Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 19.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

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. sub-neg 99.6%

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

   4. +-commutative 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-rgt-neg-in 99.6%

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

   7. fma-undefine 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

   13. unsub-neg 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;\log y + \left(\log z - \log t \cdot \left(0.5 - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log y + \left(\left(\log z + \log t \cdot a\right) - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.43)
   (+ (log y) (- (log z) (* (log t) (- 0.5 a))))
   (+ (log y) (- (+ (log z) (* (log t) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.43) {
		tmp = log(y) + (log(z) - (log(t) * (0.5 - a)));
	} else {
		tmp = log(y) + ((log(z) + (log(t) * a)) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 0.43d0) then
        tmp = log(y) + (log(z) - (log(t) * (0.5d0 - a)))
    else
        tmp = log(y) + ((log(z) + (log(t) * a)) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.43) {
		tmp = Math.log(y) + (Math.log(z) - (Math.log(t) * (0.5 - a)));
	} else {
		tmp = Math.log(y) + ((Math.log(z) + (Math.log(t) * a)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 0.43:
		tmp = math.log(y) + (math.log(z) - (math.log(t) * (0.5 - a)))
	else:
		tmp = math.log(y) + ((math.log(z) + (math.log(t) * a)) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 0.43)
		tmp = Float64(log(y) + Float64(log(z) - Float64(log(t) * Float64(0.5 - a))));
	else
		tmp = Float64(log(y) + Float64(Float64(log(z) + Float64(log(t) * a)) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 0.43)
		tmp = log(y) + (log(z) - (log(t) * (0.5 - a)));
	else
		tmp = log(y) + ((log(z) + (log(t) * a)) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 0.43], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] + N[(N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.429999999999999993

   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%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.3%

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

      4. +-commutative 99.3%

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

      5. fma-define 99.3%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 69.4%

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

      1. associate--l+ 69.4%

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

      2. remove-double-neg 69.4%

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

      3. log-rec 69.4%

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

      4. mul-1-neg 69.4%

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

      5. mul-1-neg 69.4%

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

      6. log-rec 69.4%

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

      7. remove-double-neg 69.4%

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

      8. sub-neg 69.4%

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

      9. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around 0 68.5%

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

   if 0.429999999999999993 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-define 99.9%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 71.5%

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

      1. associate--l+ 71.5%

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

      2. remove-double-neg 71.5%

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

      3. log-rec 71.5%

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

      4. mul-1-neg 71.5%

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

      5. mul-1-neg 71.5%

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

      6. log-rec 71.5%

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

      7. remove-double-neg 71.5%

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

      8. sub-neg 71.5%

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

      9. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

      1. add-cube-cbrt 71.3%

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

      2. pow3 71.3%

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

   9. Applied egg-rr 71.3%

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

   10. Taylor expanded in a around inf 71.5%

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

       1. *-commutative 71.5%

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

   12. Simplified 71.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;\log y + \left(\log z - \log t \cdot \left(0.5 - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log y + \left(\left(\log z + \log t \cdot a\right) - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot \left(0.5 - a\right)\\ \mathbf{if}\;t \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;\log y + \left(\log z - t\_1\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+99}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - t\_1\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) (- 0.5 a))))
   (if (<= t 1.9e-6)
     (+ (log y) (- (log z) t_1))
     (if (<= t 1.4e+99)
       (- (- (log (* y z)) t_1) t)
       (+ (log (+ x y)) (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * (0.5 - a);
	double tmp;
	if (t <= 1.9e-6) {
		tmp = log(y) + (log(z) - t_1);
	} else if (t <= 1.4e+99) {
		tmp = (log((y * z)) - t_1) - t;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) * (0.5d0 - a)
    if (t <= 1.9d-6) then
        tmp = log(y) + (log(z) - t_1)
    else if (t <= 1.4d+99) then
        tmp = (log((y * z)) - t_1) - t
    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 t_1 = Math.log(t) * (0.5 - a);
	double tmp;
	if (t <= 1.9e-6) {
		tmp = Math.log(y) + (Math.log(z) - t_1);
	} else if (t <= 1.4e+99) {
		tmp = (Math.log((y * z)) - t_1) - t;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * (0.5 - a)
	tmp = 0
	if t <= 1.9e-6:
		tmp = math.log(y) + (math.log(z) - t_1)
	elif t <= 1.4e+99:
		tmp = (math.log((y * z)) - t_1) - t
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * Float64(0.5 - a))
	tmp = 0.0
	if (t <= 1.9e-6)
		tmp = Float64(log(y) + Float64(log(z) - t_1));
	elseif (t <= 1.4e+99)
		tmp = Float64(Float64(log(Float64(y * z)) - t_1) - t);
	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)
	t_1 = log(t) * (0.5 - a);
	tmp = 0.0;
	if (t <= 1.9e-6)
		tmp = log(y) + (log(z) - t_1);
	elseif (t <= 1.4e+99)
		tmp = (log((y * z)) - t_1) - t;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 1.9e-6], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+99], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] - t$95$1), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.9e-6

   1. Initial program 99.4%

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

      1. 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. +-commutative 99.4%

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

      3. associate-+l+ 99.3%

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

      4. +-commutative 99.3%

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

      5. fma-define 99.3%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 68.9%

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

      1. associate--l+ 68.9%

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

      2. remove-double-neg 68.9%

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

      3. log-rec 68.9%

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

      4. mul-1-neg 68.9%

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

      5. mul-1-neg 68.9%

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

      6. log-rec 68.9%

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

      7. remove-double-neg 68.9%

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

      8. sub-neg 68.9%

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

      9. metadata-eval 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in t around 0 68.9%

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

   if 1.9e-6 < t < 1.4e99

   1. Initial program 99.7%

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

      1. associate--l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 99.7%

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

      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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 30.0%

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

      2. pow2 30.0%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}\right)}^{2}} \]

   6. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{{\left(\sqrt{\mathsf{fma}\left(\log t, a + -0.5, \log \left(\left(x + y\right) \cdot z\right) - t\right)}\right)}^{2}} \]

   7. Taylor expanded in x around 0 61.2%

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

   if 1.4e99 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;\log y + \left(\log z - \log t \cdot \left(0.5 - a\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+99}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - \log t \cdot \left(0.5 - a\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

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

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(Float64(log(Float64(x + y)) + 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[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

3. Final simplification 99.6%

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

Alternative 5: 69.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate--l+ 99.6%

