Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 29.7s

Alternatives: 17

Speedup: 0.8×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. cancel-sign-sub-inv 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. fma-def 99.6%

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

   7. neg-sub0 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

   8. sub-neg 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

   9. +-commutative 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

   10. associate--r+ 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

   11. metadata-eval 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

   12. metadata-eval 99.6%

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

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. Final simplification 99.6%

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

Alternative 2: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log z \leq 210:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (log z) 210.0)
   (- (+ (log (* z (+ x y))) (* (log t) (- a 0.5))) t)
   (+ (- (log z) t) (* (log t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (log(z) <= 210.0) {
		tmp = (log((z * (x + y))) + (log(t) * (a - 0.5))) - t;
	} else {
		tmp = (log(z) - t) + (log(t) * a);
	}
	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) <= 210.0d0) then
        tmp = (log((z * (x + y))) + (log(t) * (a - 0.5d0))) - t
    else
        tmp = (log(z) - t) + (log(t) * a)
    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) <= 210.0) {
		tmp = (Math.log((z * (x + y))) + (Math.log(t) * (a - 0.5))) - t;
	} else {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if math.log(z) <= 210.0:
		tmp = (math.log((z * (x + y))) + (math.log(t) * (a - 0.5))) - t
	else:
		tmp = (math.log(z) - t) + (math.log(t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (log(z) <= 210.0)
		tmp = Float64(Float64(log(Float64(z * Float64(x + y))) + Float64(log(t) * Float64(a - 0.5))) - t);
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (log(z) <= 210.0)
		tmp = (log((z * (x + y))) + (log(t) * (a - 0.5))) - t;
	else
		tmp = (log(z) - t) + (log(t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Log[z], $MachinePrecision], 210.0], N[(N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 z) < 210

   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+ 99.5%

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

      3. cancel-sign-sub-inv 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. fma-def 99.5%

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

      7. neg-sub0 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. associate-+r- 99.4%

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

      2. fma-udef 99.4%

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

      3. associate--r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. sum-log 93.3%

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

   5. Applied egg-rr 93.3%

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

   if 210 < (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. +-commutative 99.7%

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

      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-def 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. Taylor expanded in x around 0 73.6%

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

   5. Taylor expanded in a around inf 84.2%

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

      1. *-commutative 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log z \leq 210:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \]

Alternative 3: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log z \leq 210:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (log z) 210.0)
   (- (+ (log (* y z)) (* (log t) (- a 0.5))) t)
   (+ (- (log z) t) (* (log t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (log(z) <= 210.0) {
		tmp = (log((y * z)) + (log(t) * (a - 0.5))) - t;
	} else {
		tmp = (log(z) - t) + (log(t) * a);
	}
	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) <= 210.0d0) then
        tmp = (log((y * z)) + (log(t) * (a - 0.5d0))) - t
    else
        tmp = (log(z) - t) + (log(t) * a)
    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) <= 210.0) {
		tmp = (Math.log((y * z)) + (Math.log(t) * (a - 0.5))) - t;
	} else {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if math.log(z) <= 210.0:
		tmp = (math.log((y * z)) + (math.log(t) * (a - 0.5))) - t
	else:
		tmp = (math.log(z) - t) + (math.log(t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (log(z) <= 210.0)
		tmp = Float64(Float64(log(Float64(y * z)) + Float64(log(t) * Float64(a - 0.5))) - t);
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (log(z) <= 210.0)
		tmp = (log((y * z)) + (log(t) * (a - 0.5))) - t;
	else
		tmp = (log(z) - t) + (log(t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Log[z], $MachinePrecision], 210.0], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 z) < 210

   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+ 99.5%

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

      3. cancel-sign-sub-inv 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. fma-def 99.5%

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

      7. neg-sub0 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. associate-+r- 99.4%

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

      2. fma-udef 99.4%

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

      3. associate--r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. sum-log 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in x around 0 60.2%

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

   if 210 < (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. +-commutative 99.7%

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

      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-def 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. Taylor expanded in x around 0 73.6%

