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

Percentage Accurate: 99.9% → 99.9%

Time: 13.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+r- 99.8%

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

   4. associate--l- 99.8%

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

   5. fma-def 99.9%

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

   6. associate--l- 99.9%

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

   7. +-commutative 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   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 99.9%

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

   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. Final simplification 99.9%

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

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+24} \lor \neg \left(x \leq 64000\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.8e+24) (not (<= x 64000.0)))
   (- (+ (log t) (* x (log y))) y)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e+24) || !(x <= 64000.0)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.8d+24)) .or. (.not. (x <= 64000.0d0))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e+24) || !(x <= 64000.0)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.8e+24) or not (x <= 64000.0):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.8e+24) || !(x <= 64000.0))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.8e+24) || ~((x <= 64000.0)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.8e+24], N[Not[LessEqual[x, 64000.0]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e24 or 64000 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 82.5%

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

   if -2.8000000000000002e24 < x < 64000

   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. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+24} \lor \neg \left(x \leq 64000\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   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 99.9%

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

   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%

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

5. Final simplification 99.9%

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

Alternative 5: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.28 \cdot 10^{+98}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.28e+98) (- (+ (log t) (* x (log y))) z) (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.28e+98) {
		tmp = (log(t) + (x * log(y))) - z;
	} 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 (y <= 1.28d+98) then
        tmp = (log(t) + (x * log(y))) - z
    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 (y <= 1.28e+98) {
		tmp = (Math.log(t) + (x * Math.log(y))) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.28e+98:
		tmp = (math.log(t) + (x * math.log(y))) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.28e+98)
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.28e+98)
		tmp = (log(t) + (x * log(y))) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.28e+98], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.28000000000000006e98

