     (if (<= x -1.6e-102)
       (- y)
       (if (<= x -1.85e-283)
         (- z)
         (if (<= x 3.5e-94) (- y) (if (<= x 4.6e+73) (- z) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -225000000.0) {
		tmp = t_1;
	} else if (x <= -1.6e-102) {
		tmp = -y;
	} else if (x <= -1.85e-283) {
		tmp = -z;
	} else if (x <= 3.5e-94) {
		tmp = -y;
	} else if (x <= 4.6e+73) {
		tmp = -z;
	} 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 <= (-225000000.0d0)) then
        tmp = t_1
    else if (x <= (-1.6d-102)) then
        tmp = -y
    else if (x <= (-1.85d-283)) then
        tmp = -z
    else if (x <= 3.5d-94) then
        tmp = -y
    else if (x <= 4.6d+73) then
        tmp = -z
    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 <= -225000000.0) {
		tmp = t_1;
	} else if (x <= -1.6e-102) {
		tmp = -y;
	} else if (x <= -1.85e-283) {
		tmp = -z;
	} else if (x <= 3.5e-94) {
		tmp = -y;
	} else if (x <= 4.6e+73) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -225000000.0:
		tmp = t_1
	elif x <= -1.6e-102:
		tmp = -y
	elif x <= -1.85e-283:
		tmp = -z
	elif x <= 3.5e-94:
		tmp = -y
	elif x <= 4.6e+73:
		tmp = -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -225000000.0)
		tmp = t_1;
	elseif (x <= -1.6e-102)
		tmp = Float64(-y);
	elseif (x <= -1.85e-283)
		tmp = Float64(-z);
	elseif (x <= 3.5e-94)
		tmp = Float64(-y);
	elseif (x <= 4.6e+73)
		tmp = Float64(-z);
	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 <= -225000000.0)
		tmp = t_1;
	elseif (x <= -1.6e-102)
		tmp = -y;
	elseif (x <= -1.85e-283)
		tmp = -z;
	elseif (x <= 3.5e-94)
		tmp = -y;
	elseif (x <= 4.6e+73)
		tmp = -z;
	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, -225000000.0], t$95$1, If[LessEqual[x, -1.6e-102], (-y), If[LessEqual[x, -1.85e-283], (-z), If[LessEqual[x, 3.5e-94], (-y), If[LessEqual[x, 4.6e+73], (-z), t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e8 or 4.6e73 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. 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 z around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in x around inf 68.9%

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

   if -2.25e8 < x < -1.59999999999999993e-102 or -1.85e-283 < x < 3.49999999999999998e-94

   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 y around inf 54.5%

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

      1. mul-1-neg 54.5%

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

   7. Simplified 54.5%

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

   if -1.59999999999999993e-102 < x < -1.85e-283 or 3.49999999999999998e-94 < x < 4.6e73

   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 z around inf 50.6%

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

      1. mul-1-neg 50.6%

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

   7. Simplified 50.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -225000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-283}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -480000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-280}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 0.065:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -480000000.0)
     t_1
     (if (<= x -1.1e-203)
       t_2
       (if (<= x -2e-280)
         (- z)
         (if (<= x 0.065) t_2 (if (<= x 2e+68) (- z) 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 <= -480000000.0) {
		tmp = t_1;
	} else if (x <= -1.1e-203) {
		tmp = t_2;
	} else if (x <= -2e-280) {
		tmp = -z;
	} else if (x <= 0.065) {
		tmp = t_2;
	} else if (x <= 2e+68) {
		tmp = -z;
	} 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 <= (-480000000.0d0)) then
        tmp = t_1
    else if (x <= (-1.1d-203)) then
        tmp = t_2
    else if (x <= (-2d-280)) then
        tmp = -z
    else if (x <= 0.065d0) then
        tmp = t_2
    else if (x <= 2d+68) then
        tmp = -z
    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 <= -480000000.0) {
		tmp = t_1;
	} else if (x <= -1.1e-203) {
		tmp = t_2;
	} else if (x <= -2e-280) {
		tmp = -z;
	} else if (x <= 0.065) {
		tmp = t_2;
	} else if (x <= 2e+68) {
		tmp = -z;
	} 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 <= -480000000.0:
		tmp = t_1
	elif x <= -1.1e-203:
		tmp = t_2
	elif x <= -2e-280:
		tmp = -z
	elif x <= 0.065:
		tmp = t_2
	elif x <= 2e+68:
		tmp = -z
	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 <= -480000000.0)
		tmp = t_1;
	elseif (x <= -1.1e-203)
		tmp = t_2;
	elseif (x <= -2e-280)
		tmp = Float64(-z);
	elseif (x <= 0.065)
		tmp = t_2;
	elseif (x <= 2e+68)
		tmp = Float64(-z);
	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 <= -480000000.0)
		tmp = t_1;
	elseif (x <= -1.1e-203)
		tmp = t_2;
	elseif (x <= -2e-280)
		tmp = -z;
	elseif (x <= 0.065)
		tmp = t_2;
	elseif (x <= 2e+68)
		tmp = -z;
	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, -480000000.0], t$95$1, If[LessEqual[x, -1.1e-203], t$95$2, If[LessEqual[x, -2e-280], (-z), If[LessEqual[x, 0.065], t$95$2, If[LessEqual[x, 2e+68], (-z), t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e8 or 1.99999999999999991e68 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. 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 z around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in x around inf 68.9%