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

   5. Taylor expanded in a around inf 84.2%

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

      1. *-commutative 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log z \leq 210:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \]

Alternative 4: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 710:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 710.0)
   (+ (log (+ x y)) (+ (log z) (* (log t) (- a 0.5))))
   (+ (- (log z) t) (* (log t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 710.0) {
		tmp = log((x + y)) + (log(z) + (log(t) * (a - 0.5)));
	} else {
		tmp = (log(z) - t) + (log(t) * a);
	}
	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 <= 710.0d0) then
        tmp = log((x + y)) + (log(z) + (log(t) * (a - 0.5d0)))
    else
        tmp = (log(z) - t) + (log(t) * a)
    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 <= 710.0) {
		tmp = Math.log((x + y)) + (Math.log(z) + (Math.log(t) * (a - 0.5)));
	} else {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 710.0:
		tmp = math.log((x + y)) + (math.log(z) + (math.log(t) * (a - 0.5)))
	else:
		tmp = (math.log(z) - t) + (math.log(t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 710.0)
		tmp = Float64(log(Float64(x + y)) + Float64(log(z) + Float64(log(t) * Float64(a - 0.5))));
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 710.0)
		tmp = log((x + y)) + (log(z) + (log(t) * (a - 0.5)));
	else
		tmp = (log(z) - t) + (log(t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 710.0], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 710

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. associate--l+ 99.3%

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

      3. cancel-sign-sub-inv 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. neg-sub0 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t around 0 98.0%

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

   if 710 < 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. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.4%

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

   5. Taylor expanded in a around inf 99.1%

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

      1. *-commutative 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 710:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \]

Alternative 5: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 6: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 650:\\ \;\;\;\;\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 650.0)
   (+ (log y) (+ (log z) (* (log t) (- a 0.5))))
   (+ (- (log z) t) (* (log t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 650.0) {
		tmp = log(y) + (log(z) + (log(t) * (a - 0.5)));
	} else {
		tmp = (log(z) - t) + (log(t) * a);
	}
	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 <= 650.0d0) then
        tmp = log(y) + (log(z) + (log(t) * (a - 0.5d0)))
    else
        tmp = (log(z) - t) + (log(t) * a)
    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 <= 650.0) {
		tmp = Math.log(y) + (Math.log(z) + (Math.log(t) * (a - 0.5)));
	} else {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 650.0:
		tmp = math.log(y) + (math.log(z) + (math.log(t) * (a - 0.5)))
	else:
		tmp = (math.log(z) - t) + (math.log(t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 650.0)
		tmp = Float64(log(y) + Float64(log(z) + Float64(log(t) * Float64(a - 0.5))));
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 650.0)
		tmp = log(y) + (log(z) + (log(t) * (a - 0.5)));
	else
		tmp = (log(z) - t) + (log(t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 650.0], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 650

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. associate-+r+ 99.2%

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

      4. +-commutative 99.2%

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

      5. fma-def 99.2%

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

      6. sub-neg 99.2%

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

      7. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 62.5%

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

   5. Taylor expanded in t around 0 61.4%

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

   if 650 < 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. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.4%

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

   5. Taylor expanded in a around inf 99.1%

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

      1. *-commutative 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 650:\\ \;\;\;\;\log y + \left(\log z + \log t \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \]

Alternative 7: 69.5% 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-def 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. Taylor expanded in x around 0 70.2%