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 95.5%

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

   if 1.28000000000000006e98 < y

   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. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 91.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.28 \cdot 10^{+98}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 7: 56.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ \mathbf{if}\;z \leq -2 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (* x (log y))))
   (if (<= z -2e+150)
     (- z)
     (if (<= z -3.5e+40)
       t_2
       (if (<= z -1.9e+26)
         (- z)
         (if (<= z -1.36e-70)
           t_1
           (if (<= z -2.85e-103)
             t_2
             (if (<= z -1.2e-148)
               t_1
               (if (<= z -2.35e-225) t_2 (if (<= z 5.3e+20) t_1 (- z)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = x * log(y);
	double tmp;
	if (z <= -2e+150) {
		tmp = -z;
	} else if (z <= -3.5e+40) {
		tmp = t_2;
	} else if (z <= -1.9e+26) {
		tmp = -z;
	} else if (z <= -1.36e-70) {
		tmp = t_1;
	} else if (z <= -2.85e-103) {
		tmp = t_2;
	} else if (z <= -1.2e-148) {
		tmp = t_1;
	} else if (z <= -2.35e-225) {
		tmp = t_2;
	} else if (z <= 5.3e+20) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) - y
    t_2 = x * log(y)
    if (z <= (-2d+150)) then
        tmp = -z
    else if (z <= (-3.5d+40)) then
        tmp = t_2
    else if (z <= (-1.9d+26)) then
        tmp = -z
    else if (z <= (-1.36d-70)) then
        tmp = t_1
    else if (z <= (-2.85d-103)) then
        tmp = t_2
    else if (z <= (-1.2d-148)) then
        tmp = t_1
    else if (z <= (-2.35d-225)) then
        tmp = t_2
    else if (z <= 5.3d+20) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - y;
	double t_2 = x * Math.log(y);
	double tmp;
	if (z <= -2e+150) {
		tmp = -z;
	} else if (z <= -3.5e+40) {
		tmp = t_2;
	} else if (z <= -1.9e+26) {
		tmp = -z;
	} else if (z <= -1.36e-70) {
		tmp = t_1;
	} else if (z <= -2.85e-103) {
		tmp = t_2;
	} else if (z <= -1.2e-148) {
		tmp = t_1;
	} else if (z <= -2.35e-225) {
		tmp = t_2;
	} else if (z <= 5.3e+20) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = x * math.log(y)
	tmp = 0
	if z <= -2e+150:
		tmp = -z
	elif z <= -3.5e+40:
		tmp = t_2
	elif z <= -1.9e+26:
		tmp = -z
	elif z <= -1.36e-70:
		tmp = t_1
	elif z <= -2.85e-103:
		tmp = t_2
	elif z <= -1.2e-148:
		tmp = t_1
	elif z <= -2.35e-225:
		tmp = t_2
	elif z <= 5.3e+20:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -2e+150)
		tmp = Float64(-z);
	elseif (z <= -3.5e+40)
		tmp = t_2;
	elseif (z <= -1.9e+26)
		tmp = Float64(-z);
	elseif (z <= -1.36e-70)
		tmp = t_1;
	elseif (z <= -2.85e-103)
		tmp = t_2;
	elseif (z <= -1.2e-148)
		tmp = t_1;
	elseif (z <= -2.35e-225)
		tmp = t_2;
	elseif (z <= 5.3e+20)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = x * log(y);
	tmp = 0.0;
	if (z <= -2e+150)
		tmp = -z;
	elseif (z <= -3.5e+40)
		tmp = t_2;
	elseif (z <= -1.9e+26)
		tmp = -z;
	elseif (z <= -1.36e-70)
		tmp = t_1;
	elseif (z <= -2.85e-103)
		tmp = t_2;
	elseif (z <= -1.2e-148)
		tmp = t_1;
	elseif (z <= -2.35e-225)
		tmp = t_2;
	elseif (z <= 5.3e+20)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+150], (-z), If[LessEqual[z, -3.5e+40], t$95$2, If[LessEqual[z, -1.9e+26], (-z), If[LessEqual[z, -1.36e-70], t$95$1, If[LessEqual[z, -2.85e-103], t$95$2, If[LessEqual[z, -1.2e-148], t$95$1, If[LessEqual[z, -2.35e-225], t$95$2, If[LessEqual[z, 5.3e+20], t$95$1, (-z)]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999996e150 or -3.4999999999999999e40 < z < -1.9000000000000001e26 or 5.3e20 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 68.1%

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

      1. neg-mul-1 68.1%

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

   4. Simplified 68.1%

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

   if -1.99999999999999996e150 < z < -3.4999999999999999e40 or -1.36000000000000001e-70 < z < -2.8499999999999998e-103 or -1.2000000000000001e-148 < z < -2.35000000000000007e-225

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. associate--l- 99.7%

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

      5. fma-def 99.7%

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

      6. associate--l- 99.7%

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

      7. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 63.6%

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

   if -1.9000000000000001e26 < z < -1.36000000000000001e-70 or -2.8499999999999998e-103 < z < -1.2000000000000001e-148 or -2.35000000000000007e-225 < z < 5.3e20