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

   2. +-commutative 99.6%

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

   3. associate-+l+ 99.6%

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

   4. +-commutative 99.6%

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

   5. fma-define 99.6%

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

   6. sub-neg 99.6%

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

   7. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 70.5%

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

   1. associate--l+ 70.5%

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

   2. remove-double-neg 70.5%

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

   3. log-rec 70.5%

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

   4. mul-1-neg 70.5%

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

   5. mul-1-neg 70.5%

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

   6. log-rec 70.5%

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

   7. remove-double-neg 70.5%

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

   8. sub-neg 70.5%

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

   9. metadata-eval 70.5%

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

7. Simplified 70.5%

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

Alternative 6: 59.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ t_2 := \log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ t_3 := \log \left(x + y\right) + \left(\log z - t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.45:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-179}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 6.4:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a))
        (t_2 (- (log (* y (* z (pow t (+ a -0.5))))) t))
        (t_3 (+ (log (+ x y)) (- (log z) t))))
   (if (<= a -3.8e+183)
     t_1
     (if (<= a -3.9e+100)
       t_3
       (if (<= a -1.45)
         t_1
         (if (<= a 9.8e-293)
           t_2
           (if (<= a 2.7e-179) t_3 (if (<= a 6.4) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double t_2 = log((y * (z * pow(t, (a + -0.5))))) - t;
	double t_3 = log((x + y)) + (log(z) - t);
	double tmp;
	if (a <= -3.8e+183) {
		tmp = t_1;
	} else if (a <= -3.9e+100) {
		tmp = t_3;
	} else if (a <= -1.45) {
		tmp = t_1;
	} else if (a <= 9.8e-293) {
		tmp = t_2;
	} else if (a <= 2.7e-179) {
		tmp = t_3;
	} else if (a <= 6.4) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log(t) * a
    t_2 = log((y * (z * (t ** (a + (-0.5d0)))))) - t
    t_3 = log((x + y)) + (log(z) - t)
    if (a <= (-3.8d+183)) then
        tmp = t_1
    else if (a <= (-3.9d+100)) then
        tmp = t_3
    else if (a <= (-1.45d0)) then
        tmp = t_1
    else if (a <= 9.8d-293) then
        tmp = t_2
    else if (a <= 2.7d-179) then
        tmp = t_3
    else if (a <= 6.4d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double t_2 = Math.log((y * (z * Math.pow(t, (a + -0.5))))) - t;
	double t_3 = Math.log((x + y)) + (Math.log(z) - t);
	double tmp;
	if (a <= -3.8e+183) {
		tmp = t_1;
	} else if (a <= -3.9e+100) {
		tmp = t_3;
	} else if (a <= -1.45) {
		tmp = t_1;
	} else if (a <= 9.8e-293) {
		tmp = t_2;
	} else if (a <= 2.7e-179) {
		tmp = t_3;
	} else if (a <= 6.4) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	t_2 = math.log((y * (z * math.pow(t, (a + -0.5))))) - t
	t_3 = math.log((x + y)) + (math.log(z) - t)
	tmp = 0
	if a <= -3.8e+183:
		tmp = t_1
	elif a <= -3.9e+100:
		tmp = t_3
	elif a <= -1.45:
		tmp = t_1
	elif a <= 9.8e-293:
		tmp = t_2
	elif a <= 2.7e-179:
		tmp = t_3
	elif a <= 6.4:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	t_2 = Float64(log(Float64(y * Float64(z * (t ^ Float64(a + -0.5))))) - t)
	t_3 = Float64(log(Float64(x + y)) + Float64(log(z) - t))
	tmp = 0.0
	if (a <= -3.8e+183)
		tmp = t_1;
	elseif (a <= -3.9e+100)
		tmp = t_3;
	elseif (a <= -1.45)
		tmp = t_1;
	elseif (a <= 9.8e-293)
		tmp = t_2;
	elseif (a <= 2.7e-179)
		tmp = t_3;
	elseif (a <= 6.4)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	t_2 = log((y * (z * (t ^ (a + -0.5))))) - t;
	t_3 = log((x + y)) + (log(z) - t);
	tmp = 0.0;
	if (a <= -3.8e+183)
		tmp = t_1;
	elseif (a <= -3.9e+100)
		tmp = t_3;
	elseif (a <= -1.45)
		tmp = t_1;
	elseif (a <= 9.8e-293)
		tmp = t_2;
	elseif (a <= 2.7e-179)
		tmp = t_3;
	elseif (a <= 6.4)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[N[(y * N[(z * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+183], t$95$1, If[LessEqual[a, -3.9e+100], t$95$3, If[LessEqual[a, -1.45], t$95$1, If[LessEqual[a, 9.8e-293], t$95$2, If[LessEqual[a, 2.7e-179], t$95$3, If[LessEqual[a, 6.4], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.80000000000000001e183 or -3.9e100 < a < -1.44999999999999996 or 6.4000000000000004 < 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. associate-+l- 99.7%

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

      2. associate--l+ 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-undefine 99.7%

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

      8. sub-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 74.8%

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

      1. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   if -3.80000000000000001e183 < a < -3.9e100 or 9.8000000000000001e-293 < a < 2.69999999999999988e-179

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l+ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-undefine 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 69.1%

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

   if -1.44999999999999996 < a < 9.8000000000000001e-293 or 2.69999999999999988e-179 < a < 6.4000000000000004

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+l+ 99.5%

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

      4. +-commutative 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate--l+ 58.6%

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

      2. remove-double-neg 58.6%

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

      3. log-rec 58.6%

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

      4. mul-1-neg 58.6%

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

      5. mul-1-neg 58.6%

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

      6. log-rec 58.6%

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

      7. remove-double-neg 58.6%

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

      8. sub-neg 58.6%

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

      9. metadata-eval 58.6%

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

   7. Simplified 58.6%

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

      1. associate-+r- 58.6%

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

      2. add-log-exp 51.8%

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

      3. sum-log 36.3%

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

      4. exp-sum 36.2%

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

      5. add-exp-log 36.3%

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

      6. exp-to-pow 36.3%

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

   9. Applied egg-rr 36.3%

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

Alternative 7: 62.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ t_2 := \log \left(x + y\right) + \left(\log z - t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.5:\\ \;\;\;\;\log \left(z \cdot \left(\left(x + y\right) \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)) (t_2 (+ (log (+ x y)) (- (log z) t))))
   (if (<= a -3.8e+183)
     t_1
     (if (<= a -5.5e+100)
       t_2
       (if (<= a -5.5e+47)
         t_1
         (if (<= a 6.8e-72)
           t_2
           (if (<= a 2.5) (log (* z (* (+ x y) (pow t (+ a -0.5))))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double t_2 = log((x + y)) + (log(z) - t);
	double tmp;
	if (a <= -3.8e+183) {
		tmp = t_1;
	} else if (a <= -5.5e+100) {
		tmp = t_2;
	} else if (a <= -5.5e+47) {
		tmp = t_1;
	} else if (a <= 6.8e-72) {
		tmp = t_2;
	} else if (a <= 2.5) {
		tmp = log((z * ((x + y) * pow(t, (a + -0.5)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) * a
    t_2 = log((x + y)) + (log(z) - t)
    if (a <= (-3.8d+183)) then
        tmp = t_1
    else if (a <= (-5.5d+100)) then
        tmp = t_2
    else if (a <= (-5.5d+47)) then
        tmp = t_1
    else if (a <= 6.8d-72) then
        tmp = t_2
    else if (a <= 2.5d0) then
        tmp = log((z * ((x + y) * (t ** (a + (-0.5d0))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double t_2 = Math.log((x + y)) + (Math.log(z) - t);
	double tmp;
	if (a <= -3.8e+183) {
		tmp = t_1;
	} else if (a <= -5.5e+100) {
		tmp = t_2;
	} else if (a <= -5.5e+47) {
		tmp = t_1;
	} else if (a <= 6.8e-72) {
		tmp = t_2;
	} else if (a <= 2.5) {
		tmp = Math.log((z * ((x + y) * Math.pow(t, (a + -0.5)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	t_2 = math.log((x + y)) + (math.log(z) - t)
	tmp = 0
	if a <= -3.8e+183:
		tmp = t_1
	elif a <= -5.5e+100:
		tmp = t_2
	elif a <= -5.5e+47:
		tmp = t_1
	elif a <= 6.8e-72:
		tmp = t_2
	elif a <= 2.5:
		tmp = math.log((z * ((x + y) * math.pow(t, (a + -0.5)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	t_2 = Float64(log(Float64(x + y)) + Float64(log(z) - t))
	tmp = 0.0
	if (a <= -3.8e+183)
		tmp = t_1;
	elseif (a <= -5.5e+100)
		tmp = t_2;
	elseif (a <= -5.5e+47)
		tmp = t_1;
	elseif (a <= 6.8e-72)
		tmp = t_2;
	elseif (a <= 2.5)
		tmp = log(Float64(z * Float64(Float64(x + y) * (t ^ Float64(a + -0.5)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	t_2 = log((x + y)) + (log(z) - t);
	tmp = 0.0;
	if (a <= -3.8e+183)
		tmp = t_1;
	elseif (a <= -5.5e+100)
		tmp = t_2;
	elseif (a <= -5.5e+47)
		tmp = t_1;
	elseif (a <= 6.8e-72)
		tmp = t_2;
	elseif (a <= 2.5)
		tmp = log((z * ((x + y) * (t ^ (a + -0.5)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+183], t$95$1, If[LessEqual[a, -5.5e+100], t$95$2, If[LessEqual[a, -5.5e+47], t$95$1, If[LessEqual[a, 6.8e-72], t$95$2, If[LessEqual[a, 2.5], N[Log[N[(z * N[(N[(x + y), $MachinePrecision] * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.80000000000000001e183 or -5.5000000000000002e100 < a < -5.4999999999999998e47 or 2.5 < a

