Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 31.9s

Alternatives: 13

Speedup: 1.0×

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: 99.6% 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]

Derivation

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. Final simplification 99.6%

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

Alternative 2: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -2 \cdot 10^{+16} \lor \neg \left(a - 0.5 \leq -0.4999998\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log z + \log y\right) - t\right) + \log t \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -2e+16) (not (<= (- a 0.5) -0.4999998)))
   (+ (log (+ x y)) (- (* a (log t)) t))
   (+ (- (+ (log z) (log y)) t) (* (log t) -0.5))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -2e+16) || !((a - 0.5) <= -0.4999998)) {
		tmp = log((x + y)) + ((a * log(t)) - t);
	} else {
		tmp = ((log(z) + log(y)) - t) + (log(t) * -0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (((a - 0.5d0) <= (-2d+16)) .or. (.not. ((a - 0.5d0) <= (-0.4999998d0)))) then
        tmp = log((x + y)) + ((a * log(t)) - t)
    else
        tmp = ((log(z) + log(y)) - t) + (log(t) * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -2e+16) || !((a - 0.5) <= -0.4999998)) {
		tmp = Math.log((x + y)) + ((a * Math.log(t)) - t);
	} else {
		tmp = ((Math.log(z) + Math.log(y)) - t) + (Math.log(t) * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -2e+16) or not ((a - 0.5) <= -0.4999998):
		tmp = math.log((x + y)) + ((a * math.log(t)) - t)
	else:
		tmp = ((math.log(z) + math.log(y)) - t) + (math.log(t) * -0.5)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -2e+16) || !(Float64(a - 0.5) <= -0.4999998))
		tmp = Float64(log(Float64(x + y)) + Float64(Float64(a * log(t)) - t));
	else
		tmp = Float64(Float64(Float64(log(z) + log(y)) - t) + Float64(log(t) * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -2e+16) || ~(((a - 0.5) <= -0.4999998)))
		tmp = log((x + y)) + ((a * log(t)) - t);
	else
		tmp = ((log(z) + log(y)) - t) + (log(t) * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -2e+16], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4999998]], $MachinePrecision]], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a 1/2) < -2e16 or -0.49999979999999999 < (-.f64 a 1/2)

   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. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r- 99.6%

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

      5. fma-def 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 98.7%

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

      1. *-commutative 98.7%

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

   6. Simplified 98.7%

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

   if -2e16 < (-.f64 a 1/2) < -0.49999979999999999

   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. add-cube-cbrt 99.2%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}} \]

      2. pow3 99.2%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right)}^{3}} \]

      3. sub-neg 99.2%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t}\right)}^{3} \]

      4. metadata-eval 99.2%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\left(a + \color{blue}{-0.5}\right) \cdot \log t}\right)}^{3} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}} \]

   4. Taylor expanded in x around 0 61.3%

      \[\leadsto \left(\color{blue}{\left(\log z + \log y\right)} - t\right) + {\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3} \]

   5. Taylor expanded in a around 0 61.1%

      \[\leadsto \left(\left(\log z + \log y\right) - t\right) + \color{blue}{-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \log t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 61.1%

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

      2. *-lft-identity 61.1%

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

   7. Simplified 61.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -2 \cdot 10^{+16} \lor \neg \left(a - 0.5 \leq -0.4999998\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log z + \log y\right) - t\right) + \log t \cdot -0.5\\ \end{array} \]