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

   if -4.8e8 < x < -1.1e-203 or -1.9999999999999999e-280 < x < 0.065000000000000002

   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 99.5%

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

   6. Taylor expanded in z around 0 73.9%

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

   if -1.1e-203 < x < -1.9999999999999999e-280 or 0.065000000000000002 < x < 1.99999999999999991e68

   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- 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 z around inf 64.1%

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

      1. mul-1-neg 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -480000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-203}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-280}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 0.065:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -240000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (* x (log y))) (t_3 (- (log t) y)))
   (if (<= x -240000000.0)
     t_2
     (if (<= x -6.5e-102)
       t_3
       (if (<= x -7e-282)
         t_1
         (if (<= x 1.6e-97) t_3 (if (<= x 2.7e+64) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = x * log(y);
	double t_3 = log(t) - y;
	double tmp;
	if (x <= -240000000.0) {
		tmp = t_2;
	} else if (x <= -6.5e-102) {
		tmp = t_3;
	} else if (x <= -7e-282) {
		tmp = t_1;
	} else if (x <= 1.6e-97) {
		tmp = t_3;
	} else if (x <= 2.7e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = log(t) - z
    t_2 = x * log(y)
    t_3 = log(t) - y
    if (x <= (-240000000.0d0)) then
        tmp = t_2
    else if (x <= (-6.5d-102)) then
        tmp = t_3
    else if (x <= (-7d-282)) then
        tmp = t_1
    else if (x <= 1.6d-97) then
        tmp = t_3
    else if (x <= 2.7d+64) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = x * Math.log(y);
	double t_3 = Math.log(t) - y;
	double tmp;
	if (x <= -240000000.0) {
		tmp = t_2;
	} else if (x <= -6.5e-102) {
		tmp = t_3;
	} else if (x <= -7e-282) {
		tmp = t_1;
	} else if (x <= 1.6e-97) {
		tmp = t_3;
	} else if (x <= 2.7e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = x * math.log(y)
	t_3 = math.log(t) - y
	tmp = 0
	if x <= -240000000.0:
		tmp = t_2
	elif x <= -6.5e-102:
		tmp = t_3
	elif x <= -7e-282:
		tmp = t_1
	elif x <= 1.6e-97:
		tmp = t_3
	elif x <= 2.7e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(x * log(y))
	t_3 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -240000000.0)
		tmp = t_2;
	elseif (x <= -6.5e-102)
		tmp = t_3;
	elseif (x <= -7e-282)
		tmp = t_1;
	elseif (x <= 1.6e-97)
		tmp = t_3;
	elseif (x <= 2.7e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = x * log(y);
	t_3 = log(t) - y;
	tmp = 0.0;
	if (x <= -240000000.0)
		tmp = t_2;
	elseif (x <= -6.5e-102)
		tmp = t_3;
	elseif (x <= -7e-282)
		tmp = t_1;
	elseif (x <= 1.6e-97)
		tmp = t_3;
	elseif (x <= 2.7e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -240000000.0], t$95$2, If[LessEqual[x, -6.5e-102], t$95$3, If[LessEqual[x, -7e-282], t$95$1, If[LessEqual[x, 1.6e-97], t$95$3, If[LessEqual[x, 2.7e+64], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e8 or 2.7e64 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. 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 z around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in x around inf 68.9%

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

   if -2.4e8 < x < -6.5000000000000003e-102 or -7.00000000000000013e-282 < x < 1.5999999999999999e-97