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l+ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-undefine 99.7%

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

      8. sub-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

   7. Simplified 81.1%

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

   if -3.80000000000000001e183 < a < -5.5000000000000002e100 or -5.4999999999999998e47 < a < 6.7999999999999997e-72

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate--l+ 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-undefine 99.7%

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

      8. sub-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 61.7%

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

   if 6.7999999999999997e-72 < a < 2.5

   1. Initial program 98.7%

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

      1. associate--l+ 98.7%

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

      2. +-commutative 98.7%

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

      3. associate-+l+ 98.8%

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

      4. +-commutative 98.8%

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

      5. fma-define 98.8%

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

      6. sub-neg 98.8%

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

      7. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-undefine 98.8%

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

      3. metadata-eval 98.8%

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

      4. sub-neg 98.8%

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

      5. associate-+r+ 98.7%

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

      6. associate--l+ 98.7%

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

      7. add-log-exp 73.3%

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

      8. +-commutative 73.3%

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

      9. exp-sum 64.5%

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

   6. Applied egg-rr 65.8%

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

      1. associate-*l/ 65.8%

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

      2. *-commutative 65.8%

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

      3. +-commutative 65.8%

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

   8. Simplified 65.8%

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

   9. Taylor expanded in t around 0 73.9%

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

       1. *-commutative 73.9%

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

       2. +-commutative 73.9%

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

       3. exp-to-pow 74.7%

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

       4. sub-neg 74.7%

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

       5. metadata-eval 74.7%

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

   11. Simplified 74.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \mathbf{elif}\;a \leq 2.5:\\ \;\;\;\;\log \left(z \cdot \left(\left(x + y\right) \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {t}^{\left(a + -0.5\right)}\\ t_2 := \log t \cdot a\\ \mathbf{if}\;t \leq 7.5 \cdot 10^{-208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-173}:\\ \;\;\;\;\log \left(\left(y \cdot z\right) \cdot t\_1\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot t\_1\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (pow t (+ a -0.5))) (t_2 (* (log t) a)))
   (if (<= t 7.5e-208)
     t_2
     (if (<= t 4.2e-173)
       (log (* (* y z) t_1))
       (if (<= t 6.5e-104)
         t_2
         (if (<= t 2.85e-43)
           (log (* y (* z t_1)))
           (if (<= t 1.15e+27) t_2 (+ (log (+ x y)) (- (log z) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = pow(t, (a + -0.5));
	double t_2 = log(t) * a;
	double tmp;
	if (t <= 7.5e-208) {
		tmp = t_2;
	} else if (t <= 4.2e-173) {
		tmp = log(((y * z) * t_1));
	} else if (t <= 6.5e-104) {
		tmp = t_2;
	} else if (t <= 2.85e-43) {
		tmp = log((y * (z * t_1)));
	} else if (t <= 1.15e+27) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t ** (a + (-0.5d0))
    t_2 = log(t) * a
    if (t <= 7.5d-208) then
        tmp = t_2
    else if (t <= 4.2d-173) then
        tmp = log(((y * z) * t_1))
    else if (t <= 6.5d-104) then
        tmp = t_2
    else if (t <= 2.85d-43) then
        tmp = log((y * (z * t_1)))
    else if (t <= 1.15d+27) then
        tmp = t_2
    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 t_1 = Math.pow(t, (a + -0.5));
	double t_2 = Math.log(t) * a;
	double tmp;
	if (t <= 7.5e-208) {
		tmp = t_2;
	} else if (t <= 4.2e-173) {
		tmp = Math.log(((y * z) * t_1));
	} else if (t <= 6.5e-104) {
		tmp = t_2;
	} else if (t <= 2.85e-43) {
		tmp = Math.log((y * (z * t_1)));
	} else if (t <= 1.15e+27) {
		tmp = t_2;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.pow(t, (a + -0.5))
	t_2 = math.log(t) * a
	tmp = 0
	if t <= 7.5e-208:
		tmp = t_2
	elif t <= 4.2e-173:
		tmp = math.log(((y * z) * t_1))
	elif t <= 6.5e-104:
		tmp = t_2
	elif t <= 2.85e-43:
		tmp = math.log((y * (z * t_1)))
	elif t <= 1.15e+27:
		tmp = t_2
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = t ^ Float64(a + -0.5)
	t_2 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 7.5e-208)
		tmp = t_2;
	elseif (t <= 4.2e-173)
		tmp = log(Float64(Float64(y * z) * t_1));
	elseif (t <= 6.5e-104)
		tmp = t_2;
	elseif (t <= 2.85e-43)
		tmp = log(Float64(y * Float64(z * t_1)));
	elseif (t <= 1.15e+27)
		tmp = t_2;
	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)
	t_1 = t ^ (a + -0.5);
	t_2 = log(t) * a;
	tmp = 0.0;
	if (t <= 7.5e-208)
		tmp = t_2;
	elseif (t <= 4.2e-173)
		tmp = log(((y * z) * t_1));
	elseif (t <= 6.5e-104)
		tmp = t_2;
	elseif (t <= 2.85e-43)
		tmp = log((y * (z * t_1)));
	elseif (t <= 1.15e+27)
		tmp = t_2;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 7.5e-208], t$95$2, If[LessEqual[t, 4.2e-173], N[Log[N[(N[(y * z), $MachinePrecision] * t$95$1), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 6.5e-104], t$95$2, If[LessEqual[t, 2.85e-43], N[Log[N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 1.15e+27], t$95$2, N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 7.4999999999999999e-208 or 4.20000000000000003e-173 < t < 6.49999999999999991e-104 or 2.85e-43 < t < 1.15e27

