Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 13.8s

Alternatives: 14

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, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. +-commutative 99.6%

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

   2. associate--l+ 99.6%

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

   3. associate-+r+ 99.6%

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

   4. +-commutative 99.6%

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

   5. fma-define 99.6%

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

   6. sub-neg 99.6%

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

   7. metadata-eval 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.425:\\ \;\;\;\;\left(\log z + \log y\right) + \left(a + -0.5\right) \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \left(\log y + a \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.425)
   (+ (+ (log z) (log y)) (* (+ a -0.5) (log t)))
   (+ (- (log z) t) (+ (log y) (* a (log t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.425) {
		tmp = (log(z) + log(y)) + ((a + -0.5) * log(t));
	} else {
		tmp = (log(z) - t) + (log(y) + (a * log(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 <= 0.425d0) then
        tmp = (log(z) + log(y)) + ((a + (-0.5d0)) * log(t))
    else
        tmp = (log(z) - t) + (log(y) + (a * log(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 <= 0.425) {
		tmp = (Math.log(z) + Math.log(y)) + ((a + -0.5) * Math.log(t));
	} else {
		tmp = (Math.log(z) - t) + (Math.log(y) + (a * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 0.425:
		tmp = (math.log(z) + math.log(y)) + ((a + -0.5) * math.log(t))
	else:
		tmp = (math.log(z) - t) + (math.log(y) + (a * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 0.425)
		tmp = Float64(Float64(log(z) + log(y)) + Float64(Float64(a + -0.5) * log(t)));
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(y) + Float64(a * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 0.425)
		tmp = (log(z) + log(y)) + ((a + -0.5) * log(t));
	else
		tmp = (log(z) - t) + (log(y) + (a * log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 0.425], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] + N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.424999999999999989

   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. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 68.0%

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

   6. Taylor expanded in t around 0 67.4%

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

      1. associate-+r+ 67.5%

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

      2. sub-neg 67.5%

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

      3. metadata-eval 67.5%

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

   8. Simplified 67.5%

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

   if 0.424999999999999989 < 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. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-define 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 75.1%

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

   6. Taylor expanded in a around inf 75.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.425:\\ \;\;\;\;\left(\log z + \log y\right) + \left(a + -0.5\right) \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \left(\log y + a \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(\log z + \log y\right) + \left(a + -0.5\right) \cdot \log t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+151}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 7.5e-6)
   (+ (+ (log z) (log y)) (* (+ a -0.5) (log t)))
   (if (<= t 1.9e+151)
     (+ (* (log t) (- a 0.5)) (- (log (* z (+ x y))) t))
     (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7.5e-6) {
		tmp = (log(z) + log(y)) + ((a + -0.5) * log(t));
	} else if (t <= 1.9e+151) {
		tmp = (log(t) * (a - 0.5)) + (log((z * (x + y))) - 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 <= 7.5d-6) then
        tmp = (log(z) + log(y)) + ((a + (-0.5d0)) * log(t))
    else if (t <= 1.9d+151) then
        tmp = (log(t) * (a - 0.5d0)) + (log((z * (x + y))) - 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 <= 7.5e-6) {
		tmp = (Math.log(z) + Math.log(y)) + ((a + -0.5) * Math.log(t));
	} else if (t <= 1.9e+151) {
		tmp = (Math.log(t) * (a - 0.5)) + (Math.log((z * (x + y))) - t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 7.5e-6:
		tmp = (math.log(z) + math.log(y)) + ((a + -0.5) * math.log(t))
	elif t <= 1.9e+151:
		tmp = (math.log(t) * (a - 0.5)) + (math.log((z * (x + y))) - t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7.5e-6)
		tmp = Float64(Float64(log(z) + log(y)) + Float64(Float64(a + -0.5) * log(t)));
	elseif (t <= 1.9e+151)
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + Float64(log(Float64(z * Float64(x + y))) - t));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 7.5e-6)
		tmp = (log(z) + log(y)) + ((a + -0.5) * log(t));
	elseif (t <= 1.9e+151)
		tmp = (log(t) * (a - 0.5)) + (log((z * (x + y))) - t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7.5e-6], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+151], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], (-t)]]

Derivation

1. Split input into 3 regimes

2. if t < 7.50000000000000019e-6

   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. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 68.8%

