Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.3%

Time: 16.0s

Alternatives: 16

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + ((a - 0.5d0) * log(t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + ((a - 0.5) * Math.log(t));
}

Python

def code(x, y, z, t, a):
	return ((math.log((x + y)) + math.log(z)) - t) + ((a - 0.5) * math.log(t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(Float64(a - 0.5) * log(t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + ((a - 0.5d0) * log(t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + ((a - 0.5) * Math.log(t));
}

Python

def code(x, y, z, t, a):
	return ((math.log((x + y)) + math.log(z)) - t) + ((a - 0.5) * math.log(t))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(Float64(a - 0.5) * log(t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (- (+ (log y) (+ (log z) (* (log t) (- a 0.5)))) t))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (log(y) + (log(z) + (log(t) * (a - 0.5)))) - t;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (log(y) + (log(z) + (log(t) * (a - 0.5d0)))) - t
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (Math.log(y) + (Math.log(z) + (Math.log(t) * (a - 0.5)))) - t;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (math.log(y) + (math.log(z) + (math.log(t) * (a - 0.5)))) - t

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(log(y) + Float64(log(z) + Float64(log(t) * Float64(a - 0.5)))) - t)
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (log(y) + (log(z) + (log(t) * (a - 0.5)))) - t;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate--l+ 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

   2. sub-neg 99.5%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

   3. metadata-eval 99.5%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 69.5%

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
6. Step-by-step derivation

   1. associate-+r+ 69.5%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

   2. sub-neg 69.5%

      \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

   3. metadata-eval 69.5%

      \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

7. Simplified 69.5%

   \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

8. Taylor expanded in y around 0 69.5%

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right)} - t \]
9. Add Preprocessing

Alternative 2: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 140:\\ \;\;\;\;\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a - t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 140.0)
   (+ (log y) (+ (log z) (* (log t) (- a 0.5))))
   (- (* (log t) a) t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 140.0) {
		tmp = log(y) + (log(z) + (log(t) * (a - 0.5)));
	} else {
		tmp = (log(t) * a) - t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 140.0d0) then
        tmp = log(y) + (log(z) + (log(t) * (a - 0.5d0)))
    else
        tmp = (log(t) * a) - t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 140.0) {
		tmp = Math.log(y) + (Math.log(z) + (Math.log(t) * (a - 0.5)));
	} else {
		tmp = (Math.log(t) * a) - t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 140.0:
		tmp = math.log(y) + (math.log(z) + (math.log(t) * (a - 0.5)))
	else:
		tmp = (math.log(t) * a) - t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 140.0)
		tmp = Float64(log(y) + Float64(log(z) + Float64(log(t) * Float64(a - 0.5))));
	else
		tmp = Float64(Float64(log(t) * a) - t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 140.0)
		tmp = log(y) + (log(z) + (log(t) * (a - 0.5)));
	else
		tmp = (log(t) * a) - t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 140.0], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 140

   1. Initial program 99.2%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.2%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.2%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.2%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 64.0%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 64.0%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 64.0%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 64.0%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in y around 0 64.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right)} - t \]

   9. Taylor expanded in t around 0 63.6%

      \[\leadsto \color{blue}{\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)} \]

   if 140 < t

   1. Initial program 99.8%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 75.7%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 75.7%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 75.7%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 98.4%

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

      1. *-commutative 98.4%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 98.4%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \left(\log z - t\right) + \left(\log y + \log t \cdot \left(a - 0.5\right)\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (+ (- (log z) t) (+ (log y) (* (log t) (- a 0.5)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (log(z) - t) + (log(y) + (log(t) * (a - 0.5)));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (log(z) - t) + (log(y) + (log(t) * (a - 0.5d0)))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (Math.log(z) - t) + (Math.log(y) + (Math.log(t) * (a - 0.5)));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (math.log(z) - t) + (math.log(y) + (math.log(t) * (a - 0.5)))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(log(z) - t) + Float64(log(y) + Float64(log(t) * Float64(a - 0.5))))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (log(z) - t) + (log(y) + (log(t) * (a - 0.5)));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate--l+ 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

   2. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

   3. associate-+l+ 99.5%

      \[\leadsto \color{blue}{\left(\log z - t\right) + \left(\log \left(x + y\right) + \left(a - 0.5\right) \cdot \log t\right)} \]