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 7.4999999999999999e-208 < t < 4.20000000000000003e-173

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 99.7%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. remove-double-neg 70.7%

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

      3. log-rec 70.7%

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

      4. mul-1-neg 70.7%

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

      5. mul-1-neg 70.7%

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

      6. log-rec 70.7%

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

      7. remove-double-neg 70.7%

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

      8. sub-neg 70.7%

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

      9. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in t around 0 70.7%

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

      1. *-un-lft-identity 70.7%

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

      2. add-log-exp 41.9%

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

      3. sum-log 42.3%

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

      4. sub-neg 42.3%

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

      5. metadata-eval 42.3%

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

      6. exp-sum 42.3%

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

      7. add-exp-log 42.3%

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

      8. pow-to-exp 42.4%

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

   10. Applied egg-rr 42.4%

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

       1. *-lft-identity 42.4%

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

       2. associate-*r* 51.7%

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

   12. Simplified 51.7%

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

   if 6.49999999999999991e-104 < t < 2.85e-43

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-define 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. associate--l+ 59.6%

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

      2. remove-double-neg 59.6%

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

      3. log-rec 59.6%

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

      4. mul-1-neg 59.6%

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

      5. mul-1-neg 59.6%

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

      6. log-rec 59.6%

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

      7. remove-double-neg 59.6%

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

      8. sub-neg 59.6%

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

      9. metadata-eval 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in t around 0 59.6%

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

      1. *-un-lft-identity 59.6%

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

      2. add-log-exp 40.7%

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

      3. sum-log 33.7%

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

      4. sub-neg 33.7%

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

      5. metadata-eval 33.7%

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

      6. exp-sum 33.8%

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

      7. add-exp-log 33.8%

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

      8. pow-to-exp 33.8%

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

   10. Applied egg-rr 33.8%

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

       1. *-lft-identity 33.8%

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

   12. Simplified 33.8%

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

   if 1.15e27 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 57.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ \mathbf{if}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-175}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)))
   (if (<= t 8e-208)
     t_1
     (if (<= t 5.2e-175)
       (log (* z (* y (pow t -0.5))))
       (if (<= t 5.6e-105)
         t_1
         (if (<= t 2e-43)
           (log (* y (* z (pow t (+ a -0.5)))))
           (if (<= t 1.6e+21) t_1 (+ (log (+ x y)) (- (log z) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double tmp;
	if (t <= 8e-208) {
		tmp = t_1;
	} else if (t <= 5.2e-175) {
		tmp = log((z * (y * pow(t, -0.5))));
	} else if (t <= 5.6e-105) {
		tmp = t_1;
	} else if (t <= 2e-43) {
		tmp = log((y * (z * pow(t, (a + -0.5)))));
	} else if (t <= 1.6e+21) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) * a
    if (t <= 8d-208) then
        tmp = t_1
    else if (t <= 5.2d-175) then
        tmp = log((z * (y * (t ** (-0.5d0)))))
    else if (t <= 5.6d-105) then
        tmp = t_1
    else if (t <= 2d-43) then
        tmp = log((y * (z * (t ** (a + (-0.5d0))))))
    else if (t <= 1.6d+21) then
        tmp = t_1
    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 t_1 = Math.log(t) * a;
	double tmp;
	if (t <= 8e-208) {
		tmp = t_1;
	} else if (t <= 5.2e-175) {
		tmp = Math.log((z * (y * Math.pow(t, -0.5))));
	} else if (t <= 5.6e-105) {
		tmp = t_1;
	} else if (t <= 2e-43) {
		tmp = Math.log((y * (z * Math.pow(t, (a + -0.5)))));
	} else if (t <= 1.6e+21) {
		tmp = t_1;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	tmp = 0
	if t <= 8e-208:
		tmp = t_1
	elif t <= 5.2e-175:
		tmp = math.log((z * (y * math.pow(t, -0.5))))
	elif t <= 5.6e-105:
		tmp = t_1
	elif t <= 2e-43:
		tmp = math.log((y * (z * math.pow(t, (a + -0.5)))))
	elif t <= 1.6e+21:
		tmp = t_1
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 8e-208)
		tmp = t_1;
	elseif (t <= 5.2e-175)
		tmp = log(Float64(z * Float64(y * (t ^ -0.5))));
	elseif (t <= 5.6e-105)
		tmp = t_1;
	elseif (t <= 2e-43)
		tmp = log(Float64(y * Float64(z * (t ^ Float64(a + -0.5)))));
	elseif (t <= 1.6e+21)
		tmp = t_1;
	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)
	t_1 = log(t) * a;
	tmp = 0.0;
	if (t <= 8e-208)
		tmp = t_1;
	elseif (t <= 5.2e-175)
		tmp = log((z * (y * (t ^ -0.5))));
	elseif (t <= 5.6e-105)
		tmp = t_1;
	elseif (t <= 2e-43)
		tmp = log((y * (z * (t ^ (a + -0.5)))));
	elseif (t <= 1.6e+21)
		tmp = t_1;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 8e-208], t$95$1, If[LessEqual[t, 5.2e-175], N[Log[N[(z * N[(y * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 5.6e-105], t$95$1, If[LessEqual[t, 2e-43], N[Log[N[(y * N[(z * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 1.6e+21], t$95$1, N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 8.0000000000000008e-208 or 5.2e-175 < t < 5.6e-105 or 2.00000000000000015e-43 < t < 1.6e21

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 8.0000000000000008e-208 < t < 5.2e-175

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 99.7%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. remove-double-neg 70.7%

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

      3. log-rec 70.7%

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

      4. mul-1-neg 70.7%

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

      5. mul-1-neg 70.7%

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

      6. log-rec 70.7%

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

      7. remove-double-neg 70.7%

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

      8. sub-neg 70.7%

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

      9. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in t around 0 70.7%

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

   9. Taylor expanded in a around 0 56.3%

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

       1. +-commutative 56.3%

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

       2. *-commutative 56.3%

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

   11. Simplified 56.3%

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

       1. *-un-lft-identity 56.3%

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

       2. add-log-exp 34.2%

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

       3. sum-log 34.6%

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

       4. +-commutative 34.6%

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

       5. exp-sum 34.6%

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

       6. add-exp-log 34.5%

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

       7. pow-to-exp 34.6%

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

   13. Applied egg-rr 34.6%

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

       1. *-lft-identity 34.6%

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

       2. *-commutative 34.6%

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

       3. associate-*r* 44.0%

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

   15. Simplified 44.0%

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

   if 5.6e-105 < t < 2.00000000000000015e-43

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-define 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. associate--l+ 59.6%

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

      2. remove-double-neg 59.6%

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

      3. log-rec 59.6%

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

      4. mul-1-neg 59.6%

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

      5. mul-1-neg 59.6%

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

      6. log-rec 59.6%

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

      7. remove-double-neg 59.6%

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

      8. sub-neg 59.6%

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

      9. metadata-eval 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in t around 0 59.6%