Alternative 3: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log z \leq 200:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (log z) 200.0)
   (+ (log (* (+ x y) z)) (- (* (log t) (+ a -0.5)) t))
   (+ (log (+ x y)) (- (* a (log t)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (log(z) <= 200.0) {
		tmp = log(((x + y) * z)) + ((log(t) * (a + -0.5)) - t);
	} else {
		tmp = log((x + y)) + ((a * log(t)) - t);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (log(z) <= 200.0d0) then
        tmp = log(((x + y) * z)) + ((log(t) * (a + (-0.5d0))) - t)
    else
        tmp = log((x + y)) + ((a * log(t)) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (Math.log(z) <= 200.0) {
		tmp = Math.log(((x + y) * z)) + ((Math.log(t) * (a + -0.5)) - t);
	} else {
		tmp = Math.log((x + y)) + ((a * Math.log(t)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if math.log(z) <= 200.0:
		tmp = math.log(((x + y) * z)) + ((math.log(t) * (a + -0.5)) - t)
	else:
		tmp = math.log((x + y)) + ((a * math.log(t)) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (log(z) <= 200.0)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + Float64(Float64(log(t) * Float64(a + -0.5)) - t));
	else
		tmp = Float64(log(Float64(x + y)) + Float64(Float64(a * log(t)) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (log(z) <= 200.0)
		tmp = log(((x + y) * z)) + ((log(t) * (a + -0.5)) - t);
	else
		tmp = log((x + y)) + ((a * log(t)) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Log[z], $MachinePrecision], 200.0], N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 z) < 200

   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. +-commutative 99.5%

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

      3. sum-log 94.9%

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

      4. sub-neg 94.9%

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

      5. metadata-eval 94.9%

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

   3. Applied egg-rr 94.9%

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

   if 200 < (log.f64 z)

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+r- 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 77.9%

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

      1. *-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log z \leq 200:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \end{array} \]

Alternative 4: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log z \leq 200:\\ \;\;\;\;\left(\left(a - 0.5\right) \cdot \log t + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (log z) 200.0)
   (- (+ (* (- a 0.5) (log t)) (log (* y z))) t)
   (+ (log (+ x y)) (- (* a (log t)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (log(z) <= 200.0) {
		tmp = (((a - 0.5) * log(t)) + log((y * z))) - t;
	} else {
		tmp = log((x + y)) + ((a * log(t)) - t);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (log(z) <= 200.0d0) then
        tmp = (((a - 0.5d0) * log(t)) + log((y * z))) - t
    else
        tmp = log((x + y)) + ((a * log(t)) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (Math.log(z) <= 200.0) {
		tmp = (((a - 0.5) * Math.log(t)) + Math.log((y * z))) - t;
	} else {
		tmp = Math.log((x + y)) + ((a * Math.log(t)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if math.log(z) <= 200.0:
		tmp = (((a - 0.5) * math.log(t)) + math.log((y * z))) - t
	else:
		tmp = math.log((x + y)) + ((a * math.log(t)) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (log(z) <= 200.0)
		tmp = Float64(Float64(Float64(Float64(a - 0.5) * log(t)) + log(Float64(y * z))) - t);
	else
		tmp = Float64(log(Float64(x + y)) + Float64(Float64(a * log(t)) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (log(z) <= 200.0)
		tmp = (((a - 0.5) * log(t)) + log((y * z))) - t;
	else
		tmp = log((x + y)) + ((a * log(t)) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Log[z], $MachinePrecision], 200.0], N[(N[(N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 z) < 200

   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. +-commutative 99.5%

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

      3. sum-log 94.9%

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

      4. sub-neg 94.9%

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

      5. metadata-eval 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in x around 0 58.8%

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

   if 200 < (log.f64 z)

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+r- 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 77.9%

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

      1. *-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log z \leq 200:\\ \;\;\;\;\left(\left(a - 0.5\right) \cdot \log t + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \end{array} \]