   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 99.6%

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

   6. Taylor expanded in z around 0 80.7%

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

   if -6.5000000000000003e-102 < x < -7.00000000000000013e-282 or 1.5999999999999999e-97 < x < 2.7e64

   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 94.9%

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

   6. Taylor expanded in y around 0 69.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -240000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-282}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+64}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.2e+90) (not (<= x 1.55e+88)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.2e+90) || !(x <= 1.55e+88)) {
		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 <= (-2.2d+90)) .or. (.not. (x <= 1.55d+88))) 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 <= -2.2e+90) || !(x <= 1.55e+88)) {
		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 <= -2.2e+90) or not (x <= 1.55e+88):
		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 <= -2.2e+90) || !(x <= 1.55e+88))
		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 <= -2.2e+90) || ~((x <= 1.55e+88)))
		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, -2.2e+90], N[Not[LessEqual[x, 1.55e+88]], $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 < -2.1999999999999999e90 or 1.5500000000000001e88 < 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 66.5%

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

      1. associate--l+ 66.5%

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

      2. associate-/l* 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in x around inf 74.2%

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

   if -2.1999999999999999e90 < x < 1.5500000000000001e88

   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 93.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+84} \lor \neg \left(x \leq 7.6 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.85e+84) (not (<= x 7.6e+67)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e+84) || !(x <= 7.6e+67)) {
		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 <= (-1.85d+84)) .or. (.not. (x <= 7.6d+67))) 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 <= -1.85e+84) || !(x <= 7.6e+67)) {
		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 <= -1.85e+84) or not (x <= 7.6e+67):
		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 <= -1.85e+84) || !(x <= 7.6e+67))
		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 <= -1.85e+84) || ~((x <= 7.6e+67)))
		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, -1.85e+84], N[Not[LessEqual[x, 7.6e+67]], $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 < -1.85e84 or 7.60000000000000041e67 < 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 86.8%

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

   if -1.85e84 < x < 7.60000000000000041e67

   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 94.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+84} \lor \neg \left(x \leq 7.6 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-277}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-188}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2600000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.2e-277)
   (- z)
   (if (<= y 1.32e-188) (log t) (if (<= y 2600000000000.0) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.2e-277) {
		tmp = -z;
	} else if (y <= 1.32e-188) {
		tmp = log(t);
	} else if (y <= 2600000000000.0) {
		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 <= 5.2d-277) then
        tmp = -z
    else if (y <= 1.32d-188) then
        tmp = log(t)
    else if (y <= 2600000000000.0d0) 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 <= 5.2e-277) {
		tmp = -z;
	} else if (y <= 1.32e-188) {
		tmp = Math.log(t);
	} else if (y <= 2600000000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.2e-277:
		tmp = -z
	elif y <= 1.32e-188:
		tmp = math.log(t)
	elif y <= 2600000000000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.2e-277)
		tmp = Float64(-z);
	elseif (y <= 1.32e-188)
		tmp = log(t);
	elseif (y <= 2600000000000.0)
		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 <= 5.2e-277)
		tmp = -z;
	elseif (y <= 1.32e-188)
		tmp = log(t);
	elseif (y <= 2600000000000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.2e-277], (-z), If[LessEqual[y, 1.32e-188], N[Log[t], $MachinePrecision], If[LessEqual[y, 2600000000000.0], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.2e-277 or 1.32e-188 < y < 2.6e12

   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 z around inf 40.2%

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

      1. mul-1-neg 40.2%

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

   7. Simplified 40.2%

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

   if 5.2e-277 < y < 1.32e-188

   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 62.9%

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

   6. Taylor expanded in z around 0 43.0%

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

   7. Taylor expanded in y around 0 43.0%

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

   if 2.6e12 < 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 65.6%

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

      1. mul-1-neg 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-277}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-188}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2600000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.0% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 36000000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 36000000000000.0) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 36000000000000.0) {
		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 <= 36000000000000.0d0) 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 <= 36000000000000.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 36000000000000.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 36000000000000.0)
		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 <= 36000000000000.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 36000000000000.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.6e13

   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 35.5%

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

      1. mul-1-neg 35.5%

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

   7. Simplified 35.5%

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

   if 3.6e13 < 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 65.6%

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

      1. mul-1-neg 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 36000000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.7% 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 30.1%

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

   1. mul-1-neg 30.1%

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

7. Simplified 30.1%

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

8. Final simplification 30.1%

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

Reproduce

herbie shell --seed 2024095 
(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)))