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

5. Final simplification 70.2%

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

Alternative 8: 84.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-163} \lor \neg \left(a \leq 0.028\right):\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot -0.5\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.55e-163) (not (<= a 0.028)))
   (+ (- (log z) t) (* (log t) a))
   (- (+ (log (* z (+ x y))) (* (log t) -0.5)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e-163) || !(a <= 0.028)) {
		tmp = (log(z) - t) + (log(t) * a);
	} else {
		tmp = (log((z * (x + y))) + (log(t) * -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 <= (-1.55d-163)) .or. (.not. (a <= 0.028d0))) then
        tmp = (log(z) - t) + (log(t) * a)
    else
        tmp = (log((z * (x + y))) + (log(t) * (-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 <= -1.55e-163) || !(a <= 0.028)) {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	} else {
		tmp = (Math.log((z * (x + y))) + (Math.log(t) * -0.5)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.55e-163) or not (a <= 0.028):
		tmp = (math.log(z) - t) + (math.log(t) * a)
	else:
		tmp = (math.log((z * (x + y))) + (math.log(t) * -0.5)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.55e-163) || !(a <= 0.028))
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	else
		tmp = Float64(Float64(log(Float64(z * Float64(x + y))) + Float64(log(t) * -0.5)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.55e-163) || ~((a <= 0.028)))
		tmp = (log(z) - t) + (log(t) * a);
	else
		tmp = (log((z * (x + y))) + (log(t) * -0.5)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.55e-163], N[Not[LessEqual[a, 0.028]], $MachinePrecision]], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.54999999999999987e-163 or 0.0280000000000000006 < a

   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. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 74.8%

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

   5. Taylor expanded in a around inf 96.6%

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

      1. *-commutative 96.6%

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

   7. Simplified 96.6%

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

   if -1.54999999999999987e-163 < a < 0.0280000000000000006

   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+ 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-+r+ 96.6%

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

      3. log-prod 74.8%

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

      4. +-commutative 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-163} \lor \neg \left(a \leq 0.028\right):\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot -0.5\right) - t\\ \end{array} \]

Alternative 9: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{-163} \lor \neg \left(a \leq 0.00125\right):\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot -0.5\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.38e-163) (not (<= a 0.00125)))
   (+ (- (log z) t) (* (log t) a))
   (- (+ (log (* y z)) (* (log t) -0.5)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.38e-163) || !(a <= 0.00125)) {
		tmp = (log(z) - t) + (log(t) * a);
	} else {
		tmp = (log((y * z)) + (log(t) * -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 <= (-1.38d-163)) .or. (.not. (a <= 0.00125d0))) then
        tmp = (log(z) - t) + (log(t) * a)
    else
        tmp = (log((y * z)) + (log(t) * (-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 <= -1.38e-163) || !(a <= 0.00125)) {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	} else {
		tmp = (Math.log((y * z)) + (Math.log(t) * -0.5)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.38e-163) or not (a <= 0.00125):
		tmp = (math.log(z) - t) + (math.log(t) * a)
	else:
		tmp = (math.log((y * z)) + (math.log(t) * -0.5)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.38e-163) || !(a <= 0.00125))
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	else
		tmp = Float64(Float64(log(Float64(y * z)) + Float64(log(t) * -0.5)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.38e-163) || ~((a <= 0.00125)))
		tmp = (log(z) - t) + (log(t) * a);
	else
		tmp = (log((y * z)) + (log(t) * -0.5)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.38e-163], N[Not[LessEqual[a, 0.00125]], $MachinePrecision]], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.37999999999999999e-163 or 0.00125000000000000003 < a

   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. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 74.8%

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

   5. Taylor expanded in a around inf 96.6%

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

      1. *-commutative 96.6%

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

   7. Simplified 96.6%

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

   if -1.37999999999999999e-163 < a < 0.00125000000000000003

   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. +-commutative 99.3%

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

      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-def 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. Taylor expanded in x around 0 62.1%

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

   5. Taylor expanded in a around 0 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-+r+ 61.2%

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

      3. log-prod 43.9%

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

   7. Simplified 43.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{-163} \lor \neg \left(a \leq 0.00125\right):\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot -0.5\right) - t\\ \end{array} \]