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

      1. *-un-lft-identity 59.6%

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

      2. add-log-exp 40.7%

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

      3. sum-log 33.7%

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

      4. sub-neg 33.7%

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

      5. metadata-eval 33.7%

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

      6. exp-sum 33.8%

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

      7. add-exp-log 33.8%

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

      8. pow-to-exp 33.8%

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

   10. Applied egg-rr 33.8%

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

       1. *-lft-identity 33.8%

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

   12. Simplified 33.8%

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

   if 1.6e21 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-175}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-105}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ \mathbf{if}\;t \leq 7.3 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)))
   (if (<= t 7.3e-208)
     t_1
     (if (<= t 1.8e-174)
       (log (* z (* y (pow t -0.5))))
       (if (<= t 6.4e-103)
         t_1
         (if (<= t 2e-43)
           (log (* y (* z (pow t -0.5))))
           (if (<= t 4.4e+25) t_1 (+ (log (+ x y)) (- (log z) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double tmp;
	if (t <= 7.3e-208) {
		tmp = t_1;
	} else if (t <= 1.8e-174) {
		tmp = log((z * (y * pow(t, -0.5))));
	} else if (t <= 6.4e-103) {
		tmp = t_1;
	} else if (t <= 2e-43) {
		tmp = log((y * (z * pow(t, -0.5))));
	} else if (t <= 4.4e+25) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) * a
    if (t <= 7.3d-208) then
        tmp = t_1
    else if (t <= 1.8d-174) then
        tmp = log((z * (y * (t ** (-0.5d0)))))
    else if (t <= 6.4d-103) then
        tmp = t_1
    else if (t <= 2d-43) then
        tmp = log((y * (z * (t ** (-0.5d0)))))
    else if (t <= 4.4d+25) then
        tmp = t_1
    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 t_1 = Math.log(t) * a;
	double tmp;
	if (t <= 7.3e-208) {
		tmp = t_1;
	} else if (t <= 1.8e-174) {
		tmp = Math.log((z * (y * Math.pow(t, -0.5))));
	} else if (t <= 6.4e-103) {
		tmp = t_1;
	} else if (t <= 2e-43) {
		tmp = Math.log((y * (z * Math.pow(t, -0.5))));
	} else if (t <= 4.4e+25) {
		tmp = t_1;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	tmp = 0
	if t <= 7.3e-208:
		tmp = t_1
	elif t <= 1.8e-174:
		tmp = math.log((z * (y * math.pow(t, -0.5))))
	elif t <= 6.4e-103:
		tmp = t_1
	elif t <= 2e-43:
		tmp = math.log((y * (z * math.pow(t, -0.5))))
	elif t <= 4.4e+25:
		tmp = t_1
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 7.3e-208)
		tmp = t_1;
	elseif (t <= 1.8e-174)
		tmp = log(Float64(z * Float64(y * (t ^ -0.5))));
	elseif (t <= 6.4e-103)
		tmp = t_1;
	elseif (t <= 2e-43)
		tmp = log(Float64(y * Float64(z * (t ^ -0.5))));
	elseif (t <= 4.4e+25)
		tmp = t_1;
	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)
	t_1 = log(t) * a;
	tmp = 0.0;
	if (t <= 7.3e-208)
		tmp = t_1;
	elseif (t <= 1.8e-174)
		tmp = log((z * (y * (t ^ -0.5))));
	elseif (t <= 6.4e-103)
		tmp = t_1;
	elseif (t <= 2e-43)
		tmp = log((y * (z * (t ^ -0.5))));
	elseif (t <= 4.4e+25)
		tmp = t_1;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 7.3e-208], t$95$1, If[LessEqual[t, 1.8e-174], N[Log[N[(z * N[(y * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 6.4e-103], t$95$1, If[LessEqual[t, 2e-43], N[Log[N[(y * N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 4.4e+25], t$95$1, N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 7.30000000000000002e-208 or 1.79999999999999999e-174 < t < 6.39999999999999953e-103 or 2.00000000000000015e-43 < t < 4.4000000000000001e25

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 7.30000000000000002e-208 < t < 1.79999999999999999e-174

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 99.7%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. remove-double-neg 70.7%

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

      3. log-rec 70.7%

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

      4. mul-1-neg 70.7%

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

      5. mul-1-neg 70.7%

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

      6. log-rec 70.7%

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

      7. remove-double-neg 70.7%

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

      8. sub-neg 70.7%

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

      9. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in t around 0 70.7%

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

   9. Taylor expanded in a around 0 56.3%

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

       1. +-commutative 56.3%

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

       2. *-commutative 56.3%

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

   11. Simplified 56.3%

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

       1. *-un-lft-identity 56.3%

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

       2. add-log-exp 34.2%

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

       3. sum-log 34.6%

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

       4. +-commutative 34.6%

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

       5. exp-sum 34.6%

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

       6. add-exp-log 34.5%

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

       7. pow-to-exp 34.6%

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

   13. Applied egg-rr 34.6%

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

       1. *-lft-identity 34.6%

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

       2. *-commutative 34.6%

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

       3. associate-*r* 44.0%

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

   15. Simplified 44.0%

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

   if 6.39999999999999953e-103 < t < 2.00000000000000015e-43

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-define 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. associate--l+ 59.6%

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

      2. remove-double-neg 59.6%

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

      3. log-rec 59.6%

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

      4. mul-1-neg 59.6%

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

      5. mul-1-neg 59.6%

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

      6. log-rec 59.6%

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

      7. remove-double-neg 59.6%

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

      8. sub-neg 59.6%

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

      9. metadata-eval 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in t around 0 59.6%