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

   6. Taylor expanded in t around 0 68.6%

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

      1. associate-+r+ 68.7%

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

      2. sub-neg 68.7%

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

      3. metadata-eval 68.7%

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

   8. Simplified 68.7%

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

   if 7.50000000000000019e-6 < t < 1.9e151

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sum-log 80.2%

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

   4. Applied egg-rr 80.2%

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

   if 1.9e151 < 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+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      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 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(\log z + \log y\right) + \left(a + -0.5\right) \cdot \log t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+151}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\log y + \left(\log z + t\_1\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+150}:\\ \;\;\;\;t\_1 + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) (- a 0.5))))
   (if (<= t 1.6e-5)
     (+ (log y) (+ (log z) t_1))
     (if (<= t 7.6e+150) (+ t_1 (- (log (* z (+ x y))) t)) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * (a - 0.5);
	double tmp;
	if (t <= 1.6e-5) {
		tmp = log(y) + (log(z) + t_1);
	} else if (t <= 7.6e+150) {
		tmp = t_1 + (log((z * (x + y))) - 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) * (a - 0.5d0)
    if (t <= 1.6d-5) then
        tmp = log(y) + (log(z) + t_1)
    else if (t <= 7.6d+150) then
        tmp = t_1 + (log((z * (x + y))) - 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 t_1 = Math.log(t) * (a - 0.5);
	double tmp;
	if (t <= 1.6e-5) {
		tmp = Math.log(y) + (Math.log(z) + t_1);
	} else if (t <= 7.6e+150) {
		tmp = t_1 + (Math.log((z * (x + y))) - t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * (a - 0.5)
	tmp = 0
	if t <= 1.6e-5:
		tmp = math.log(y) + (math.log(z) + t_1)
	elif t <= 7.6e+150:
		tmp = t_1 + (math.log((z * (x + y))) - t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * Float64(a - 0.5))
	tmp = 0.0
	if (t <= 1.6e-5)
		tmp = Float64(log(y) + Float64(log(z) + t_1));
	elseif (t <= 7.6e+150)
		tmp = Float64(t_1 + Float64(log(Float64(z * Float64(x + y))) - t));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * (a - 0.5);
	tmp = 0.0;
	if (t <= 1.6e-5)
		tmp = log(y) + (log(z) + t_1);
	elseif (t <= 7.6e+150)
		tmp = t_1 + (log((z * (x + y))) - t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 1.6e-5], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+150], N[(t$95$1 + N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], (-t)]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.59999999999999993e-5

   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. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 68.8%

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

   6. Taylor expanded in t around 0 68.6%

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

   if 1.59999999999999993e-5 < t < 7.59999999999999978e150

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sum-log 80.2%

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

   4. Applied egg-rr 80.2%

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

   if 7.59999999999999978e150 < 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+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      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 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+150}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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((x + y))) - t) + (log(t) * (a - 0.5d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.6%

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

Alternative 6: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision]), $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. 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. Final simplification 99.6%

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

Alternative 7: 68.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) - t) + (log(y) + (log(t) * (a - 0.5d0)))
end function

Java

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

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

Julia

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

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

Wolfram

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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate--l+ 99.6%

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

   3. associate-+r+ 99.6%

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

   4. +-commutative 99.6%

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

   5. fma-define 99.6%

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

   6. sub-neg 99.6%

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

   7. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 71.5%

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

Alternative 8: 77.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.3 \cdot 10^{+151}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.3e+151)
   (+ (* (log t) (- a 0.5)) (- (log (* z (+ x y))) t))
   (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.3e+151) {
		tmp = (log(t) * (a - 0.5)) + (log((z * (x + y))) - 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 <= 4.3d+151) then
        tmp = (log(t) * (a - 0.5d0)) + (log((z * (x + y))) - 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 <= 4.3e+151) {
		tmp = (Math.log(t) * (a - 0.5)) + (Math.log((z * (x + y))) - t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.3e+151:
		tmp = (math.log(t) * (a - 0.5)) + (math.log((z * (x + y))) - t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.3e+151)
		tmp = Float64(Float64(log(t) * Float64(a - 0.5)) + Float64(log(Float64(z * Float64(x + y))) - t));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.3e+151)
		tmp = (log(t) * (a - 0.5)) + (log((z * (x + y))) - t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.3e+151], N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 4.29999999999999983e151

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sum-log 76.1%

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

   4. Applied egg-rr 76.1%

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

   if 4.29999999999999983e151 < 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+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      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 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.3 \cdot 10^{+151}:\\ \;\;\;\;\log t \cdot \left(a - 0.5\right) + \left(\log \left(z \cdot \left(x + y\right)\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -820000000000 \lor \neg \left(a \leq 2.25 \cdot 10^{+26}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -820000000000.0) (not (<= a 2.25e+26)))
   (* a (log t))
   (+ (- (log z) t) (log y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -820000000000.0) || !(a <= 2.25e+26)) {
		tmp = a * log(t);
	} else {
		tmp = (log(z) - t) + log(y);
	}
	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 <= (-820000000000.0d0)) .or. (.not. (a <= 2.25d+26))) then
        tmp = a * log(t)
    else
        tmp = (log(z) - t) + log(y)
    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 <= -820000000000.0) || !(a <= 2.25e+26)) {
		tmp = a * Math.log(t);
	} else {
		tmp = (Math.log(z) - t) + Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -820000000000.0) or not (a <= 2.25e+26):
		tmp = a * math.log(t)
	else:
		tmp = (math.log(z) - t) + math.log(y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -820000000000.0) || !(a <= 2.25e+26))
		tmp = Float64(a * log(t));
	else
		tmp = Float64(Float64(log(z) - t) + log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -820000000000.0) || ~((a <= 2.25e+26)))
		tmp = a * log(t);
	else
		tmp = (log(z) - t) + log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -820000000000.0], N[Not[LessEqual[a, 2.25e+26]], $MachinePrecision]], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2e11 or 2.24999999999999989e26 < 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. associate--l+ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-undefine 99.6%