   4. +-commutative 99.5%

      \[\leadsto \left(\log z - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log t + \log \left(x + y\right)\right)} \]

   5. fma-define 99.5%

      \[\leadsto \left(\log z - t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, \log t, \log \left(x + y\right)\right)} \]

   6. sub-neg 99.5%

      \[\leadsto \left(\log z - t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, \log t, \log \left(x + y\right)\right) \]

   7. metadata-eval 99.5%

      \[\leadsto \left(\log z - t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, \log t, \log \left(x + y\right)\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 69.5%

   \[\leadsto \left(\log z - t\right) + \color{blue}{\left(\log y + \log t \cdot \left(a - 0.5\right)\right)} \]
6. Add Preprocessing

Alternative 4: 85.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 175\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(y + x\right)\right) - t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-108) (not (<= a 175.0)))
   (- (* (log t) a) t)
   (+ (* (log t) (- a 0.5)) (- (log (* z (+ y x))) t))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 175.0)) {
		tmp = (log(t) * a) - t;
	} else {
		tmp = (log(t) * (a - 0.5)) + (log((z * (y + x))) - t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-108)) .or. (.not. (a <= 175.0d0))) then
        tmp = (log(t) * a) - t
    else
        tmp = (log(t) * (a - 0.5d0)) + (log((z * (y + x))) - t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 175.0)) {
		tmp = (Math.log(t) * a) - t;
	} else {
		tmp = (Math.log(t) * (a - 0.5)) + (Math.log((z * (y + x))) - t);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-108) or not (a <= 175.0):
		tmp = (math.log(t) * a) - t
	else:
		tmp = (math.log(t) * (a - 0.5)) + (math.log((z * (y + x))) - t)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-108) || !(a <= 175.0))
		tmp = Float64(Float64(log(t) * a) - t);
	else
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + Float64(log(Float64(z * Float64(y + x))) - t));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-108) || ~((a <= 175.0)))
		tmp = (log(t) * a) - t;
	else
		tmp = (log(t) * (a - 0.5)) + (log((z * (y + x))) - t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-108], N[Not[LessEqual[a, 175.0]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Log[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000034e-108 or 175 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 93.6%

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

      1. *-commutative 93.6%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 93.6%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -4.80000000000000034e-108 < a < 175

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sum-log 78.2%

         \[\leadsto \left(\color{blue}{\log \left(\left(x + y\right) \cdot z\right)} - t\right) + \left(a - 0.5\right) \cdot \log t \]

   4. Applied egg-rr 78.2%

      \[\leadsto \left(\color{blue}{\log \left(\left(x + y\right) \cdot z\right)} - t\right) + \left(a - 0.5\right) \cdot \log t \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 175\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(y + x\right)\right) - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \log t \cdot a - t\\ \mathbf{if}\;a \leq -2.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-52}:\\ \;\;\;\;\left(\log y + \log z\right) - t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;\log \left(y \cdot z\right) + \log t \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (log t) a) t)))
   (if (<= a -2.1)
     t_1
     (if (<= a 9e-52)
       (- (+ (log y) (log z)) t)
       (if (<= a 2.3e-15) (+ (log (* y z)) (* (log t) -0.5)) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (log(t) * a) - t;
	double tmp;
	if (a <= -2.1) {
		tmp = t_1;
	} else if (a <= 9e-52) {
		tmp = (log(y) + log(z)) - t;
	} else if (a <= 2.3e-15) {
		tmp = log((y * z)) + (log(t) * -0.5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (log(t) * a) - t
    if (a <= (-2.1d0)) then
        tmp = t_1
    else if (a <= 9d-52) then
        tmp = (log(y) + log(z)) - t
    else if (a <= 2.3d-15) then
        tmp = log((y * z)) + (log(t) * (-0.5d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (Math.log(t) * a) - t;
	double tmp;
	if (a <= -2.1) {
		tmp = t_1;
	} else if (a <= 9e-52) {
		tmp = (Math.log(y) + Math.log(z)) - t;
	} else if (a <= 2.3e-15) {
		tmp = Math.log((y * z)) + (Math.log(t) * -0.5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (math.log(t) * a) - t
	tmp = 0
	if a <= -2.1:
		tmp = t_1
	elif a <= 9e-52:
		tmp = (math.log(y) + math.log(z)) - t
	elif a <= 2.3e-15:
		tmp = math.log((y * z)) + (math.log(t) * -0.5)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(log(t) * a) - t)
	tmp = 0.0
	if (a <= -2.1)
		tmp = t_1;
	elseif (a <= 9e-52)
		tmp = Float64(Float64(log(y) + log(z)) - t);
	elseif (a <= 2.3e-15)
		tmp = Float64(log(Float64(y * z)) + Float64(log(t) * -0.5));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (log(t) * a) - t;
	tmp = 0.0;
	if (a <= -2.1)
		tmp = t_1;
	elseif (a <= 9e-52)
		tmp = (log(y) + log(z)) - t;
	elseif (a <= 2.3e-15)
		tmp = log((y * z)) + (log(t) * -0.5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[a, -2.1], t$95$1, If[LessEqual[a, 9e-52], N[(N[(N[Log[y], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 2.3e-15], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.10000000000000009 or 2.2999999999999999e-15 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.5%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.5%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.5%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.5%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 97.8%

