Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 16.9s

Alternatives: 19

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: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y \cdot z\right)\\ t_2 := \log z + \log y\\ t_3 := \log t \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t \leq 2.3 \cdot 10^{-6}:\\ \;\;\;\;t\_2 + t\_3\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+98}:\\ \;\;\;\;\left(t\_1 + t\_3\right) - t\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+229}:\\ \;\;\;\;t\_1 - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (* y z)))
        (t_2 (+ (log z) (log y)))
        (t_3 (* (log t) (- a 0.5))))
   (if (<= t 2.3e-6)
     (+ t_2 t_3)
     (if (<= t 6.6e+98)
       (- (+ t_1 t_3) t)
       (if (<= t 1.85e+167)
         (- t)
         (if (<= t 1.2e+229) (- t_1 (fma (log t) (- 0.5 a) t)) (- t_2 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y * z));
	double t_2 = log(z) + log(y);
	double t_3 = log(t) * (a - 0.5);
	double tmp;
	if (t <= 2.3e-6) {
		tmp = t_2 + t_3;
	} else if (t <= 6.6e+98) {
		tmp = (t_1 + t_3) - t;
	} else if (t <= 1.85e+167) {
		tmp = -t;
	} else if (t <= 1.2e+229) {
		tmp = t_1 - fma(log(t), (0.5 - a), t);
	} else {
		tmp = t_2 - t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y * z))
	t_2 = Float64(log(z) + log(y))
	t_3 = Float64(log(t) * Float64(a - 0.5))
	tmp = 0.0
	if (t <= 2.3e-6)
		tmp = Float64(t_2 + t_3);
	elseif (t <= 6.6e+98)
		tmp = Float64(Float64(t_1 + t_3) - t);
	elseif (t <= 1.85e+167)
		tmp = Float64(-t);
	elseif (t <= 1.2e+229)
		tmp = Float64(t_1 - fma(log(t), Float64(0.5 - a), t));
	else
		tmp = Float64(t_2 - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2.3e-6], N[(t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[t, 6.6e+98], N[(N[(t$95$1 + t$95$3), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t, 1.85e+167], (-t), If[LessEqual[t, 1.2e+229], N[(t$95$1 - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < 2.3e-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%

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

      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 x around 0 68.8%

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

   6. Taylor expanded in t around 0 68.8%

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

   if 2.3e-6 < t < 6.60000000000000056e98

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 97.8%

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

      2. pow3 97.9%

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

      3. +-commutative 97.9%

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

      4. *-commutative 97.9%

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

      5. fma-define 97.9%

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

      6. sub-neg 97.9%

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

      7. metadata-eval 97.9%

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

      8. sum-log 86.3%

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

   4. Applied egg-rr 86.3%

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

   5. 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 6.60000000000000056e98 < 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 < 1.2e229

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l+ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-undefine 99.8%

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

      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 x around 0 88.2%

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

      1. sub-neg 88.2%

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

      2. sum-log 73.7%

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

      3. +-commutative 73.7%

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

      4. fma-define 73.7%

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

   7. Applied egg-rr 73.7%

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

      1. sub-neg 73.7%

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

      2. *-commutative 73.7%

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

   9. Simplified 73.7%

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

   if 1.2e229 < 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 x around 0 59.1%

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

   6. Taylor expanded in a around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in a around 0 55.9%

      \[\leadsto \color{blue}{\left(\log y + \log z\right) - t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{-6}:\\ \;\;\;\;\left(\log z + \log y\right) + \log t \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+98}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+229}:\\ \;\;\;\;\log \left(y \cdot z\right) - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.505 \lor \neg \left(a - 0.5 \leq 5 \cdot 10^{+14}\right):\\ \;\;\;\;\log \left(y \cdot z\right) - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\log y + \left(\log z - \left(t + \log t \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -0.505) (not (<= (- a 0.5) 5e+14)))
   (- (log (* y z)) (fma (log t) (- 0.5 a) t))
   (+ (log y) (- (log z) (+ t (* (log t) 0.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -0.505) || !((a - 0.5) <= 5e+14)) {
		tmp = log((y * z)) - fma(log(t), (0.5 - a), t);
	} else {
		tmp = log(y) + (log(z) - (t + (log(t) * 0.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -0.505) || !(Float64(a - 0.5) <= 5e+14))
		tmp = Float64(log(Float64(y * z)) - fma(log(t), Float64(0.5 - a), t));
	else
		tmp = Float64(log(y) + Float64(log(z) - Float64(t + Float64(log(t) * 0.5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -0.505], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], 5e+14]], $MachinePrecision]], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * N[(0.5 - a), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(t + N[(N[Log[t], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -0.505000000000000004 or 5e14 < (-.f64 a #s(literal 1/2 binary64))

