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

Percentage Accurate: 99.9% → 99.9%

Time: 14.3s

Alternatives: 14

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

\[\begin{array}{l} \\ \left(\left(\log t - \log \left(\frac{1}{y}\right) \cdot x\right) - z\right) - y \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (- (- (log t) (* (log (/ 1.0 y)) x)) z) y))

C

double code(double x, double y, double z, double t) {
	return ((log(t) - (log((1.0 / y)) * x)) - 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 = ((log(t) - (log((1.0d0 / y)) * x)) - z) - y
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((Math.log(t) - (Math.log((1.0 / y)) * x)) - z) - y;
}

Python

def code(x, y, z, t):
	return ((math.log(t) - (math.log((1.0 / y)) * x)) - z) - y

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(log(t) - Float64(log(Float64(1.0 / y)) * x)) - z) - y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((log(t) - (log((1.0 / y)) * x)) - z) - y;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[t], $MachinePrecision] - N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $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. +-commutative 99.9%

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

   4. associate--r+ 99.9%

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

   5. fma-neg 99.9%

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

   6. neg-sub0 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

   7. associate-+l- 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

   8. neg-sub0 99.9%

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

   9. +-commutative 99.9%

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

   10. unsub-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 40\right):\\ \;\;\;\;\left(t_1 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (or (<= z -290000.0) (not (<= z 40.0)))
     (- (- t_1 z) y)
     (- (+ (log t) t_1) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if ((z <= -290000.0) || !(z <= 40.0)) {
		tmp = (t_1 - z) - y;
	} else {
		tmp = (log(t) + t_1) - 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 = x * log(y)
    if ((z <= (-290000.0d0)) .or. (.not. (z <= 40.0d0))) then
        tmp = (t_1 - z) - y
    else
        tmp = (log(t) + t_1) - y
    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 ((z <= -290000.0) || !(z <= 40.0)) {
		tmp = (t_1 - z) - y;
	} else {
		tmp = (Math.log(t) + t_1) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if (z <= -290000.0) or not (z <= 40.0):
		tmp = (t_1 - z) - y
	else:
		tmp = (math.log(t) + t_1) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if ((z <= -290000.0) || !(z <= 40.0))
		tmp = Float64(Float64(t_1 - z) - y);
	else
		tmp = Float64(Float64(log(t) + t_1) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if ((z <= -290000.0) || ~((z <= 40.0)))
		tmp = (t_1 - z) - y;
	else
		tmp = (log(t) + t_1) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -290000.0], N[Not[LessEqual[z, 40.0]], $MachinePrecision]], N[(N[(t$95$1 - z), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e5 or 40 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r+ 99.9%

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

      5. fma-neg 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. associate-*r* 99.2%

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

      2. mul-1-neg 99.2%

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

      3. log-rec 99.2%

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

      4. remove-double-neg 99.2%

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

   7. Simplified 99.2%

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

   if -2.9e5 < z < 40

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 40\right):\\ \;\;\;\;\left(x \cdot \log y - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00039:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.00039)
   (- (+ (log t) (* x (log y))) z)
   (- (- (* (log (/ 1.0 y)) (- x)) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.00039) {
		tmp = (log(t) + (x * log(y))) - z;
	} else {
		tmp = ((log((1.0 / y)) * -x) - 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 <= 0.00039d0) then
        tmp = (log(t) + (x * log(y))) - z
    else
        tmp = ((log((1.0d0 / y)) * -x) - 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 <= 0.00039) {
		tmp = (Math.log(t) + (x * Math.log(y))) - z;
	} else {
		tmp = ((Math.log((1.0 / y)) * -x) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 0.00039:
		tmp = (math.log(t) + (x * math.log(y))) - z
	else:
		tmp = ((math.log((1.0 / y)) * -x) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.00039)
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - z);
	else
		tmp = Float64(Float64(Float64(log(Float64(1.0 / y)) * Float64(-x)) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 0.00039)
		tmp = (log(t) + (x * log(y))) - z;
	else
		tmp = ((log((1.0 / y)) * -x) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.00039], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.89999999999999993e-4

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.2%

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

   if 3.89999999999999993e-4 < 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. +-commutative 99.9%

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

      4. associate--r+ 99.9%

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

      5. fma-neg 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

   5. Taylor expanded in x around inf 99.5%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00039:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y\\ \end{array} \]

Alternative 4: 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. Final simplification 99.9%