Alternative 5: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(x + y\right)\\ \mathbf{if}\;t \leq 0.00172:\\ \;\;\;\;\left(t_1 + \log z\right) + \left(a - 0.5\right) \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a \cdot \log t - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (+ x y))))
   (if (<= t 0.00172)
     (+ (+ t_1 (log z)) (* (- a 0.5) (log t)))
     (+ t_1 (- (* a (log t)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((x + y));
	double tmp;
	if (t <= 0.00172) {
		tmp = (t_1 + log(z)) + ((a - 0.5) * log(t));
	} else {
		tmp = t_1 + ((a * log(t)) - t);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log((x + y))
    if (t <= 0.00172d0) then
        tmp = (t_1 + log(z)) + ((a - 0.5d0) * log(t))
    else
        tmp = t_1 + ((a * log(t)) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log((x + y));
	double tmp;
	if (t <= 0.00172) {
		tmp = (t_1 + Math.log(z)) + ((a - 0.5) * Math.log(t));
	} else {
		tmp = t_1 + ((a * Math.log(t)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log((x + y))
	tmp = 0
	if t <= 0.00172:
		tmp = (t_1 + math.log(z)) + ((a - 0.5) * math.log(t))
	else:
		tmp = t_1 + ((a * math.log(t)) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(x + y))
	tmp = 0.0
	if (t <= 0.00172)
		tmp = Float64(Float64(t_1 + log(z)) + Float64(Float64(a - 0.5) * log(t)));
	else
		tmp = Float64(t_1 + Float64(Float64(a * log(t)) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log((x + y));
	tmp = 0.0;
	if (t <= 0.00172)
		tmp = (t_1 + log(z)) + ((a - 0.5) * log(t));
	else
		tmp = t_1 + ((a * log(t)) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 0.00172], N[(N[(t$95$1 + N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 0.00171999999999999996

   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. Taylor expanded in t around 0 98.7%

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

   if 0.00171999999999999996 < 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%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r- 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 99.0%

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

      1. *-commutative 99.0%

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

   6. Simplified 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.00172:\\ \;\;\;\;\left(\log \left(x + y\right) + \log z\right) + \left(a - 0.5\right) \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \end{array} \]

Alternative 6: 69.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((log(z) + (log(t) * (a + -0.5))) + log(y)) - 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(z) + (log(t) * (a + (-0.5d0)))) + log(y)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+r- 99.5%

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

   5. fma-def 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around 0 65.6%

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

   1. associate--l+ 65.6%

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

   2. associate--l+ 65.6%

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

   3. remove-double-neg 65.6%

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

   4. log-rec 65.6%

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

   5. mul-1-neg 65.6%

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

   6. associate--l+ 65.6%

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

   7. associate--l+ 65.6%

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

6. Simplified 29.4%

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

   1. *-commutative 29.4%

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

   2. log-prod 31.4%

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

   3. pow-to-exp 31.4%

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

   4. +-commutative 31.4%

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

   5. *-commutative 31.4%

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

   6. add-cube-cbrt 31.3%

      \[\leadsto \left(\left(\log \left(e^{\color{blue}{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a + -0.5\right) \cdot \log t}}}\right) + \log z\right) + \log y\right) - t \]

   7. unpow3 31.3%

      \[\leadsto \left(\left(\log \left(e^{\color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}}}\right) + \log z\right) + \log y\right) - t \]

   8. add-log-exp 65.2%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}} + \log z\right) + \log y\right) - t \]

   9. unpow3 65.2%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a + -0.5\right) \cdot \log t}} + \log z\right) + \log y\right) - t \]