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.1%

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

   3. Taylor expanded in x around 0 66.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-70}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+20}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 57.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-299}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -4.8e+196)
     t_2
     (if (<= x -1.5e+93)
       t_3
       (if (<= x -1.2e+24)
         t_2
         (if (<= x -5e-232)
           t_1
           (if (<= x 1.35e-299) t_3 (if (<= x 4e+45) 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 <= -4.8e+196) {
		tmp = t_2;
	} else if (x <= -1.5e+93) {
		tmp = t_3;
	} else if (x <= -1.2e+24) {
		tmp = t_2;
	} else if (x <= -5e-232) {
		tmp = t_1;
	} else if (x <= 1.35e-299) {
		tmp = t_3;
	} else if (x <= 4e+45) {
		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 <= (-4.8d+196)) then
        tmp = t_2
    else if (x <= (-1.5d+93)) then
        tmp = t_3
    else if (x <= (-1.2d+24)) then
        tmp = t_2
    else if (x <= (-5d-232)) then
        tmp = t_1
    else if (x <= 1.35d-299) then
        tmp = t_3
    else if (x <= 4d+45) 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 <= -4.8e+196) {
		tmp = t_2;
	} else if (x <= -1.5e+93) {
		tmp = t_3;
	} else if (x <= -1.2e+24) {
		tmp = t_2;
	} else if (x <= -5e-232) {
		tmp = t_1;
	} else if (x <= 1.35e-299) {
		tmp = t_3;
	} else if (x <= 4e+45) {
		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 <= -4.8e+196:
		tmp = t_2
	elif x <= -1.5e+93:
		tmp = t_3
	elif x <= -1.2e+24:
		tmp = t_2
	elif x <= -5e-232:
		tmp = t_1
	elif x <= 1.35e-299:
		tmp = t_3
	elif x <= 4e+45:
		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 <= -4.8e+196)
		tmp = t_2;
	elseif (x <= -1.5e+93)
		tmp = t_3;
	elseif (x <= -1.2e+24)
		tmp = t_2;
	elseif (x <= -5e-232)
		tmp = t_1;
	elseif (x <= 1.35e-299)
		tmp = t_3;
	elseif (x <= 4e+45)
		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 <= -4.8e+196)
		tmp = t_2;
	elseif (x <= -1.5e+93)
		tmp = t_3;
	elseif (x <= -1.2e+24)
		tmp = t_2;
	elseif (x <= -5e-232)
		tmp = t_1;
	elseif (x <= 1.35e-299)
		tmp = t_3;
	elseif (x <= 4e+45)
		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, -4.8e+196], t$95$2, If[LessEqual[x, -1.5e+93], t$95$3, If[LessEqual[x, -1.2e+24], t$95$2, If[LessEqual[x, -5e-232], t$95$1, If[LessEqual[x, 1.35e-299], t$95$3, If[LessEqual[x, 4e+45], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000001e196 or -1.49999999999999989e93 < x < -1.2e24 or 3.9999999999999997e45 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. associate--l- 99.7%

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

      5. fma-def 99.7%

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

      6. associate--l- 99.7%

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

      7. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.5%

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

   if -4.8000000000000001e196 < x < -1.49999999999999989e93 or -4.9999999999999999e-232 < x < 1.35000000000000001e-299

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 86.7%

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

   3. Taylor expanded in x around 0 67.7%

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

   if -1.2e24 < x < -4.9999999999999999e-232 or 1.35000000000000001e-299 < x < 3.9999999999999997e45

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. fma-def 73.7%

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

   4. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, \log t\right) - z} \]
   5. Step-by-step derivation