Alternative 10: 65.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+56} \lor \neg \left(a \leq 1.06 \cdot 10^{+52}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e+56) (not (<= a 1.06e+52)))
   (* (log t) a)
   (+ (log (+ x y)) (- (log z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e+56) || !(a <= 1.06e+52)) {
		tmp = log(t) * a;
	} else {
		tmp = log((x + y)) + (log(z) - 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 <= (-2.4d+56)) .or. (.not. (a <= 1.06d+52))) then
        tmp = log(t) * a
    else
        tmp = log((x + y)) + (log(z) - 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 <= -2.4e+56) || !(a <= 1.06e+52)) {
		tmp = Math.log(t) * a;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.4e+56) or not (a <= 1.06e+52):
		tmp = math.log(t) * a
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.4e+56) || !(a <= 1.06e+52))
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(log(Float64(x + y)) + Float64(log(z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.4e+56) || ~((a <= 1.06e+52)))
		tmp = log(t) * a;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.4e+56], N[Not[LessEqual[a, 1.06e+52]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.40000000000000013e56 or 1.0599999999999999e52 < 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. +-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-def 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. Taylor expanded in x around 0 74.7%

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

      1. flip-- 32.4%

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

      2. metadata-eval 32.4%

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

      3. metadata-eval 32.4%

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

      4. fma-neg 32.4%

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

      5. metadata-eval 32.4%

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

      6. metadata-eval 32.4%

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

      7. associate-*r/ 32.3%

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

      8. associate-*l/ 32.3%

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

      9. associate-/r/ 32.4%

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

      10. clear-num 32.3%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \color{blue}{\frac{1}{\frac{\frac{a + 0.5}{\mathsf{fma}\left(a, a, -0.25\right)}}{\log t}}}\right) \]

      11. clear-num 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(a, a, -0.25\right)}{a + 0.5}}}}{\log t}}\right) \]

      12. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{\mathsf{fma}\left(a, a, \color{blue}{-0.25}\right)}{a + 0.5}}}{\log t}}\right) \]

      13. metadata-eval 32.4%

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

      14. fma-neg 32.4%

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

      15. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{a \cdot a - \color{blue}{0.25}}{a + 0.5}}}{\log t}}\right) \]

      16. metadata-eval 32.4%

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

      17. flip-- 74.5%

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

      18. sub-neg 74.5%

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

      19. metadata-eval 74.5%

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

   6. Applied egg-rr 74.5%

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

   7. Taylor expanded in a around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -2.40000000000000013e56 < a < 1.0599999999999999e52

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. associate--l+ 99.5%

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

      3. cancel-sign-sub-inv 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. fma-def 99.5%

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

      7. neg-sub0 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 58.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+56} \lor \neg \left(a \leq 1.06 \cdot 10^{+52}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]

Alternative 11: 74.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-81}:\\ \;\;\;\;\log \left(y \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 8e-81)
   (+ (log (* y z)) (* (log t) (+ a -0.5)))
   (+ (- (log z) t) (* (log t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 8e-81) {
		tmp = log((y * z)) + (log(t) * (a + -0.5));
	} else {
		tmp = (log(z) - t) + (log(t) * a);
	}
	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 <= 8d-81) then
        tmp = log((y * z)) + (log(t) * (a + (-0.5d0)))
    else
        tmp = (log(z) - t) + (log(t) * a)
    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 <= 8e-81) {
		tmp = Math.log((y * z)) + (Math.log(t) * (a + -0.5));
	} else {
		tmp = (Math.log(z) - t) + (Math.log(t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 8e-81:
		tmp = math.log((y * z)) + (math.log(t) * (a + -0.5))
	else:
		tmp = (math.log(z) - t) + (math.log(t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 8e-81)
		tmp = Float64(log(Float64(y * z)) + Float64(log(t) * Float64(a + -0.5)));
	else
		tmp = Float64(Float64(log(z) - t) + Float64(log(t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 8e-81)
		tmp = log((y * z)) + (log(t) * (a + -0.5));
	else
		tmp = (log(z) - t) + (log(t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 8e-81], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.9999999999999997e-81

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. fma-def 99.3%

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

      6. sub-neg 99.3%

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

      7. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 60.1%

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

   5. Taylor expanded in t around 0 60.1%

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

      1. associate-+r+ 60.1%

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

      2. log-prod 46.6%

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

      3. sub-neg 46.6%

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

      4. metadata-eval 46.6%

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

   7. Simplified 46.6%

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

   if 7.9999999999999997e-81 < 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+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 75.7%