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

   9. Taylor expanded in a around 0 40.1%

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

       1. +-commutative 40.1%

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

       2. *-commutative 40.1%

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

   11. Simplified 40.1%

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

       1. *-un-lft-identity 40.1%

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

       2. add-log-exp 40.1%

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

       3. sum-log 33.1%

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

       4. +-commutative 33.1%

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

       5. exp-sum 33.2%

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

       6. add-exp-log 33.2%

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

       7. pow-to-exp 33.2%

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

   13. Applied egg-rr 33.2%

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

       1. *-lft-identity 33.2%

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

   15. Simplified 33.2%

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

   if 4.4000000000000001e25 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.3 \cdot 10^{-208}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-103}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+25}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ \mathbf{if}\;t \leq 7.5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-175}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)))
   (if (<= t 7.5e-208)
     t_1
     (if (<= t 6.2e-175)
       (log (* z (* y (pow t -0.5))))
       (if (<= t 7.2e-106)
         t_1
         (if (<= t 2.5e-43)
           (log (* y (* z (pow t -0.5))))
           (if (<= t 4.8e+22) t_1 (- t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double tmp;
	if (t <= 7.5e-208) {
		tmp = t_1;
	} else if (t <= 6.2e-175) {
		tmp = log((z * (y * pow(t, -0.5))));
	} else if (t <= 7.2e-106) {
		tmp = t_1;
	} else if (t <= 2.5e-43) {
		tmp = log((y * (z * pow(t, -0.5))));
	} else if (t <= 4.8e+22) {
		tmp = t_1;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) * a
    if (t <= 7.5d-208) then
        tmp = t_1
    else if (t <= 6.2d-175) then
        tmp = log((z * (y * (t ** (-0.5d0)))))
    else if (t <= 7.2d-106) then
        tmp = t_1
    else if (t <= 2.5d-43) then
        tmp = log((y * (z * (t ** (-0.5d0)))))
    else if (t <= 4.8d+22) then
        tmp = t_1
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double tmp;
	if (t <= 7.5e-208) {
		tmp = t_1;
	} else if (t <= 6.2e-175) {
		tmp = Math.log((z * (y * Math.pow(t, -0.5))));
	} else if (t <= 7.2e-106) {
		tmp = t_1;
	} else if (t <= 2.5e-43) {
		tmp = Math.log((y * (z * Math.pow(t, -0.5))));
	} else if (t <= 4.8e+22) {
		tmp = t_1;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	tmp = 0
	if t <= 7.5e-208:
		tmp = t_1
	elif t <= 6.2e-175:
		tmp = math.log((z * (y * math.pow(t, -0.5))))
	elif t <= 7.2e-106:
		tmp = t_1
	elif t <= 2.5e-43:
		tmp = math.log((y * (z * math.pow(t, -0.5))))
	elif t <= 4.8e+22:
		tmp = t_1
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 7.5e-208)
		tmp = t_1;
	elseif (t <= 6.2e-175)
		tmp = log(Float64(z * Float64(y * (t ^ -0.5))));
	elseif (t <= 7.2e-106)
		tmp = t_1;
	elseif (t <= 2.5e-43)
		tmp = log(Float64(y * Float64(z * (t ^ -0.5))));
	elseif (t <= 4.8e+22)
		tmp = t_1;
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	tmp = 0.0;
	if (t <= 7.5e-208)
		tmp = t_1;
	elseif (t <= 6.2e-175)
		tmp = log((z * (y * (t ^ -0.5))));
	elseif (t <= 7.2e-106)
		tmp = t_1;
	elseif (t <= 2.5e-43)
		tmp = log((y * (z * (t ^ -0.5))));
	elseif (t <= 4.8e+22)
		tmp = t_1;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 7.5e-208], t$95$1, If[LessEqual[t, 6.2e-175], N[Log[N[(z * N[(y * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 7.2e-106], t$95$1, If[LessEqual[t, 2.5e-43], N[Log[N[(y * N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 4.8e+22], t$95$1, (-t)]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 7.4999999999999999e-208 or 6.19999999999999997e-175 < t < 7.20000000000000025e-106 or 2.50000000000000009e-43 < t < 4.8e22

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 7.4999999999999999e-208 < t < 6.19999999999999997e-175

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 99.7%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. remove-double-neg 70.7%

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

      3. log-rec 70.7%

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

      4. mul-1-neg 70.7%

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

      5. mul-1-neg 70.7%

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

      6. log-rec 70.7%

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

      7. remove-double-neg 70.7%

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

      8. sub-neg 70.7%

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

      9. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in t around 0 70.7%

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

   9. Taylor expanded in a around 0 56.3%

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

       1. +-commutative 56.3%

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

       2. *-commutative 56.3%

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

   11. Simplified 56.3%

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

       1. *-un-lft-identity 56.3%

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

       2. add-log-exp 34.2%

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

       3. sum-log 34.6%

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

       4. +-commutative 34.6%

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

       5. exp-sum 34.6%

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

       6. add-exp-log 34.5%

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

       7. pow-to-exp 34.6%

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

   13. Applied egg-rr 34.6%

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

       1. *-lft-identity 34.6%

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

       2. *-commutative 34.6%

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

       3. associate-*r* 44.0%

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

   15. Simplified 44.0%

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

   if 7.20000000000000025e-106 < t < 2.50000000000000009e-43

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-define 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. associate--l+ 59.6%

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

      2. remove-double-neg 59.6%

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

      3. log-rec 59.6%

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

      4. mul-1-neg 59.6%

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

      5. mul-1-neg 59.6%

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

      6. log-rec 59.6%

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

      7. remove-double-neg 59.6%

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

      8. sub-neg 59.6%

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

      9. metadata-eval 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in t around 0 59.6%

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

   9. Taylor expanded in a around 0 40.1%

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

       1. +-commutative 40.1%

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

       2. *-commutative 40.1%

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

   11. Simplified 40.1%

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

       1. *-un-lft-identity 40.1%

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

       2. add-log-exp 40.1%

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

       3. sum-log 33.1%

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

       4. +-commutative 33.1%

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

       5. exp-sum 33.2%

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

       6. add-exp-log 33.2%

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

       7. pow-to-exp 33.2%

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

   13. Applied egg-rr 33.2%

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

       1. *-lft-identity 33.2%

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

   15. Simplified 33.2%

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

   if 4.8e22 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

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

      1. neg-mul-1 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-208}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-175}:\\ \;\;\;\;\log \left(z \cdot \left(y \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ t_2 := \log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right)\\ \mathbf{if}\;t \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)) (t_2 (log (* y (* z (pow t -0.5))))))
   (if (<= t 2.5e-207)
     t_1
     (if (<= t 5.8e-175)
       t_2
       (if (<= t 9.2e-103)
         t_1
         (if (<= t 9.5e-43) t_2 (if (<= t 4.2e+21) t_1 (- t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double t_2 = log((y * (z * pow(t, -0.5))));
	double tmp;
	if (t <= 2.5e-207) {
		tmp = t_1;
	} else if (t <= 5.8e-175) {
		tmp = t_2;
	} else if (t <= 9.2e-103) {
		tmp = t_1;
	} else if (t <= 9.5e-43) {
		tmp = t_2;
	} else if (t <= 4.2e+21) {
		tmp = t_1;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) * a
    t_2 = log((y * (z * (t ** (-0.5d0)))))
    if (t <= 2.5d-207) then
        tmp = t_1
    else if (t <= 5.8d-175) then
        tmp = t_2
    else if (t <= 9.2d-103) then
        tmp = t_1
    else if (t <= 9.5d-43) then
        tmp = t_2
    else if (t <= 4.2d+21) then
        tmp = t_1
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double t_2 = Math.log((y * (z * Math.pow(t, -0.5))));
	double tmp;
	if (t <= 2.5e-207) {
		tmp = t_1;
	} else if (t <= 5.8e-175) {
		tmp = t_2;
	} else if (t <= 9.2e-103) {
		tmp = t_1;
	} else if (t <= 9.5e-43) {
		tmp = t_2;
	} else if (t <= 4.2e+21) {
		tmp = t_1;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	t_2 = math.log((y * (z * math.pow(t, -0.5))))
	tmp = 0
	if t <= 2.5e-207:
		tmp = t_1
	elif t <= 5.8e-175:
		tmp = t_2
	elif t <= 9.2e-103:
		tmp = t_1
	elif t <= 9.5e-43:
		tmp = t_2
	elif t <= 4.2e+21:
		tmp = t_1
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	t_2 = log(Float64(y * Float64(z * (t ^ -0.5))))
	tmp = 0.0
	if (t <= 2.5e-207)
		tmp = t_1;
	elseif (t <= 5.8e-175)
		tmp = t_2;
	elseif (t <= 9.2e-103)
		tmp = t_1;
	elseif (t <= 9.5e-43)
		tmp = t_2;
	elseif (t <= 4.2e+21)
		tmp = t_1;
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	t_2 = log((y * (z * (t ^ -0.5))));
	tmp = 0.0;
	if (t <= 2.5e-207)
		tmp = t_1;
	elseif (t <= 5.8e-175)
		tmp = t_2;
	elseif (t <= 9.2e-103)
		tmp = t_1;
	elseif (t <= 9.5e-43)
		tmp = t_2;
	elseif (t <= 4.2e+21)
		tmp = t_1;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[Log[N[(y * N[(z * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 2.5e-207], t$95$1, If[LessEqual[t, 5.8e-175], t$95$2, If[LessEqual[t, 9.2e-103], t$95$1, If[LessEqual[t, 9.5e-43], t$95$2, If[LessEqual[t, 4.2e+21], t$95$1, (-t)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.50000000000000007e-207 or 5.79999999999999998e-175 < t < 9.2000000000000003e-103 or 9.50000000000000044e-43 < t < 4.2e21