      1. fma-udef 73.7%

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

   6. Applied egg-rr 73.7%

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

   7. Taylor expanded in x around 0 70.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+93}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-232}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-299}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+45}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 9: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(\log t - z\right) - y\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- (log t) z) y)))
   (if (<= x -1.05e+228)
     t_1
     (if (<= x -8e+84)
       t_2
       (if (<= x -3.2e+58)
         t_1
         (if (<= x 1.05e+46) t_2 (* (log (/ 1.0 y)) (- x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (log(t) - z) - y;
	double tmp;
	if (x <= -1.05e+228) {
		tmp = t_1;
	} else if (x <= -8e+84) {
		tmp = t_2;
	} else if (x <= -3.2e+58) {
		tmp = t_1;
	} else if (x <= 1.05e+46) {
		tmp = t_2;
	} else {
		tmp = log((1.0 / y)) * -x;
	}
	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) - z) - y
    if (x <= (-1.05d+228)) then
        tmp = t_1
    else if (x <= (-8d+84)) then
        tmp = t_2
    else if (x <= (-3.2d+58)) then
        tmp = t_1
    else if (x <= 1.05d+46) then
        tmp = t_2
    else
        tmp = log((1.0d0 / y)) * -x
    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) - z) - y;
	double tmp;
	if (x <= -1.05e+228) {
		tmp = t_1;
	} else if (x <= -8e+84) {
		tmp = t_2;
	} else if (x <= -3.2e+58) {
		tmp = t_1;
	} else if (x <= 1.05e+46) {
		tmp = t_2;
	} else {
		tmp = Math.log((1.0 / y)) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (math.log(t) - z) - y
	tmp = 0
	if x <= -1.05e+228:
		tmp = t_1
	elif x <= -8e+84:
		tmp = t_2
	elif x <= -3.2e+58:
		tmp = t_1
	elif x <= 1.05e+46:
		tmp = t_2
	else:
		tmp = math.log((1.0 / y)) * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(log(t) - z) - y)
	tmp = 0.0
	if (x <= -1.05e+228)
		tmp = t_1;
	elseif (x <= -8e+84)
		tmp = t_2;
	elseif (x <= -3.2e+58)
		tmp = t_1;
	elseif (x <= 1.05e+46)
		tmp = t_2;
	else
		tmp = Float64(log(Float64(1.0 / y)) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (log(t) - z) - y;
	tmp = 0.0;
	if (x <= -1.05e+228)
		tmp = t_1;
	elseif (x <= -8e+84)
		tmp = t_2;
	elseif (x <= -3.2e+58)
		tmp = t_1;
	elseif (x <= 1.05e+46)
		tmp = t_2;
	else
		tmp = log((1.0 / y)) * -x;
	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[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -1.05e+228], t$95$1, If[LessEqual[x, -8e+84], t$95$2, If[LessEqual[x, -3.2e+58], t$95$1, If[LessEqual[x, 1.05e+46], t$95$2, N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04999999999999997e228 or -8.00000000000000046e84 < x < -3.20000000000000015e58

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+r- 99.6%

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

      4. associate--l- 99.6%

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

      5. fma-def 99.7%

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

      6. associate--l- 99.7%

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

      7. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 86.9%

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

   if -1.04999999999999997e228 < x < -8.00000000000000046e84 or -3.20000000000000015e58 < x < 1.05e46

   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 x around 0 90.9%

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

   if 1.05e46 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 82.1%

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

   3. Taylor expanded in y around inf 82.1%

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

   4. Taylor expanded in x around inf 72.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+84}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \end{array} \]

Alternative 10: 80.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+228} \lor \neg \left(x \leq -2.7 \cdot 10^{+90}\right) \land \left(x \leq -3.2 \cdot 10^{+58} \lor \neg \left(x \leq 8.2 \cdot 10^{+45}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e+228)
         (and (not (<= x -2.7e+90)) (or (<= x -3.2e+58) (not (<= x 8.2e+45)))))
   (* x (log y))
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+228) || (!(x <= -2.7e+90) && ((x <= -3.2e+58) || !(x <= 8.2e+45)))) {
		tmp = x * log(y);
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.05d+228)) .or. (.not. (x <= (-2.7d+90))) .and. (x <= (-3.2d+58)) .or. (.not. (x <= 8.2d+45))) then
        tmp = x * log(y)
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+228) || (!(x <= -2.7e+90) && ((x <= -3.2e+58) || !(x <= 8.2e+45)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e+228) or (not (x <= -2.7e+90) and ((x <= -3.2e+58) or not (x <= 8.2e+45))):
		tmp = x * math.log(y)
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e+228) || (!(x <= -2.7e+90) && ((x <= -3.2e+58) || !(x <= 8.2e+45))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.05e+228) || (~((x <= -2.7e+90)) && ((x <= -3.2e+58) || ~((x <= 8.2e+45)))))
		tmp = x * log(y);
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e+228], And[N[Not[LessEqual[x, -2.7e+90]], $MachinePrecision], Or[LessEqual[x, -3.2e+58], N[Not[LessEqual[x, 8.2e+45]], $MachinePrecision]]]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999997e228 or -2.7e90 < x < -3.20000000000000015e58 or 8.20000000000000025e45 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. associate--l- 99.7%