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

      8. sub-neg 99.6%

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

      9. +-commutative 99.6%

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

      10. distribute-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around inf 74.7%

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

      1. *-commutative 74.7%

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

   7. Simplified 74.7%

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

   if -8.2e11 < a < 2.24999999999999989e26

   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. associate--l+ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-undefine 99.6%

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

      8. sub-neg 99.6%

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

      9. +-commutative 99.6%

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

      10. distribute-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. associate-/l* 98.8%

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

      3. distribute-lft-neg-in 98.8%

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

      4. log-rec 98.8%

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

      5. remove-double-neg 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 67.1%

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

   9. Taylor expanded in t around inf 42.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -820000000000 \lor \neg \left(a \leq 2.25 \cdot 10^{+26}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.65e+14) (* a (log t)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.65e+14) {
		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 <= 2.65d+14) 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 <= 2.65e+14) {
		tmp = a * Math.log(t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.65e+14:
		tmp = a * math.log(t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.65e+14)
		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 <= 2.65e+14)
		tmp = a * log(t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.65e+14], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 2.65e14

   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 a around inf 54.0%

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

      1. *-commutative 54.0%

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

   7. Simplified 54.0%

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

   if 2.65e14 < 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%

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

      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 77.4%

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

      1. neg-mul-1 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(\frac{1}{t} + -1\right) + -1 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (t * ((1.0 / t) + -1.0)) + -1.0;
}

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 * ((1.0d0 / t) + (-1.0d0))) + (-1.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (t * ((1.0 / t) + -1.0)) + -1.0;
}

Python

def code(x, y, z, t, a):
	return (t * ((1.0 / t) + -1.0)) + -1.0

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(t * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + -1.0), $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%

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

   2. associate--l+ 99.6%

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

   3. sub-neg 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-rgt-neg-in 99.6%

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

   7. fma-undefine 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

   13. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around inf 38.3%

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

   1. neg-mul-1 38.3%

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

7. Simplified 38.3%

   \[\leadsto \color{blue}{-t} \]
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 38.3%

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

    4. unsub-neg 38.3%

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

    5. metadata-eval 38.3%

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

11. Simplified 38.3%

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

12. Taylor expanded in t around inf 38.4%

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

13. Final simplification 38.4%

    \[\leadsto t \cdot \left(\frac{1}{t} + -1\right) + -1 \]
14. Add Preprocessing

Alternative 12: 37.7% accurate, 62.6× speedup

Math

\[\begin{array}{l} \\ -1 + \left(1 - t\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ -1.0 (- 1.0 t)))

C

double code(double x, double y, double z, double t, double a) {
	return -1.0 + (1.0 - 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 = (-1.0d0) + (1.0d0 - t)
end function

Java

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

Python

def code(x, y, z, t, a):
	return -1.0 + (1.0 - t)

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -1.0 + (1.0 - t);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-1.0 + N[(1.0 - 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%

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

   2. associate--l+ 99.6%

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

   3. sub-neg 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-rgt-neg-in 99.6%

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

   7. fma-undefine 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

   13. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around inf 38.3%

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

   1. neg-mul-1 38.3%

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

7. Simplified 38.3%

   \[\leadsto \color{blue}{-t} \]
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 38.3%

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

    4. unsub-neg 38.3%

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

    5. metadata-eval 38.3%

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

11. Simplified 38.3%

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

12. Final simplification 38.3%

    \[\leadsto -1 + \left(1 - t\right) \]
13. Add Preprocessing

Alternative 13: 37.7% 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%

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

   2. associate--l+ 99.6%

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

   3. sub-neg 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-rgt-neg-in 99.6%

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

   7. fma-undefine 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

   13. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around inf 38.3%

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

   1. neg-mul-1 38.3%

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

7. Simplified 38.3%

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

Alternative 14: 2.4% accurate, 313.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

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

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 = 0.0d0
end function

Java

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

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

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%

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

   2. associate--l+ 99.6%

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

   3. sub-neg 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-rgt-neg-in 99.6%

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

   7. fma-undefine 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

   13. unsub-neg 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around inf 38.3%

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

   1. neg-mul-1 38.3%

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

7. Simplified 38.3%

   \[\leadsto \color{blue}{-t} \]
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 38.3%

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

    4. unsub-neg 38.3%

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

    5. metadata-eval 38.3%

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

11. Simplified 38.3%

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

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 2024144 
(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))))