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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

Alternatives: 7

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: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+22} \lor \neg \left(z \leq 8.8 \cdot 10^{+51}\right):\\ \;\;\;\;\log t - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+22) (not (<= z 8.8e+51)))
   (- (log t) (+ z y))
   (+ (- (* x (log y)) y) (log t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+22) || !(z <= 8.8e+51)) {
		tmp = log(t) - (z + y);
	} else {
		tmp = ((x * log(y)) - y) + log(t);
	}
	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 <= (-5.2d+22)) .or. (.not. (z <= 8.8d+51))) then
        tmp = log(t) - (z + y)
    else
        tmp = ((x * log(y)) - y) + log(t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+22) || !(z <= 8.8e+51)) {
		tmp = Math.log(t) - (z + y);
	} else {
		tmp = ((x * Math.log(y)) - y) + Math.log(t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e+22) or not (z <= 8.8e+51):
		tmp = math.log(t) - (z + y)
	else:
		tmp = ((x * math.log(y)) - y) + math.log(t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e+22) || !(z <= 8.8e+51))
		tmp = Float64(log(t) - Float64(z + y));
	else
		tmp = Float64(Float64(Float64(x * log(y)) - y) + log(t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e+22) || ~((z <= 8.8e+51)))
		tmp = log(t) - (z + y);
	else
		tmp = ((x * log(y)) - y) + log(t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e+22], N[Not[LessEqual[z, 8.8e+51]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e22 or 8.79999999999999967e51 < 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 88.0%

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

      1. mul-1-neg 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. sub-neg 88.0%

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

      3. associate--r+ 88.0%

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

      4. +-commutative 88.0%

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

   8. Simplified 88.0%

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

   if -5.2e22 < z < 8.79999999999999967e51

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 57.0%

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

      2. pow2 57.0%

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

   4. Applied egg-rr 57.0%

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

   5. Taylor expanded in z around 0 98.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+22} \lor \neg \left(z \leq 8.8 \cdot 10^{+51}\right):\\ \;\;\;\;\log t - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+182} \lor \neg \left(x \leq 5.8 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e+182) (not (<= x 5.8e+183)))
   (+ (* x (log y)) (log t))
   (- (log t) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+182) || !(x <= 5.8e+183)) {
		tmp = (x * log(y)) + log(t);
	} else {
		tmp = log(t) - (z + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.25d+182)) .or. (.not. (x <= 5.8d+183))) then
        tmp = (x * log(y)) + log(t)
    else
        tmp = log(t) - (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+182) || !(x <= 5.8e+183)) {
		tmp = (x * Math.log(y)) + Math.log(t);
	} else {
		tmp = Math.log(t) - (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e+182) or not (x <= 5.8e+183):
		tmp = (x * math.log(y)) + math.log(t)
	else:
		tmp = math.log(t) - (z + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e+182) || !(x <= 5.8e+183))
		tmp = Float64(Float64(x * log(y)) + log(t));
	else
		tmp = Float64(log(t) - Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e+182) || ~((x <= 5.8e+183)))
		tmp = (x * log(y)) + log(t);
	else
		tmp = log(t) - (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e+182], N[Not[LessEqual[x, 5.8e+183]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999993e182 or 5.8000000000000001e183 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 87.8%

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

   4. Taylor expanded in x around inf 79.1%

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

   if -1.24999999999999993e182 < x < 5.8000000000000001e183

   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 84.4%

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

      1. mul-1-neg 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in y around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. sub-neg 84.4%

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

      3. associate--r+ 84.4%

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

      4. +-commutative 84.4%

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

   8. Simplified 84.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+182} \lor \neg \left(x \leq 5.8 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+59} \lor \neg \left(z \leq 3.7 \cdot 10^{+68}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+59) (not (<= z 3.7e+68))) (- z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+59) || !(z <= 3.7e+68)) {
		tmp = -z;
	} else {
		tmp = log(t) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.8d+59)) .or. (.not. (z <= 3.7d+68))) then
        tmp = -z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+59) || !(z <= 3.7e+68)) {
		tmp = -z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e+59) or not (z <= 3.7e+68):
		tmp = -z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+59) || !(z <= 3.7e+68))
		tmp = Float64(-z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e+59) || ~((z <= 3.7e+68)))
		tmp = -z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+59], N[Not[LessEqual[z, 3.7e+68]], $MachinePrecision]], (-z), N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000043e59 or 3.69999999999999998e68 < 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 87.3%

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

      1. mul-1-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 70.2%

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

      1. mul-1-neg 70.2%

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

   8. Simplified 70.2%

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

   if -7.80000000000000043e59 < z < 3.69999999999999998e68

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in z around 0 55.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+59} \lor \neg \left(z \leq 3.7 \cdot 10^{+68}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return log(t) - (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) - (y + z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] - N[(y + 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. Taylor expanded in x around 0 70.8%

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

   1. mul-1-neg 70.8%

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

5. Simplified 70.8%

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

6. Taylor expanded in y around 0 70.8%

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

   1. mul-1-neg 70.8%

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

   2. sub-neg 70.8%

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

   3. associate--r+ 70.8%

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

   4. +-commutative 70.8%

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

8. Simplified 70.8%

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

9. Final simplification 70.8%

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

Alternative 6: 48.2% accurate, 17.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+59} \lor \neg \left(z \leq 8.2 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e+59) (not (<= z 8.2e+70))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+59) || !(z <= 8.2e+70)) {
		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 ((z <= (-7.6d+59)) .or. (.not. (z <= 8.2d+70))) 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 ((z <= -7.6e+59) || !(z <= 8.2e+70)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e+59) or not (z <= 8.2e+70):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e+59) || !(z <= 8.2e+70))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e+59) || ~((z <= 8.2e+70)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e+59], N[Not[LessEqual[z, 8.2e+70]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000002e59 or 8.2000000000000004e70 < 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 87.3%

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

      1. mul-1-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 70.2%

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

      1. mul-1-neg 70.2%

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

   8. Simplified 70.2%

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

   if -7.6000000000000002e59 < z < 8.2000000000000004e70

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in y around inf 40.3%

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

      1. mul-1-neg 40.3%

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

   8. Simplified 40.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+59} \lor \neg \left(z \leq 8.2 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.9% 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 x around 0 70.8%

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

   1. mul-1-neg 70.8%

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

5. Simplified 70.8%

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

6. Taylor expanded in y around inf 30.7%

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

   1. mul-1-neg 30.7%

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

8. Simplified 30.7%

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

9. Final simplification 30.7%

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

Reproduce

herbie shell --seed 2024046 
(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)))