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

   5. Taylor expanded in a around inf 91.2%

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

      1. *-commutative 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-81}:\\ \;\;\;\;\log \left(y \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log t \cdot a\\ \end{array} \]

Alternative 12: 65.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;\log \left(x + y\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.02e+30) (+ (log (+ x y)) (* (log t) a)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.02e+30) {
		tmp = log((x + y)) + (log(t) * a);
	} 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 <= 1.02d+30) then
        tmp = log((x + y)) + (log(t) * a)
    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 <= 1.02e+30) {
		tmp = Math.log((x + y)) + (Math.log(t) * a);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.02e+30:
		tmp = math.log((x + y)) + (math.log(t) * a)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.02e+30)
		tmp = Float64(log(Float64(x + y)) + Float64(log(t) * a));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.02e+30)
		tmp = log((x + y)) + (log(t) * a);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.02e+30], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 1.02e30

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. associate--l+ 99.3%

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

      3. cancel-sign-sub-inv 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. neg-sub0 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around inf 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   if 1.02e30 < 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. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 78.4%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. mul-1-neg 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;\log \left(x + y\right) + \log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 13: 76.9% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

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(t) * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $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-def 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. Taylor expanded in x around 0 70.2%

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

5. Taylor expanded in a around inf 79.4%

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

   1. *-commutative 79.4%

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

7. Simplified 79.4%

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

8. Final simplification 79.4%

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

Alternative 14: 61.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+56} \lor \neg \left(a \leq 6 \cdot 10^{+54}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.25e+56) (not (<= a 6e+54))) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.25e+56) || !(a <= 6e+54)) {
		tmp = log(t) * a;
	} 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 ((a <= (-1.25d+56)) .or. (.not. (a <= 6d+54))) then
        tmp = log(t) * a
    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 ((a <= -1.25e+56) || !(a <= 6e+54)) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.25e+56) or not (a <= 6e+54):
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.25e+56) || !(a <= 6e+54))
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.25e+56) || ~((a <= 6e+54)))
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.25e+56], N[Not[LessEqual[a, 6e+54]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if a < -1.25000000000000006e56 or 5.9999999999999998e54 < 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. +-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-def 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. Taylor expanded in x around 0 74.7%

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

      1. flip-- 32.4%

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

      2. metadata-eval 32.4%

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

      3. metadata-eval 32.4%

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

      4. fma-neg 32.4%

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

      5. metadata-eval 32.4%

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

      6. metadata-eval 32.4%

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

      7. associate-*r/ 32.3%

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

      8. associate-*l/ 32.3%

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

      9. associate-/r/ 32.4%

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

      10. clear-num 32.3%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \color{blue}{\frac{1}{\frac{\frac{a + 0.5}{\mathsf{fma}\left(a, a, -0.25\right)}}{\log t}}}\right) \]

      11. clear-num 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(a, a, -0.25\right)}{a + 0.5}}}}{\log t}}\right) \]

      12. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{\mathsf{fma}\left(a, a, \color{blue}{-0.25}\right)}{a + 0.5}}}{\log t}}\right) \]

      13. metadata-eval 32.4%

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

      14. fma-neg 32.4%

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

      15. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{a \cdot a - \color{blue}{0.25}}{a + 0.5}}}{\log t}}\right) \]

      16. metadata-eval 32.4%

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

      17. flip-- 74.5%

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

      18. sub-neg 74.5%

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

      19. metadata-eval 74.5%

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

   6. Applied egg-rr 74.5%

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

   7. Taylor expanded in a around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -1.25000000000000006e56 < a < 5.9999999999999998e54

   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. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 66.0%