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

      1. *-commutative 97.8%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 97.8%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -2.10000000000000009 < a < 9.0000000000000001e-52

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.4%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.4%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 99.3%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t \cdot \left(1 + -1 \cdot \frac{\log \left(\frac{1}{t}\right) \cdot \left(0.5 - a\right)}{t}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\left(-\frac{\log \left(\frac{1}{t}\right) \cdot \left(0.5 - a\right)}{t}\right)}\right)\right) \]

      2. associate-/l* 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \left(-\color{blue}{\log \left(\frac{1}{t}\right) \cdot \frac{0.5 - a}{t}}\right)\right)\right) \]

      3. distribute-lft-neg-in 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\left(-\log \left(\frac{1}{t}\right)\right) \cdot \frac{0.5 - a}{t}}\right)\right) \]

      4. log-rec 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \left(-\color{blue}{\left(-\log t\right)}\right) \cdot \frac{0.5 - a}{t}\right)\right) \]

      5. remove-double-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\log t} \cdot \frac{0.5 - a}{t}\right)\right) \]

   7. Simplified 99.4%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t \cdot \left(1 + \log t \cdot \frac{0.5 - a}{t}\right)}\right) \]

   8. Taylor expanded in x around 0 69.2%

      \[\leadsto \color{blue}{\left(\log y + \log z\right) - t \cdot \left(1 + \frac{\log t \cdot \left(0.5 - a\right)}{t}\right)} \]

   9. Taylor expanded in t around inf 45.9%

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

   if 9.0000000000000001e-52 < a < 2.2999999999999999e-15

   1. Initial program 99.3%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.3%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 45.5%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 45.6%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 45.6%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 45.6%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 45.6%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]
   8. Step-by-step derivation

      1. associate--l+ 45.6%

         \[\leadsto \color{blue}{\left(\log y + \log z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]

      2. sum-log 44.0%

         \[\leadsto \color{blue}{\log \left(y \cdot z\right)} + \left(\log t \cdot \left(a + -0.5\right) - t\right) \]

   9. Applied egg-rr 44.0%

      \[\leadsto \color{blue}{\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]
   10. Step-by-step derivation

       1. +-commutative 44.0%

          \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)} \]

       2. *-commutative 44.0%

          \[\leadsto \left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 44.0%

       \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(z \cdot y\right)} \]

   12. Taylor expanded in a around 0 44.0%

       \[\leadsto \color{blue}{\left(-0.5 \cdot \log t - t\right)} + \log \left(z \cdot y\right) \]
   13. Step-by-step derivation

       1. *-commutative 44.0%

          \[\leadsto \left(\color{blue}{\log t \cdot -0.5} - t\right) + \log \left(z \cdot y\right) \]

   14. Simplified 44.0%

       \[\leadsto \color{blue}{\left(\log t \cdot -0.5 - t\right)} + \log \left(z \cdot y\right) \]

   15. Taylor expanded in t around 0 34.8%

       \[\leadsto \color{blue}{\log \left(y \cdot z\right) + -0.5 \cdot \log t} \]
   16. Step-by-step derivation

       1. +-commutative 34.8%

          \[\leadsto \color{blue}{-0.5 \cdot \log t + \log \left(y \cdot z\right)} \]

       2. *-commutative 34.8%

          \[\leadsto \color{blue}{\log t \cdot -0.5} + \log \left(y \cdot z\right) \]