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

      5. fma-def 99.7%

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

      6. associate--l- 99.7%

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

      7. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 76.9%

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

   if -1.04999999999999997e228 < x < -2.7e90 or -3.20000000000000015e58 < x < 8.20000000000000025e45

   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 x around 0 90.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+228} \lor \neg \left(x \leq -2.7 \cdot 10^{+90}\right) \land \left(x \leq -3.2 \cdot 10^{+58} \lor \neg \left(x \leq 8.2 \cdot 10^{+45}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 11: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 1.8e-71)
     t_1
     (if (<= y 8.2e-45)
       (- z)
       (if (<= y 3.05e-31) t_1 (if (<= y 3.75e+99) (- z) (- y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 1.8e-71) {
		tmp = t_1;
	} else if (y <= 8.2e-45) {
		tmp = -z;
	} else if (y <= 3.05e-31) {
		tmp = t_1;
	} else if (y <= 3.75e+99) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 1.8d-71) then
        tmp = t_1
    else if (y <= 8.2d-45) then
        tmp = -z
    else if (y <= 3.05d-31) then
        tmp = t_1
    else if (y <= 3.75d+99) 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 t_1 = x * Math.log(y);
	double tmp;
	if (y <= 1.8e-71) {
		tmp = t_1;
	} else if (y <= 8.2e-45) {
		tmp = -z;
	} else if (y <= 3.05e-31) {
		tmp = t_1;
	} else if (y <= 3.75e+99) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 1.8e-71:
		tmp = t_1
	elif y <= 8.2e-45:
		tmp = -z
	elif y <= 3.05e-31:
		tmp = t_1
	elif y <= 3.75e+99:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.8e-71)
		tmp = t_1;
	elseif (y <= 8.2e-45)
		tmp = Float64(-z);
	elseif (y <= 3.05e-31)
		tmp = t_1;
	elseif (y <= 3.75e+99)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 1.8e-71)
		tmp = t_1;
	elseif (y <= 8.2e-45)
		tmp = -z;
	elseif (y <= 3.05e-31)
		tmp = t_1;
	elseif (y <= 3.75e+99)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.8e-71], t$95$1, If[LessEqual[y, 8.2e-45], (-z), If[LessEqual[y, 3.05e-31], t$95$1, If[LessEqual[y, 3.75e+99], (-z), (-y)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.8e-71 or 8.1999999999999998e-45 < y < 3.0499999999999999e-31

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. associate--l- 99.7%

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

      5. fma-def 99.8%

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

      6. associate--l- 99.8%

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

      7. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 49.3%

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

   if 1.8e-71 < y < 8.1999999999999998e-45 or 3.0499999999999999e-31 < y < 3.74999999999999982e99

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. neg-mul-1 55.0%

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

   4. Simplified 55.0%

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

   if 3.74999999999999982e99 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+r- 100.0%

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

      4. associate--l- 100.0%

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

      5. fma-def 100.0%

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

      6. associate--l- 100.0%

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

      7. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. neg-mul-1 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 12: 48.2% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1e+99) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e+99) {
		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 <= 1d+99) 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 <= 1e+99) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1e+99:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1e+99)
		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 <= 1e+99)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1e+99], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 9.9999999999999997e98

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 38.1%

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

      1. neg-mul-1 38.1%

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

   4. Simplified 38.1%

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

   if 9.9999999999999997e98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+r- 100.0%

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

      4. associate--l- 100.0%

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

      5. fma-def 100.0%

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

      6. associate--l- 100.0%

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

      7. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. neg-mul-1 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+99}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 13: 30.7% 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 99.8%

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

2. Taylor expanded in x around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+r- 99.8%

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

   4. associate--l- 99.8%

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

   5. fma-def 99.9%

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

   6. associate--l- 99.9%

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

   7. +-commutative 99.9%

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

4. Simplified 99.9%

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

5. Taylor expanded in y around inf 25.7%

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

   1. neg-mul-1 25.7%

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

7. Simplified 25.7%

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

8. Final simplification 25.7%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023277 
(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)))