   10. add-cube-cbrt 65.6%

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

   11. *-commutative 65.6%

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

8. Applied egg-rr 65.6%

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

9. Final simplification 65.6%

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

Alternative 7: 72.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-11} \lor \neg \left(a \leq 5.2 \cdot 10^{-9}\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5e-11) (not (<= a 5.2e-9)))
   (+ (log (+ x y)) (- (* a (log t)) t))
   (- (log (* y (* z (pow t (+ a -0.5))))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5e-11) || !(a <= 5.2e-9)) {
		tmp = log((x + y)) + ((a * log(t)) - t);
	} else {
		tmp = log((y * (z * pow(t, (a + -0.5))))) - t;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-5d-11)) .or. (.not. (a <= 5.2d-9))) then
        tmp = log((x + y)) + ((a * log(t)) - t)
    else
        tmp = log((y * (z * (t ** (a + (-0.5d0)))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5e-11) || !(a <= 5.2e-9)) {
		tmp = Math.log((x + y)) + ((a * Math.log(t)) - t);
	} else {
		tmp = Math.log((y * (z * Math.pow(t, (a + -0.5))))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5e-11) or not (a <= 5.2e-9):
		tmp = math.log((x + y)) + ((a * math.log(t)) - t)
	else:
		tmp = math.log((y * (z * math.pow(t, (a + -0.5))))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5e-11) || !(a <= 5.2e-9))
		tmp = Float64(log(Float64(x + y)) + Float64(Float64(a * log(t)) - t));
	else
		tmp = Float64(log(Float64(y * Float64(z * (t ^ Float64(a + -0.5))))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5e-11) || ~((a <= 5.2e-9)))
		tmp = log((x + y)) + ((a * log(t)) - t);
	else
		tmp = log((y * (z * (t ^ (a + -0.5))))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5e-11], N[Not[LessEqual[a, 5.2e-9]], $MachinePrecision]], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(y * N[(z * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.00000000000000018e-11 or 5.2000000000000002e-9 < 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. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r- 99.6%

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

      5. fma-def 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 98.2%

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

      1. *-commutative 98.2%

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

   6. Simplified 98.2%

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

   if -5.00000000000000018e-11 < a < 5.2000000000000002e-9

   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. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+r- 99.5%

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

      5. fma-def 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate--l+ 61.0%

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

      3. remove-double-neg 61.0%

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

      4. log-rec 61.0%

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

      5. mul-1-neg 61.0%

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

      6. associate--l+ 61.0%

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

      7. associate--l+ 61.0%

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

   6. Simplified 56.5%

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

      1. sum-log 43.0%

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

      2. +-commutative 43.0%

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

   8. Applied egg-rr 43.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-11} \lor \neg \left(a \leq 5.2 \cdot 10^{-9}\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ \end{array} \]

Alternative 8: 72.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-12} \lor \neg \left(a \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-12) (not (<= a 6.8e-9)))
   (+ (log (+ x y)) (- (* a (log t)) t))
   (- (log (* y (* z (sqrt (/ 1.0 t))))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-12) || !(a <= 6.8e-9)) {
		tmp = log((x + y)) + ((a * log(t)) - t);
	} else {
		tmp = log((y * (z * sqrt((1.0 / t))))) - t;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-4.8d-12)) .or. (.not. (a <= 6.8d-9))) then
        tmp = log((x + y)) + ((a * log(t)) - t)
    else
        tmp = log((y * (z * sqrt((1.0d0 / t))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-12) || !(a <= 6.8e-9)) {
		tmp = Math.log((x + y)) + ((a * Math.log(t)) - t);
	} else {
		tmp = Math.log((y * (z * Math.sqrt((1.0 / t))))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-12) or not (a <= 6.8e-9):
		tmp = math.log((x + y)) + ((a * math.log(t)) - t)
	else:
		tmp = math.log((y * (z * math.sqrt((1.0 / t))))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-12) || !(a <= 6.8e-9))
		tmp = Float64(log(Float64(x + y)) + Float64(Float64(a * log(t)) - t));
	else
		tmp = Float64(log(Float64(y * Float64(z * sqrt(Float64(1.0 / t))))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-12) || ~((a <= 6.8e-9)))
		tmp = log((x + y)) + ((a * log(t)) - t);
	else
		tmp = log((y * (z * sqrt((1.0 / t))))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-12], N[Not[LessEqual[a, 6.8e-9]], $MachinePrecision]], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(y * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.79999999999999974e-12 or 6.7999999999999997e-9 < 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. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r- 99.6%