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

   5. Taylor expanded in t around inf 51.6%

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

      1. mul-1-neg 51.6%

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

   7. Simplified 51.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+56} \lor \neg \left(a \leq 6 \cdot 10^{+54}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 15: 56.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+55} \lor \neg \left(a \leq 1.95 \cdot 10^{+52}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.5e+55) (not (<= a 1.95e+52))) (* (log t) a) (- (log y) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+55) || !(a <= 1.95e+52)) {
		tmp = log(t) * a;
	} else {
		tmp = 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 <= (-4.5d+55)) .or. (.not. (a <= 1.95d+52))) then
        tmp = log(t) * a
    else
        tmp = 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 <= -4.5e+55) || !(a <= 1.95e+52)) {
		tmp = Math.log(t) * a;
	} else {
		tmp = Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.5e+55) or not (a <= 1.95e+52):
		tmp = math.log(t) * a
	else:
		tmp = math.log(y) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.5e+55) || !(a <= 1.95e+52))
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(log(y) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.5e+55) || ~((a <= 1.95e+52)))
		tmp = log(t) * a;
	else
		tmp = log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.5e+55], N[Not[LessEqual[a, 1.95e+52]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], N[(N[Log[y], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999998e55 or 1.95e52 < 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. +-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-def 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. Taylor expanded in x around 0 74.7%

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

      1. flip-- 32.4%

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

      2. metadata-eval 32.4%

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

      3. metadata-eval 32.4%

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

      4. fma-neg 32.4%

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

      5. metadata-eval 32.4%

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

      6. metadata-eval 32.4%

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

      7. associate-*r/ 32.3%

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

      8. associate-*l/ 32.3%

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

      9. associate-/r/ 32.4%

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

      10. clear-num 32.3%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \color{blue}{\frac{1}{\frac{\frac{a + 0.5}{\mathsf{fma}\left(a, a, -0.25\right)}}{\log t}}}\right) \]

      11. clear-num 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(a, a, -0.25\right)}{a + 0.5}}}}{\log t}}\right) \]

      12. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{\mathsf{fma}\left(a, a, \color{blue}{-0.25}\right)}{a + 0.5}}}{\log t}}\right) \]

      13. metadata-eval 32.4%

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

      14. fma-neg 32.4%

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

      15. metadata-eval 32.4%

          \[\leadsto \left(\log z - t\right) + \left(\log y + \frac{1}{\frac{\frac{1}{\frac{a \cdot a - \color{blue}{0.25}}{a + 0.5}}}{\log t}}\right) \]

      16. metadata-eval 32.4%

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

      17. flip-- 74.5%

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

      18. sub-neg 74.5%

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

      19. metadata-eval 74.5%

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

   6. Applied egg-rr 74.5%

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

   7. Taylor expanded in a around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -4.49999999999999998e55 < a < 1.95e52

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. associate--l+ 99.5%

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

      3. cancel-sign-sub-inv 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. fma-def 99.5%

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

      7. neg-sub0 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.5%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.5%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 56.8%

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

      1. mul-1-neg 56.8%

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

   6. Simplified 56.8%

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

   7. Taylor expanded in x around 0 45.6%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+55} \lor \neg \left(a \leq 1.95 \cdot 10^{+52}\right):\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \]

Alternative 16: 41.6% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 580.0)
		tmp = log(Float64(x + y));
	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((x + y));
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < 580

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. associate--l+ 99.3%

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

      3. cancel-sign-sub-inv 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. neg-sub0 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0 - \left(a - 0.5\right)}, t\right)\right) \]

      8. sub-neg 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.3%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0 - \color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. associate--r+ 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(0 - \left(-0.5\right)\right) - a}, t\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(0 - \color{blue}{-0.5}\right) - a, t\right)\right) \]

      12. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t around inf 8.7%

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

      1. mul-1-neg 8.7%

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

   6. Simplified 8.7%

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

   7. Taylor expanded in t around 0 8.9%

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

      1. +-commutative 8.9%

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

   9. Simplified 8.9%

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

   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. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.4%

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

   5. Taylor expanded in t around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   7. Simplified 68.6%

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

4. Final simplification 39.9%

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

Alternative 17: 38.3% 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. +-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-def 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. Taylor expanded in x around 0 70.2%

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

5. Taylor expanded in t around inf 37.0%

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

   1. mul-1-neg 37.0%

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

7. Simplified 37.0%

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

8. Final simplification 37.0%

   \[\leadsto -t \]

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 2023297 
(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))))