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

Alternative 5: 98.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot \log y - z\right) - y\\ \mathbf{elif}\;x \leq 3.5:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.95e+31)
   (- (- (* x (log y)) z) y)
   (if (<= x 3.5) (- (log t) (+ y z)) (- (- (* (log (/ 1.0 y)) (- x)) z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.95e+31) {
		tmp = ((x * log(y)) - z) - y;
	} else if (x <= 3.5) {
		tmp = log(t) - (y + z);
	} else {
		tmp = ((log((1.0 / y)) * -x) - 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 <= (-1.95d+31)) then
        tmp = ((x * log(y)) - z) - y
    else if (x <= 3.5d0) then
        tmp = log(t) - (y + z)
    else
        tmp = ((log((1.0d0 / y)) * -x) - 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 <= -1.95e+31) {
		tmp = ((x * Math.log(y)) - z) - y;
	} else if (x <= 3.5) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = ((Math.log((1.0 / y)) * -x) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.95e+31:
		tmp = ((x * math.log(y)) - z) - y
	elif x <= 3.5:
		tmp = math.log(t) - (y + z)
	else:
		tmp = ((math.log((1.0 / y)) * -x) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.95e+31)
		tmp = Float64(Float64(Float64(x * log(y)) - z) - y);
	elseif (x <= 3.5)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(Float64(log(Float64(1.0 / y)) * Float64(-x)) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.95e+31)
		tmp = ((x * log(y)) - z) - y;
	elseif (x <= 3.5)
		tmp = log(t) - (y + z);
	else
		tmp = ((log((1.0 / y)) * -x) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.95e+31], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 3.5], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95e31

   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. +-commutative 99.8%

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

      4. associate--r+ 99.8%

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

      5. fma-neg 99.8%

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

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.8%

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

      9. +-commutative 99.8%

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

      10. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 99.8%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. mul-1-neg 99.8%

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

      3. log-rec 99.8%

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

      4. remove-double-neg 99.8%

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

   7. Simplified 99.8%

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

   if -1.95e31 < x < 3.5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.3%

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

   if 3.5 < 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. +-commutative 99.7%

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

      4. associate--r+ 99.7%

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

      5. fma-neg 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot \log y - z\right) - y\\ \mathbf{elif}\;x \leq 3.5:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y\\ \end{array} \]

Alternative 6: 98.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+31} \lor \neg \left(x \leq 0.102\right):\\ \;\;\;\;\left(x \cdot \log y - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.95e+31) (not (<= x 0.102)))
   (- (- (* x (log y)) z) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e+31) || !(x <= 0.102)) {
		tmp = ((x * log(y)) - z) - 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 <= (-1.95d+31)) .or. (.not. (x <= 0.102d0))) then
        tmp = ((x * log(y)) - z) - 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 <= -1.95e+31) || !(x <= 0.102)) {
		tmp = ((x * Math.log(y)) - z) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.95e+31) or not (x <= 0.102):
		tmp = ((x * math.log(y)) - z) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.95e+31) || !(x <= 0.102))
		tmp = Float64(Float64(Float64(x * log(y)) - z) - 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 <= -1.95e+31) || ~((x <= 0.102)))
		tmp = ((x * log(y)) - z) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.95e+31], N[Not[LessEqual[x, 0.102]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e31 or 0.101999999999999993 < 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. +-commutative 99.8%

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

      4. associate--r+ 99.8%

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

      5. fma-neg 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.8%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. mul-1-neg 99.8%

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

      3. log-rec 99.8%

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

      4. remove-double-neg 99.8%

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

   7. Simplified 99.8%

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

   if -1.95e31 < x < 0.101999999999999993

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+31} \lor \neg \left(x \leq 0.102\right):\\ \;\;\;\;\left(x \cdot \log y - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 7: 89.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+64} \lor \neg \left(x \leq 1.65 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e+64) (not (<= x 1.65e+61)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e+64) || !(x <= 1.65e+61)) {
		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 <= (-3d+64)) .or. (.not. (x <= 1.65d+61))) 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 <= -3e+64) || !(x <= 1.65e+61)) {
		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 <= -3e+64) or not (x <= 1.65e+61):
		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 <= -3e+64) || !(x <= 1.65e+61))
		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 <= -3e+64) || ~((x <= 1.65e+61)))
		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, -3e+64], N[Not[LessEqual[x, 1.65e+61]], $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 < -3.0000000000000002e64 or 1.6499999999999999e61 < 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. +-commutative 99.7%

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

      4. associate--r+ 99.7%

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

      5. fma-neg 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

   6. Taylor expanded in z around 0 81.7%

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

      1. associate-*r* 81.7%

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

      2. fma-neg 81.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \log \left(\frac{1}{y}\right), x, -y\right)} \]

      3. log-rec 81.7%

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(-\log y\right)}, x, -y\right) \]

      4. neg-mul-1 81.7%

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(-1 \cdot \log y\right)}, x, -y\right) \]

      5. associate-*r* 81.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(-1 \cdot -1\right) \cdot \log y}, x, -y\right) \]

      6. metadata-eval 81.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{1} \cdot \log y, x, -y\right) \]