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

      5. fma-def 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 98.2%

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

      1. *-commutative 98.2%

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

   6. Simplified 98.2%

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

   if -4.79999999999999974e-12 < a < 6.7999999999999997e-9

   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. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+r- 99.5%

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

      5. fma-def 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate--l+ 61.0%

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

      3. remove-double-neg 61.0%

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

      4. log-rec 61.0%

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

      5. mul-1-neg 61.0%

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

      6. associate--l+ 61.0%

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

      7. associate--l+ 61.0%

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

   6. Simplified 56.5%

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

      1. sum-log 43.0%

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

      2. +-commutative 43.0%

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

   8. Applied egg-rr 43.0%

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

   9. Taylor expanded in a around 0 42.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-12} \lor \neg \left(a \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;\log \left(x + y\right) + \left(a \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)\right) - t\\ \end{array} \]

Alternative 9: 57.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+53} \lor \neg \left(a \leq 5.8 \cdot 10^{+40}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e+53) (not (<= a 5.8e+40)))
   (* a (log t))
   (- (+ (log z) (log y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+53) || !(a <= 5.8e+40)) {
		tmp = a * log(t);
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-1.8d+53)) .or. (.not. (a <= 5.8d+40))) then
        tmp = a * log(t)
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+53) || !(a <= 5.8e+40)) {
		tmp = a * Math.log(t);
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e+53) or not (a <= 5.8e+40):
		tmp = a * math.log(t)
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e+53) || !(a <= 5.8e+40))
		tmp = Float64(a * log(t));
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e+53) || ~((a <= 5.8e+40)))
		tmp = a * log(t);
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e+53], N[Not[LessEqual[a, 5.8e+40]], $MachinePrecision]], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e53 or 5.80000000000000035e40 < 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%

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

      2. +-commutative 99.6%

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

      3. sum-log 82.3%

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

      4. sub-neg 82.3%

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

      5. metadata-eval 82.3%

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

   3. Applied egg-rr 82.3%

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

      1. rem-cube-cbrt 81.4%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}}\right) \]

   5. Applied egg-rr 81.4%

      \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}}\right) \]
   6. Step-by-step derivation

      1. rem-cube-cbrt 82.3%

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

      2. flip-+ 40.3%

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

      3. associate-*l/ 40.3%

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

      4. fma-neg 40.3%

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

      5. metadata-eval 40.3%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -\color{blue}{0.25}\right) \cdot \log t}{a - -0.5}\right) \]

      6. metadata-eval 40.3%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, \color{blue}{-0.25}\right) \cdot \log t}{a - -0.5}\right) \]

      7. sub-neg 40.3%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{\color{blue}{a + \left(--0.5\right)}}\right) \]

      8. metadata-eval 40.3%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{a + \color{blue}{0.5}}\right) \]

   7. Applied egg-rr 40.3%

      \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{\frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{a + 0.5}}\right) \]

   8. Taylor expanded in a around inf 81.9%

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

      1. *-commutative 81.9%

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

   10. Simplified 81.9%

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

   if -1.8e53 < a < 5.80000000000000035e40

   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. add-cube-cbrt 99.3%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}} \]

      2. pow3 99.3%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right)}^{3}} \]

      3. sub-neg 99.3%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t}\right)}^{3} \]

      4. metadata-eval 99.3%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\left(a + \color{blue}{-0.5}\right) \cdot \log t}\right)}^{3} \]

   3. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}} \]

   4. Taylor expanded in x around 0 61.3%

      \[\leadsto \left(\color{blue}{\left(\log z + \log y\right)} - t\right) + {\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3} \]

   5. Taylor expanded in a around inf 43.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+53} \lor \neg \left(a \leq 5.8 \cdot 10^{+40}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]

Alternative 10: 77.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+r- 99.5%

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

   5. fma-def 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in a around inf 77.6%