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 55.1%

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

      1. *-commutative 55.1%

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

   7. Simplified 55.1%

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

   if 2.50000000000000007e-207 < t < 5.79999999999999998e-175 or 9.2000000000000003e-103 < t < 9.50000000000000044e-43

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.2%

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

      4. +-commutative 99.2%

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

      5. fma-define 99.2%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 61.7%

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

      1. associate--l+ 61.7%

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

      2. remove-double-neg 61.7%

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

      3. log-rec 61.7%

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

      4. mul-1-neg 61.7%

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

      5. mul-1-neg 61.7%

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

      6. log-rec 61.7%

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

      7. remove-double-neg 61.7%

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

      8. sub-neg 61.7%

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

      9. metadata-eval 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in t around 0 61.7%

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

   9. Taylor expanded in a around 0 43.2%

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

       1. +-commutative 43.2%

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

       2. *-commutative 43.2%

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

   11. Simplified 43.2%

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

       1. *-un-lft-identity 43.2%

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

       2. add-log-exp 39.5%

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

       3. sum-log 34.4%

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

       4. +-commutative 34.4%

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

       5. exp-sum 34.5%

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

       6. add-exp-log 34.5%

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

       7. pow-to-exp 34.5%

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

   13. Applied egg-rr 34.5%

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

       1. *-lft-identity 34.5%

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

   15. Simplified 34.5%

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

   if 4.2e21 < t

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-undefine 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

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

      1. neg-mul-1 78.9%

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

   7. Simplified 78.9%

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

Alternative 13: 75.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - \log t \cdot \left(0.5 - a\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 5.2e+96)
   (- (+ (log (* z (+ x y))) (* (log t) (- a 0.5))) t)
   (if (<= t 1.85e+167)
     (- t)
     (if (<= t 1.12e+229)
       (- (- (log (* y z)) (* (log t) (- 0.5 a))) t)
       (+ (log (+ x y)) (- (log z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.2e+96) {
		tmp = (log((z * (x + y))) + (log(t) * (a - 0.5))) - t;
	} else if (t <= 1.85e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = (log((y * z)) - (log(t) * (0.5 - a))) - t;
	} 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 (t <= 5.2d+96) then
        tmp = (log((z * (x + y))) + (log(t) * (a - 0.5d0))) - t
    else if (t <= 1.85d+167) then
        tmp = -t
    else if (t <= 1.12d+229) then
        tmp = (log((y * z)) - (log(t) * (0.5d0 - a))) - t
    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 (t <= 5.2e+96) {
		tmp = (Math.log((z * (x + y))) + (Math.log(t) * (a - 0.5))) - t;
	} else if (t <= 1.85e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = (Math.log((y * z)) - (Math.log(t) * (0.5 - a))) - t;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.2e+96:
		tmp = (math.log((z * (x + y))) + (math.log(t) * (a - 0.5))) - t
	elif t <= 1.85e+167:
		tmp = -t
	elif t <= 1.12e+229:
		tmp = (math.log((y * z)) - (math.log(t) * (0.5 - a))) - t
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.2e+96)
		tmp = Float64(Float64(log(Float64(z * Float64(x + y))) + Float64(log(t) * Float64(a - 0.5))) - t);
	elseif (t <= 1.85e+167)
		tmp = Float64(-t);
	elseif (t <= 1.12e+229)
		tmp = Float64(Float64(log(Float64(y * z)) - Float64(log(t) * Float64(0.5 - a))) - t);
	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 (t <= 5.2e+96)
		tmp = (log((z * (x + y))) + (log(t) * (a - 0.5))) - t;
	elseif (t <= 1.85e+167)
		tmp = -t;
	elseif (t <= 1.12e+229)
		tmp = (log((y * z)) - (log(t) * (0.5 - a))) - t;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5.2e+96], 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], If[LessEqual[t, 1.85e+167], (-t), If[LessEqual[t, 1.12e+229], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < 5.2e96

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-undefine 99.4%

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

      8. sub-neg 99.4%

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

      9. +-commutative 99.4%

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

      10. distribute-neg-in 99.4%

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

      11. metadata-eval 99.4%

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

      12. metadata-eval 99.4%

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

      13. unsub-neg 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing
   5. 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-undefine 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. sum-log 75.5%

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

   6. Applied egg-rr 75.5%

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

   if 5.2e96 < t < 1.85e167

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. fma-undefine 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 85.3%

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

      1. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if 1.85e167 < t < 1.12e229

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-define 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 26.8%

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

      2. pow2 26.8%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}\right)}^{2}} \]

   6. Applied egg-rr 26.8%

      \[\leadsto \color{blue}{{\left(\sqrt{\mathsf{fma}\left(\log t, a + -0.5, \log \left(\left(x + y\right) \cdot z\right) - t\right)}\right)}^{2}} \]

   7. Taylor expanded in x around 0 73.7%

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

   if 1.12e229 < t

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. fma-undefine 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 96.8%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;\left(\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - \log t \cdot \left(0.5 - a\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{+95}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - \log t \cdot \left(0.5 - a\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3.1e+95)
   (- (- (log (* y z)) (* (log t) (- 0.5 a))) t)
   (+ (log (+ x y)) (- (log z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.1e+95) {
		tmp = (log((y * z)) - (log(t) * (0.5 - a))) - t;
	} 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 (t <= 3.1d+95) then
        tmp = (log((y * z)) - (log(t) * (0.5d0 - a))) - t
    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 (t <= 3.1e+95) {
		tmp = (Math.log((y * z)) - (Math.log(t) * (0.5 - a))) - t;
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 3.1e+95:
		tmp = (math.log((y * z)) - (math.log(t) * (0.5 - a))) - t
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.1e+95)
		tmp = Float64(Float64(log(Float64(y * z)) - Float64(log(t) * Float64(0.5 - a))) - t);
	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 (t <= 3.1e+95)
		tmp = (log((y * z)) - (log(t) * (0.5 - a))) - t;
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3.1e+95], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $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 t < 3.1000000000000003e95

   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%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

         \[\leadsto \left(\log z - t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, \log t, \log \left(x + y\right)\right)} \]

      6. sub-neg 99.4%

         \[\leadsto \left(\log z - t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, \log t, \log \left(x + y\right)\right) \]

      7. metadata-eval 99.4%

         \[\leadsto \left(\log z - t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, \log t, \log \left(x + y\right)\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 55.0%

         \[\leadsto \color{blue}{\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)} \cdot \sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}} \]

      2. pow2 55.0%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}\right)}^{2}} \]

   6. Applied egg-rr 40.6%

      \[\leadsto \color{blue}{{\left(\sqrt{\mathsf{fma}\left(\log t, a + -0.5, \log \left(\left(x + y\right) \cdot z\right) - t\right)}\right)}^{2}} \]