   17. Simplified 34.8%

       \[\leadsto \color{blue}{\log t \cdot -0.5 + \log \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1:\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-52}:\\ \;\;\;\;\left(\log y + \log z\right) - t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;\log \left(y \cdot z\right) + \log t \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a - t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 55000\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-108) (not (<= a 55000.0)))
   (- (* (log t) a) t)
   (+ (- (* (log t) (+ a -0.5)) t) (log (* y z)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 55000.0)) {
		tmp = (log(t) * a) - t;
	} else {
		tmp = ((log(t) * (a + -0.5)) - t) + log((y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-108)) .or. (.not. (a <= 55000.0d0))) then
        tmp = (log(t) * a) - t
    else
        tmp = ((log(t) * (a + (-0.5d0))) - t) + log((y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 55000.0)) {
		tmp = (Math.log(t) * a) - t;
	} else {
		tmp = ((Math.log(t) * (a + -0.5)) - t) + Math.log((y * z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-108) or not (a <= 55000.0):
		tmp = (math.log(t) * a) - t
	else:
		tmp = ((math.log(t) * (a + -0.5)) - t) + math.log((y * z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-108) || !(a <= 55000.0))
		tmp = Float64(Float64(log(t) * a) - t);
	else
		tmp = Float64(Float64(Float64(log(t) * Float64(a + -0.5)) - t) + log(Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-108) || ~((a <= 55000.0)))
		tmp = (log(t) * a) - t;
	else
		tmp = ((log(t) * (a + -0.5)) - t) + log((y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-108], N[Not[LessEqual[a, 55000.0]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000034e-108 or 55000 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 93.6%

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

      1. *-commutative 93.6%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 93.6%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -4.80000000000000034e-108 < a < 55000

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.3%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 66.1%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 66.1%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]
   8. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{\left(\log y + \log z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]

      2. sum-log 55.0%

         \[\leadsto \color{blue}{\log \left(y \cdot z\right)} + \left(\log t \cdot \left(a + -0.5\right) - t\right) \]

   9. Applied egg-rr 55.0%

      \[\leadsto \color{blue}{\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]
   10. Step-by-step derivation

       1. +-commutative 55.0%

          \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)} \]

       2. *-commutative 55.0%

          \[\leadsto \left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 55.0%

       \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(z \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 55000\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 0.142\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot -0.5\right) - t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-108) (not (<= a 0.142)))
   (- (* (log t) a) t)
   (- (+ (log (* y z)) (* (log t) -0.5)) t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 0.142)) {
		tmp = (log(t) * a) - t;
	} else {
		tmp = (log((y * z)) + (log(t) * -0.5)) - t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-108)) .or. (.not. (a <= 0.142d0))) then
        tmp = (log(t) * a) - t
    else
        tmp = (log((y * z)) + (log(t) * (-0.5d0))) - t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 0.142)) {
		tmp = (Math.log(t) * a) - t;
	} else {
		tmp = (Math.log((y * z)) + (Math.log(t) * -0.5)) - t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-108) or not (a <= 0.142):
		tmp = (math.log(t) * a) - t
	else:
		tmp = (math.log((y * z)) + (math.log(t) * -0.5)) - t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-108) || !(a <= 0.142))
		tmp = Float64(Float64(log(t) * a) - t);
	else
		tmp = Float64(Float64(log(Float64(y * z)) + Float64(log(t) * -0.5)) - t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-108) || ~((a <= 0.142)))
		tmp = (log(t) * a) - t;
	else
		tmp = (log((y * z)) + (log(t) * -0.5)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-108], N[Not[LessEqual[a, 0.142]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000034e-108 or 0.141999999999999987 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 93.6%

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

      1. *-commutative 93.6%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 93.6%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -4.80000000000000034e-108 < a < 0.141999999999999987

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.3%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 66.1%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 66.1%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]
   8. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{\left(\log y + \log z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]

      2. sum-log 55.0%

         \[\leadsto \color{blue}{\log \left(y \cdot z\right)} + \left(\log t \cdot \left(a + -0.5\right) - t\right) \]

   9. Applied egg-rr 55.0%

      \[\leadsto \color{blue}{\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]
   10. Step-by-step derivation

       1. +-commutative 55.0%

          \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)} \]

       2. *-commutative 55.0%

          \[\leadsto \left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 55.0%

       \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(z \cdot y\right)} \]