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

   1. *-commutative 77.6%

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

6. Simplified 77.6%

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

7. Final simplification 77.6%

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

Alternative 11: 39.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 580:\\ \;\;\;\;\log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 580.0) (log (* y z)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 580.0) {
		tmp = log((y * z));
	} else {
		tmp = -t;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= 580.0d0) then
        tmp = log((y * z))
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 580.0) {
		tmp = Math.log((y * z));
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 580.0:
		tmp = math.log((y * z))
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 580.0)
		tmp = log(Float64(y * z));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 580.0)
		tmp = log((y * z));
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 580.0], N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 580

   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. add-cube-cbrt 98.4%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t} \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right) \cdot \sqrt[3]{\left(a - 0.5\right) \cdot \log t}} \]

      2. pow3 98.4%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a - 0.5\right) \cdot \log t}\right)}^{3}} \]

      3. sub-neg 98.4%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \log t}\right)}^{3} \]

      4. metadata-eval 98.4%

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + {\left(\sqrt[3]{\left(a + \color{blue}{-0.5}\right) \cdot \log t}\right)}^{3} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}} \]

   4. Taylor expanded in x around 0 57.0%

      \[\leadsto \left(\color{blue}{\left(\log z + \log y\right)} - t\right) + {\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3} \]

   5. Taylor expanded in a around inf 6.1%

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

      1. log-prod 5.6%

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

   7. Simplified 5.6%

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

   8. Taylor expanded in t around 0 5.6%

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

   if 580 < 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%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r- 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 73.5%

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

      1. neg-mul-1 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 580:\\ \;\;\;\;\log \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 12: 62.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 5.5e+27) (* a (log t)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.5e+27) {
		tmp = a * log(t);
	} else {
		tmp = -t;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= 5.5d+27) then
        tmp = a * log(t)
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.5e+27) {
		tmp = a * Math.log(t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.5e+27:
		tmp = a * math.log(t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.5e+27)
		tmp = Float64(a * log(t));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 5.5e+27)
		tmp = a * log(t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5.5e+27], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 5.49999999999999966e27

   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. +-commutative 99.3%

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

      3. sum-log 81.1%

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

      4. sub-neg 81.1%

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

      5. metadata-eval 81.1%

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

   3. Applied egg-rr 81.1%

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

      1. rem-cube-cbrt 80.2%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}}\right) \]

   5. Applied egg-rr 80.2%

      \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{{\left(\sqrt[3]{\left(a + -0.5\right) \cdot \log t}\right)}^{3}}\right) \]
   6. Step-by-step derivation

      1. rem-cube-cbrt 81.1%

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

      2. flip-+ 60.4%

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

      3. associate-*l/ 60.4%

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

      4. fma-neg 60.4%

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

      5. metadata-eval 60.4%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -\color{blue}{0.25}\right) \cdot \log t}{a - -0.5}\right) \]

      6. metadata-eval 60.4%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, \color{blue}{-0.25}\right) \cdot \log t}{a - -0.5}\right) \]

      7. sub-neg 60.4%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{\color{blue}{a + \left(--0.5\right)}}\right) \]

      8. metadata-eval 60.4%

         \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{a + \color{blue}{0.5}}\right) \]

   7. Applied egg-rr 60.4%

      \[\leadsto \log \left(z \cdot \left(x + y\right)\right) - \left(t - \color{blue}{\frac{\mathsf{fma}\left(a, a, -0.25\right) \cdot \log t}{a + 0.5}}\right) \]

   8. Taylor expanded in a around inf 53.0%

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

      1. *-commutative 53.0%

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

   10. Simplified 53.0%

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

   if 5.49999999999999966e27 < 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%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r- 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 77.5%

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

      1. neg-mul-1 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 13: 38.0% accurate, 156.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+r- 99.5%

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

   5. fma-def 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in t around inf 36.5%

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

   1. neg-mul-1 36.5%

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

6. Simplified 36.5%

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

7. Final simplification 36.5%

   \[\leadsto -t \]

Developer target: 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 2023274 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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