      7. *-lft-identity 81.7%

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

      8. fma-neg 81.7%

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

   8. Simplified 81.7%

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

   if -3.0000000000000002e64 < x < 1.6499999999999999e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+64} \lor \neg \left(x \leq 1.65 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 8: 89.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+69} \lor \neg \left(x \leq 6 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e+69) (not (<= x 6e+43)))
   (- (* x (log y)) z)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e+69) || !(x <= 6e+43)) {
		tmp = (x * log(y)) - 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 ((x <= (-3.6d+69)) .or. (.not. (x <= 6d+43))) then
        tmp = (x * log(y)) - 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 ((x <= -3.6e+69) || !(x <= 6e+43)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e+69) or not (x <= 6e+43):
		tmp = (x * math.log(y)) - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e+69) || !(x <= 6e+43))
		tmp = Float64(Float64(x * log(y)) - 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 ((x <= -3.6e+69) || ~((x <= 6e+43)))
		tmp = (x * log(y)) - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e+69], N[Not[LessEqual[x, 6e+43]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6000000000000003e69 or 6.00000000000000033e43 < 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. +-commutative 99.7%

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

      4. associate--r+ 99.7%

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

      5. fma-neg 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.8%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. add-sqr-sqrt 38.6%

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

      2. pow2 38.6%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(-1 \cdot \left(\log \left(\frac{1}{y}\right) \cdot x\right) - z\right) - y}\right)}^{2}} \]

   7. Applied egg-rr 38.6%

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

   8. Taylor expanded in y around 0 89.3%

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

   if -3.6000000000000003e69 < x < 6.00000000000000033e43

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.2%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+69} \lor \neg \left(x \leq 6 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 9: 70.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 340\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -290000.0) (not (<= z 340.0))) (- (- z) y) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -290000.0) || !(z <= 340.0)) {
		tmp = -z - y;
	} 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 <= (-290000.0d0)) .or. (.not. (z <= 340.0d0))) then
        tmp = -z - y
    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 <= -290000.0) || !(z <= 340.0)) {
		tmp = -z - y;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -290000.0) or not (z <= 340.0):
		tmp = -z - y
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -290000.0) || !(z <= 340.0))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -290000.0) || ~((z <= 340.0)))
		tmp = -z - y;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -290000.0], N[Not[LessEqual[z, 340.0]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e5 or 340 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r+ 99.9%

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

      5. fma-neg 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

   5. Taylor expanded in x around inf 99.2%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. neg-mul-1 77.7%

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

      2. +-commutative 77.7%

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

      3. distribute-neg-in 77.7%

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

      4. sub-neg 77.7%

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

   8. Simplified 77.7%

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

   if -2.9e5 < z < 340

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. neg-mul-1 58.6%

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

   4. Simplified 58.6%

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

   5. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. +-commutative 58.6%

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

      3. sub-neg 58.6%

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

   7. Simplified 58.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -290000 \lor \neg \left(z \leq 340\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 10: 70.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00039:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.00039) (- (log t) z) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.00039) {
		tmp = log(t) - z;
	} else {
		tmp = -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 <= 0.00039d0) then
        tmp = log(t) - z
    else
        tmp = -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 <= 0.00039) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 0.00039:
		tmp = math.log(t) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.00039)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 0.00039)
		tmp = log(t) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.00039], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.89999999999999993e-4

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 61.1%

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

   3. Taylor expanded in y around 0 60.8%

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

   if 3.89999999999999993e-4 < 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. +-commutative 99.9%

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

      4. associate--r+ 99.9%

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

      5. fma-neg 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

   5. Taylor expanded in x around inf 99.5%

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

   6. Taylor expanded in x around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. +-commutative 75.6%

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

      3. distribute-neg-in 75.6%

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

      4. sub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00039:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 11: 70.7% 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. Taylor expanded in x around 0 69.0%

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

3. Final simplification 69.0%

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

Alternative 12: 48.7% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.9e+32) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+32) {
		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 <= 1.9d+32) 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 <= 1.9e+32) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.9e+32:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9e+32)
		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 <= 1.9e+32)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9e+32], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.9000000000000002e32

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

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

      2. pow3 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in z around inf 40.7%

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

      1. neg-mul-1 40.7%

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

   6. Simplified 40.7%

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

   if 1.9000000000000002e32 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. neg-mul-1 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 13: 58.3% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-z) - y), $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. +-commutative 99.9%

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

   4. associate--r+ 99.9%

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

   5. fma-neg 99.9%

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

   6. neg-sub0 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

   7. associate-+l- 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

   8. neg-sub0 99.9%

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

   9. +-commutative 99.9%

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

   10. unsub-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 99.9%

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

5. Taylor expanded in x around inf 88.7%

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

6. Taylor expanded in x around 0 58.5%

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

   1. neg-mul-1 58.5%

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

   2. +-commutative 58.5%

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

   3. distribute-neg-in 58.5%

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

   4. sub-neg 58.5%

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

8. Simplified 58.5%

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

9. Final simplification 58.5%

   \[\leadsto \left(-z\right) - y \]

Alternative 14: 30.2% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around inf 41.1%

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

   1. neg-mul-1 41.1%

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

4. Simplified 41.1%

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

5. Taylor expanded in y around inf 31.1%

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

   1. mul-1-neg 31.1%

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

7. Simplified 31.1%

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

8. Final simplification 31.1%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023274 
(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)))