   12. Taylor expanded in a around 0 55.0%

       \[\leadsto \color{blue}{\left(\log \left(y \cdot z\right) + -0.5 \cdot \log t\right) - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 0.142\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot -0.5\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 0.00068\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot -0.5 - t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-108) (not (<= a 0.00068)))
   (- (* (log t) a) t)
   (+ (log (* y z)) (- (* (log t) -0.5) t))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 0.00068)) {
		tmp = (log(t) * a) - t;
	} else {
		tmp = log((y * z)) + ((log(t) * -0.5) - t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-108)) .or. (.not. (a <= 0.00068d0))) then
        tmp = (log(t) * a) - t
    else
        tmp = log((y * z)) + ((log(t) * (-0.5d0)) - t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-108) || !(a <= 0.00068)) {
		tmp = (Math.log(t) * a) - t;
	} else {
		tmp = Math.log((y * z)) + ((Math.log(t) * -0.5) - t);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-108) or not (a <= 0.00068):
		tmp = (math.log(t) * a) - t
	else:
		tmp = math.log((y * z)) + ((math.log(t) * -0.5) - t)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-108) || !(a <= 0.00068))
		tmp = Float64(Float64(log(t) * a) - t);
	else
		tmp = Float64(log(Float64(y * z)) + Float64(Float64(log(t) * -0.5) - t));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-108) || ~((a <= 0.00068)))
		tmp = (log(t) * a) - t;
	else
		tmp = log((y * z)) + ((log(t) * -0.5) - t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-108], N[Not[LessEqual[a, 0.00068]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000034e-108 or 6.8e-4 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.9%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 93.6%

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

      1. *-commutative 93.6%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 93.6%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -4.80000000000000034e-108 < a < 6.8e-4

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.3%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.3%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 66.1%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 66.1%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 66.1%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]
   8. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{\left(\log y + \log z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]

      2. sum-log 55.0%

         \[\leadsto \color{blue}{\log \left(y \cdot z\right)} + \left(\log t \cdot \left(a + -0.5\right) - t\right) \]

   9. Applied egg-rr 55.0%

      \[\leadsto \color{blue}{\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]
   10. Step-by-step derivation

       1. +-commutative 55.0%

          \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)} \]

       2. *-commutative 55.0%

          \[\leadsto \left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 55.0%

       \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(z \cdot y\right)} \]

   12. Taylor expanded in a around 0 55.0%

       \[\leadsto \color{blue}{\left(-0.5 \cdot \log t - t\right)} + \log \left(z \cdot y\right) \]
   13. Step-by-step derivation

       1. *-commutative 55.0%

          \[\leadsto \left(\color{blue}{\log t \cdot -0.5} - t\right) + \log \left(z \cdot y\right) \]

   14. Simplified 55.0%

       \[\leadsto \color{blue}{\left(\log t \cdot -0.5 - t\right)} + \log \left(z \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-108} \lor \neg \left(a \leq 0.00068\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot -0.5 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -0.98 \lor \neg \left(a \leq 2.6\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \log z\right) - t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.98) (not (<= a 2.6)))
   (- (* (log t) a) t)
   (- (+ (log y) (log z)) t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.98) || !(a <= 2.6)) {
		tmp = (log(t) * a) - t;
	} else {
		tmp = (log(y) + log(z)) - t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.98d0)) .or. (.not. (a <= 2.6d0))) then
        tmp = (log(t) * a) - t
    else
        tmp = (log(y) + log(z)) - t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.98) || !(a <= 2.6)) {
		tmp = (Math.log(t) * a) - t;
	} else {
		tmp = (Math.log(y) + Math.log(z)) - t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.98) or not (a <= 2.6):
		tmp = (math.log(t) * a) - t
	else:
		tmp = (math.log(y) + math.log(z)) - t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.98) || !(a <= 2.6))
		tmp = Float64(Float64(log(t) * a) - t);
	else
		tmp = Float64(Float64(log(y) + log(z)) - t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.98) || ~((a <= 2.6)))
		tmp = (log(t) * a) - t;
	else
		tmp = (log(y) + log(z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.98], N[Not[LessEqual[a, 2.6]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.97999999999999998 or 2.60000000000000009 < a

   1. Initial program 99.6%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.5%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 71.5%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 71.5%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 71.5%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 97.8%