   7. Taylor expanded in x around 0 49.9%

      \[\leadsto \color{blue}{\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t} \]

   if 3.1000000000000003e95 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 100.0%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 100.0%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 100.0%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 100.0%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{+95}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) - \log t \cdot \left(0.5 - a\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\log t \cdot \left(a + -0.5\right) + \log \left(z \cdot \left(x + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3.5e+20)
   (+ (* (log t) (+ a -0.5)) (log (* z (+ x y))))
   (+ (log (+ x y)) (- (log z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.5e+20) {
		tmp = (log(t) * (a + -0.5)) + log((z * (x + y)));
	} 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 (t <= 3.5d+20) then
        tmp = (log(t) * (a + (-0.5d0))) + log((z * (x + y)))
    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 (t <= 3.5e+20) {
		tmp = (Math.log(t) * (a + -0.5)) + Math.log((z * (x + y)));
	} else {
		tmp = Math.log((x + y)) + (Math.log(z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 3.5e+20:
		tmp = (math.log(t) * (a + -0.5)) + math.log((z * (x + y)))
	else:
		tmp = math.log((x + y)) + (math.log(z) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.5e+20)
		tmp = Float64(Float64(log(t) * Float64(a + -0.5)) + log(Float64(z * Float64(x + y))));
	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 (t <= 3.5e+20)
		tmp = (log(t) * (a + -0.5)) + log((z * (x + y)));
	else
		tmp = log((x + y)) + (log(z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3.5e+20], N[(N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $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 t < 3.5e20

   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%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      2. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} + \left(a - 0.5\right) \cdot \log t \]

      3. associate-+l+ 99.4%

         \[\leadsto \color{blue}{\left(\log z - t\right) + \left(\log \left(x + y\right) + \left(a - 0.5\right) \cdot \log t\right)} \]

      4. +-commutative 99.4%

         \[\leadsto \left(\log z - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log t + \log \left(x + y\right)\right)} \]

      5. fma-define 99.3%

         \[\leadsto \left(\log z - t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, \log t, \log \left(x + y\right)\right)} \]

      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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 61.2%

         \[\leadsto \color{blue}{\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)} \cdot \sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}} \]

      2. pow2 61.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(\log z - t\right) + \mathsf{fma}\left(a + -0.5, \log t, \log \left(x + y\right)\right)}\right)}^{2}} \]

   6. Applied egg-rr 45.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\mathsf{fma}\left(\log t, a + -0.5, \log \left(\left(x + y\right) \cdot z\right) - t\right)}\right)}^{2}} \]

   7. Taylor expanded in t around 0 70.7%

      \[\leadsto \color{blue}{\log \left(z \cdot \left(x + y\right)\right) + \log t \cdot \left(a - 0.5\right)} \]
   8. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto \color{blue}{\log t \cdot \left(a - 0.5\right) + \log \left(z \cdot \left(x + y\right)\right)} \]

      2. sub-neg 70.7%

         \[\leadsto \log t \cdot \color{blue}{\left(a + \left(-0.5\right)\right)} + \log \left(z \cdot \left(x + y\right)\right) \]

      3. metadata-eval 70.7%

         \[\leadsto \log t \cdot \left(a + \color{blue}{-0.5}\right) + \log \left(z \cdot \left(x + y\right)\right) \]

      4. +-commutative 70.7%

         \[\leadsto \log t \cdot \left(a + -0.5\right) + \log \left(z \cdot \color{blue}{\left(y + x\right)}\right) \]

   9. Simplified 70.7%

      \[\leadsto \color{blue}{\log t \cdot \left(a + -0.5\right) + \log \left(z \cdot \left(y + x\right)\right)} \]

   if 3.5e20 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.9%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{t}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\log t \cdot \left(a + -0.5\right) + \log \left(z \cdot \left(x + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) + \left(\log z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+22}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 5.2e+22) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.2e+22) {
		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 (t <= 5.2d+22) 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 (t <= 5.2e+22) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.2e+22:
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.2e+22)
		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 (t <= 5.2e+22)
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5.2e+22], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 5.2e22

   1. Initial program 99.4%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.4%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.4%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.4%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.4%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 46.8%

      \[\leadsto \color{blue}{a \cdot \log t} \]
   6. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \color{blue}{\log t \cdot a} \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{\log t \cdot a} \]

   if 5.2e22 < t

   1. Initial program 99.9%

      \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

      3. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

      4. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

      5. *-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

      7. fma-undefine 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

      8. sub-neg 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

      9. +-commutative 99.9%

         \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

      10. distribute-neg-in 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

      13. unsub-neg 99.9%

          \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.9%

      \[\leadsto \color{blue}{-1 \cdot t} \]
   6. Step-by-step derivation

      1. neg-mul-1 78.9%

         \[\leadsto \color{blue}{-t} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{-t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 37.7% accurate, 156.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- t))

C

double code(double x, double y, double z, double t, double a) {
	return -t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = -t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -t;
}

Python

def code(x, y, z, t, a):
	return -t

Julia

function code(x, y, z, t, a)
	return Float64(-t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -t;
end

Wolfram

code[x_, y_, z_, t_, a_] := (-t)

Derivation

1. Initial program 99.6%

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t \]
2. Step-by-step derivation

   1. associate-+l- 99.6%

      \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - 0.5\right) \cdot \log t\right)} \]

   2. associate--l+ 99.6%

      \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \left(t - \left(a - 0.5\right) \cdot \log t\right)\right)} \]

   3. sub-neg 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(t + \left(-\left(a - 0.5\right) \cdot \log t\right)\right)}\right) \]

   4. +-commutative 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\left(\left(-\left(a - 0.5\right) \cdot \log t\right) + t\right)}\right) \]

   5. *-commutative 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\left(-\color{blue}{\log t \cdot \left(a - 0.5\right)}\right) + t\right)\right) \]

   6. distribute-rgt-neg-in 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \left(\color{blue}{\log t \cdot \left(-\left(a - 0.5\right)\right)} + t\right)\right) \]

   7. fma-undefine 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \color{blue}{\mathsf{fma}\left(\log t, -\left(a - 0.5\right), t\right)}\right) \]

   8. sub-neg 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(a + \left(-0.5\right)\right)}, t\right)\right) \]

   9. +-commutative 99.6%

      \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, -\color{blue}{\left(\left(-0.5\right) + a\right)}, t\right)\right) \]

   10. distribute-neg-in 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{\left(-\left(-0.5\right)\right) + \left(-a\right)}, t\right)\right) \]

   11. metadata-eval 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \left(-\color{blue}{-0.5}\right) + \left(-a\right), t\right)\right) \]

   12. metadata-eval 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5} + \left(-a\right), t\right)\right) \]

   13. unsub-neg 99.6%

       \[\leadsto \log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, \color{blue}{0.5 - a}, t\right)\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\log z - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 40.7%

   \[\leadsto \color{blue}{-1 \cdot t} \]
6. Step-by-step derivation

   1. neg-mul-1 40.7%

      \[\leadsto \color{blue}{-t} \]

7. Simplified 40.7%

   \[\leadsto \color{blue}{-t} \]
8. Add Preprocessing

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 2024096 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))