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

      1. *-commutative 97.8%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 97.8%

       \[\leadsto \color{blue}{\log t \cdot a} - t \]

   if -0.97999999999999998 < a < 2.60000000000000009

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.4%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.4%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 99.4%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t \cdot \left(1 + -1 \cdot \frac{\log \left(\frac{1}{t}\right) \cdot \left(0.5 - a\right)}{t}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\left(-\frac{\log \left(\frac{1}{t}\right) \cdot \left(0.5 - a\right)}{t}\right)}\right)\right) \]

      2. associate-/l* 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \left(-\color{blue}{\log \left(\frac{1}{t}\right) \cdot \frac{0.5 - a}{t}}\right)\right)\right) \]

      3. distribute-lft-neg-in 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\left(-\log \left(\frac{1}{t}\right)\right) \cdot \frac{0.5 - a}{t}}\right)\right) \]

      4. log-rec 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \left(-\color{blue}{\left(-\log t\right)}\right) \cdot \frac{0.5 - a}{t}\right)\right) \]

      5. remove-double-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - t \cdot \left(1 + \color{blue}{\log t} \cdot \frac{0.5 - a}{t}\right)\right) \]

   7. Simplified 99.4%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t \cdot \left(1 + \log t \cdot \frac{0.5 - a}{t}\right)}\right) \]

   8. Taylor expanded in x around 0 67.2%

      \[\leadsto \color{blue}{\left(\log y + \log z\right) - t \cdot \left(1 + \frac{\log t \cdot \left(0.5 - a\right)}{t}\right)} \]

   9. Taylor expanded in t around inf 43.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.98 \lor \neg \left(a \leq 2.6\right):\\ \;\;\;\;\log t \cdot a - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \log z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 0.0136:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a - t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.0136)
   (+ (* (log t) (- a 0.5)) (log (* y z)))
   (- (* (log t) a) t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.0136) {
		tmp = (log(t) * (a - 0.5)) + log((y * z));
	} else {
		tmp = (log(t) * a) - t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 0.0136d0) then
        tmp = (log(t) * (a - 0.5d0)) + log((y * z))
    else
        tmp = (log(t) * a) - t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.0136) {
		tmp = (Math.log(t) * (a - 0.5)) + Math.log((y * z));
	} else {
		tmp = (Math.log(t) * a) - t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 0.0136:
		tmp = (math.log(t) * (a - 0.5)) + math.log((y * z))
	else:
		tmp = (math.log(t) * a) - t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 0.0136)
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z)));
	else
		tmp = Float64(Float64(log(t) * a) - t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 0.0136)
		tmp = (log(t) * (a - 0.5)) + log((y * z));
	else
		tmp = (log(t) * a) - t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 0.0136], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.0135999999999999992

   1. Initial program 99.2%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.2%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.2%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.2%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.2%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 64.3%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 64.3%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 64.3%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 64.3%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]
   8. Step-by-step derivation

      1. associate--l+ 64.3%

         \[\leadsto \color{blue}{\left(\log y + \log z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]

      2. sum-log 45.9%

         \[\leadsto \color{blue}{\log \left(y \cdot z\right)} + \left(\log t \cdot \left(a + -0.5\right) - t\right) \]

   9. Applied egg-rr 45.9%

      \[\leadsto \color{blue}{\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)} \]
   10. Step-by-step derivation

       1. +-commutative 45.9%

          \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(y \cdot z\right)} \]

       2. *-commutative 45.9%

          \[\leadsto \left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 45.9%

       \[\leadsto \color{blue}{\left(\log t \cdot \left(a + -0.5\right) - t\right) + \log \left(z \cdot y\right)} \]

   12. Taylor expanded in t around 0 45.5%

       \[\leadsto \color{blue}{\log t \cdot \left(a - 0.5\right)} + \log \left(z \cdot y\right) \]

   if 0.0135999999999999992 < t

   1. Initial program 99.8%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.0%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 75.0%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 75.0%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 75.0%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 96.8%

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

      1. *-commutative 96.8%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 96.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.0136:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a - t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \log t \cdot a\\ \mathbf{if}\;t \leq 120:\\ \;\;\;\;t\_1 + \log \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)))
   (if (<= t 120.0) (+ t_1 (log (+ y x))) (- t_1 t))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double tmp;
	if (t <= 120.0) {
		tmp = t_1 + log((y + x));
	} else {
		tmp = t_1 - t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) * a
    if (t <= 120.0d0) then
        tmp = t_1 + log((y + x))
    else
        tmp = t_1 - t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double tmp;
	if (t <= 120.0) {
		tmp = t_1 + Math.log((y + x));
	} else {
		tmp = t_1 - t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	tmp = 0
	if t <= 120.0:
		tmp = t_1 + math.log((y + x))
	else:
		tmp = t_1 - t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 120.0)
		tmp = Float64(t_1 + log(Float64(y + x)));
	else
		tmp = Float64(t_1 - t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	tmp = 0.0;
	if (t <= 120.0)
		tmp = t_1 + log((y + x));
	else
		tmp = t_1 - t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 120.0], N[(t$95$1 + N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$1 - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 120

   1. Initial program 99.2%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.2%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.3%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 99.2%

      \[\leadsto \log \left(x + y\right) + \color{blue}{a \cdot \left(\frac{\log z}{a} - \left(-1 \cdot \log t + \left(0.5 \cdot \frac{\log t}{a} + \frac{t}{a}\right)\right)\right)} \]

   6. Taylor expanded in a around inf 56.5%

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

   if 120 < t

   1. Initial program 99.8%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. sub-neg 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

      3. metadata-eval 99.8%

         \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
   6. Step-by-step derivation

      1. associate-+r+ 75.7%

         \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

      2. sub-neg 75.7%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

      3. metadata-eval 75.7%

         \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

   8. Taylor expanded in a around inf 98.4%

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

      1. *-commutative 98.4%

         \[\leadsto \color{blue}{\log t \cdot a} - t \]

   10. Simplified 98.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 120:\\ \;\;\;\;\log t \cdot a + \log \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 12500000000000:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 12500000000000.0) (* (log t) a) (- t)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 12500000000000.0) {
		tmp = log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 12500000000000.0d0) then
        tmp = log(t) * a
    else
        tmp = -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 12500000000000.0) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 12500000000000.0:
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 12500000000000.0)
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 12500000000000.0)
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 12500000000000.0], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 1.25e13

   1. Initial program 99.3%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.3%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.3%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if 1.25e13 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.8%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.8%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.8%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.5%

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

      1. neg-mul-1 73.5%

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

   7. Simplified 73.5%

      \[\leadsto \color{blue}{-t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 73.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \log t \cdot a - t \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (- (* (log t) a) t))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (log(t) * a) - t;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (log(t) * a) - t
end function

Java

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

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (math.log(t) * a) - t

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(log(t) * a) - t)
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (log(t) * a) - t;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate--l+ 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

   2. sub-neg 99.5%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t \]

   3. metadata-eval 99.5%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \log t \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a + -0.5\right) \cdot \log t} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 69.5%

   \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\right) - t} \]
6. Step-by-step derivation

   1. associate-+r+ 69.5%

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - 0.5\right)\right)} - t \]

   2. sub-neg 69.5%

      \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) - t \]

   3. metadata-eval 69.5%

      \[\leadsto \left(\left(\log y + \log z\right) + \log t \cdot \left(a + \color{blue}{-0.5}\right)\right) - t \]

7. Simplified 69.5%

   \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a + -0.5\right)\right) - t} \]

8. Taylor expanded in a around inf 73.6%

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

   1. *-commutative 73.6%

      \[\leadsto \color{blue}{\log t \cdot a} - t \]

10. Simplified 73.6%

    \[\leadsto \color{blue}{\log t \cdot a} - t \]
11. Add Preprocessing

Alternative 14: 37.5% accurate, 62.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \left(1 - t\right) + -1 \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (+ (- 1.0 t) -1.0))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (1.0 - t) + -1.0;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (1.0d0 - t) + (-1.0d0)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (1.0 - t) + -1.0;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (1.0 - t) + -1.0

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(1.0 - t) + -1.0)
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (1.0 - t) + -1.0;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(1.0 - t), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate-+l- 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

   2. associate--l+ 99.5%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

   3. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

   4. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

   5. *-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

   6. distribute-rgt-neg-in 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

   7. fma-undefine 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

   8. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

   9. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

   10. distribute-neg-in 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

   11. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

   12. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

   13. unsub-neg 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 35.2%

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

   1. neg-mul-1 35.2%

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

7. Simplified 35.2%

   \[\leadsto \color{blue}{-t} \]
8. Step-by-step derivation

   1. expm1-log1p-u 1.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

   2. expm1-undefine 1.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

9. Applied egg-rr 1.4%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
10. Step-by-step derivation

    1. sub-neg 1.4%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

    2. log1p-undefine 1.4%

       \[\leadsto e^{\color{blue}{\log \left(1 + \left(-t\right)\right)}} + \left(-1\right) \]

    3. rem-exp-log 35.2%

       \[\leadsto \color{blue}{\left(1 + \left(-t\right)\right)} + \left(-1\right) \]

    4. unsub-neg 35.2%

       \[\leadsto \color{blue}{\left(1 - t\right)} + \left(-1\right) \]

    5. metadata-eval 35.2%

       \[\leadsto \left(1 - t\right) + \color{blue}{-1} \]

11. Simplified 35.2%

    \[\leadsto \color{blue}{\left(1 - t\right) + -1} \]
12. Add Preprocessing

Alternative 15: 37.5% accurate, 156.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -t \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (- t))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -t;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = -t
end function

Java

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

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -t

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-t)
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -t;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := (-t)

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate-+l- 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

   2. associate--l+ 99.5%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

   3. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

   4. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

   5. *-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

   6. distribute-rgt-neg-in 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

   7. fma-undefine 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

   8. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

   9. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

   10. distribute-neg-in 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

   11. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

   12. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

   13. unsub-neg 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 35.2%

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

   1. neg-mul-1 35.2%

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

7. Simplified 35.2%

   \[\leadsto \color{blue}{-t} \]
8. Add Preprocessing

Alternative 16: 2.4% accurate, 313.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ 0 \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 0.0)

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return 0.0

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return 0.0
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 99.5%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate-+l- 99.5%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

   2. associate--l+ 99.5%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

   3. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

   4. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

   5. *-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

   6. distribute-rgt-neg-in 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

   7. fma-undefine 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

   8. sub-neg 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

   9. +-commutative 99.5%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

   10. distribute-neg-in 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

   11. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

   12. metadata-eval 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

   13. unsub-neg 99.5%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 35.2%

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

   1. neg-mul-1 35.2%

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

7. Simplified 35.2%

   \[\leadsto \color{blue}{-t} \]
8. Step-by-step derivation

   1. expm1-log1p-u 1.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

   2. expm1-undefine 1.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

9. Applied egg-rr 1.4%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
10. Step-by-step derivation

    1. sub-neg 1.4%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

    2. log1p-undefine 1.4%

       \[\leadsto e^{\color{blue}{\log \left(1 + \left(-t\right)\right)}} + \left(-1\right) \]

    3. rem-exp-log 35.2%

       \[\leadsto \color{blue}{\left(1 + \left(-t\right)\right)} + \left(-1\right) \]

    4. unsub-neg 35.2%

       \[\leadsto \color{blue}{\left(1 - t\right)} + \left(-1\right) \]

    5. metadata-eval 35.2%

       \[\leadsto \left(1 - t\right) + \color{blue}{-1} \]

11. Simplified 35.2%

    \[\leadsto \color{blue}{\left(1 - t\right) + -1} \]

12. Taylor expanded in t around 0 2.4%

    \[\leadsto \color{blue}{1} + -1 \]
13. Step-by-step derivation

    1. metadata-eval 2.4%

       \[\leadsto \color{blue}{0} \]

14. Applied egg-rr 2.4%

    \[\leadsto \color{blue}{0} \]
15. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t)))))

C

double code(double x, double y, double z, double t, double a) {
	return log((x + y)) + ((log(z) - t) + ((a - 0.5) * log(t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = log((x + y)) + ((log(z) - t) + ((a - 0.5d0) * log(t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return Math.log((x + y)) + ((Math.log(z) - t) + ((a - 0.5) * Math.log(t)));
}

Python

def code(x, y, z, t, a):
	return math.log((x + y)) + ((math.log(z) - t) + ((a - 0.5) * math.log(t)))

Julia

function code(x, y, z, t, a)
	return Float64(log(Float64(x + y)) + Float64(Float64(log(z) - t) + Float64(Float64(a - 0.5) * log(t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = log((x + y)) + ((log(z) - t) + ((a - 0.5) * log(t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (log (+ x y)) (+ (- (log z) t) (* (- a 1/2) (log t)))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))