   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 x around 0 76.0%

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

      1. sub-neg 76.0%

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

      2. sum-log 61.8%

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

      3. +-commutative 61.8%

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

      4. fma-define 61.8%

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

   7. Applied egg-rr 61.8%

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

      1. sub-neg 61.8%

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

      2. *-commutative 61.8%

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

   9. Simplified 61.8%

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

   if -0.505000000000000004 < (-.f64 a #s(literal 1/2 binary64)) < 5e14

   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 x around 0 65.6%

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

   6. Taylor expanded in a around 0 64.5%

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

      1. associate--l+ 64.6%

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

      2. *-commutative 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.505 \lor \neg \left(a - 0.5 \leq 5 \cdot 10^{+14}\right):\\ \;\;\;\;\log \left(y \cdot z\right) - \mathsf{fma}\left(\log t, 0.5 - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\log y + \left(\log z - \left(t + \log t \cdot 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot \left(a - 0.5\right)\\ \mathbf{if}\;a - 0.5 \leq -0.505:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + t\_1\right) - t\\ \mathbf{elif}\;a - 0.5 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\log y + \left(\log z - \left(t + \log t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + t\_1\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) (- a 0.5))))
   (if (<= (- a 0.5) -0.505)
     (- (+ (log (* y z)) t_1) t)
     (if (<= (- a 0.5) 5e+14)
       (+ (log y) (- (log z) (+ t (* (log t) 0.5))))
       (- (+ (log (* (+ x y) z)) t_1) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * (a - 0.5);
	double tmp;
	if ((a - 0.5) <= -0.505) {
		tmp = (log((y * z)) + t_1) - t;
	} else if ((a - 0.5) <= 5e+14) {
		tmp = log(y) + (log(z) - (t + (log(t) * 0.5)));
	} else {
		tmp = (log(((x + y) * z)) + t_1) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) * (a - 0.5d0)
    if ((a - 0.5d0) <= (-0.505d0)) then
        tmp = (log((y * z)) + t_1) - t
    else if ((a - 0.5d0) <= 5d+14) then
        tmp = log(y) + (log(z) - (t + (log(t) * 0.5d0)))
    else
        tmp = (log(((x + y) * z)) + t_1) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * (a - 0.5);
	double tmp;
	if ((a - 0.5) <= -0.505) {
		tmp = (Math.log((y * z)) + t_1) - t;
	} else if ((a - 0.5) <= 5e+14) {
		tmp = Math.log(y) + (Math.log(z) - (t + (Math.log(t) * 0.5)));
	} else {
		tmp = (Math.log(((x + y) * z)) + t_1) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * (a - 0.5)
	tmp = 0
	if (a - 0.5) <= -0.505:
		tmp = (math.log((y * z)) + t_1) - t
	elif (a - 0.5) <= 5e+14:
		tmp = math.log(y) + (math.log(z) - (t + (math.log(t) * 0.5)))
	else:
		tmp = (math.log(((x + y) * z)) + t_1) - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(a - 0.5) <= -0.505)
		tmp = Float64(Float64(log(Float64(y * z)) + t_1) - t);
	elseif (Float64(a - 0.5) <= 5e+14)
		tmp = Float64(log(y) + Float64(log(z) - Float64(t + Float64(log(t) * 0.5))));
	else
		tmp = Float64(Float64(log(Float64(Float64(x + y) * z)) + t_1) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * (a - 0.5);
	tmp = 0.0;
	if ((a - 0.5) <= -0.505)
		tmp = (log((y * z)) + t_1) - t;
	elseif ((a - 0.5) <= 5e+14)
		tmp = log(y) + (log(z) - (t + (log(t) * 0.5)));
	else
		tmp = (log(((x + y) * z)) + t_1) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.505], N[(N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(a - 0.5), $MachinePrecision], 5e+14], N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] - N[(t + N[(N[Log[t], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -0.505000000000000004

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

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

      2. pow3 98.2%

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

      3. +-commutative 98.2%

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

      4. *-commutative 98.2%

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

      5. fma-define 98.2%

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

      6. sub-neg 98.2%

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

      7. metadata-eval 98.2%

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

      8. sum-log 79.0%

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

   4. Applied egg-rr 79.0%

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

   5. Taylor expanded in x around 0 61.0%

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

   if -0.505000000000000004 < (-.f64 a #s(literal 1/2 binary64)) < 5e14

   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 x around 0 65.6%

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

   6. Taylor expanded in a around 0 64.5%

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

      1. associate--l+ 64.6%

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

      2. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if 5e14 < (-.f64 a #s(literal 1/2 binary64))

   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. Step-by-step derivation

      1. associate-+r- 99.7%

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

      2. fma-undefine 99.6%

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

      3. associate--r+ 99.6%

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

      4. sum-log 80.5%

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

   6. Applied egg-rr 80.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.505:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;a - 0.5 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\log y + \left(\log z - \left(t + \log t \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.43)
   (+ (log z) (+ (log (+ x y)) (* (log t) (- a 0.5))))
   (- (+ (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(z) + (log((x + y)) + (log(t) * (a - 0.5)));
	} 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(z) + (log((x + y)) + (log(t) * (a - 0.5d0)))
    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(z) + (Math.log((x + y)) + (Math.log(t) * (a - 0.5)));
	} 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(z) + (math.log((x + y)) + (math.log(t) * (a - 0.5)))
	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(z) + Float64(log(Float64(x + y)) + Float64(log(t) * Float64(a - 0.5))));
	else
		tmp = Float64(Float64(log(y) + 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(z) + (log((x + y)) + (log(t) * (a - 0.5)));
	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[z], $MachinePrecision] + N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $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. Add Preprocessing

   3. Taylor expanded in t around 0 98.4%

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

   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%

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

      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 x around 0 71.5%

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

   6. Taylor expanded in a around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in a around 0 71.5%

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

4. Final simplification 84.3%

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

Alternative 6: 68.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.43)
   (+ (+ (log z) (log y)) (* (log t) (- a 0.5)))
   (- (+ (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(z) + log(y)) + (log(t) * (a - 0.5));
	} 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(z) + log(y)) + (log(t) * (a - 0.5d0))
    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(z) + Math.log(y)) + (Math.log(t) * (a - 0.5));
	} 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(z) + math.log(y)) + (math.log(t) * (a - 0.5))
	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(Float64(log(z) + log(y)) + Float64(log(t) * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(log(y) + 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(z) + log(y)) + (log(t) * (a - 0.5));
	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[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $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%

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

      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 x around 0 69.3%

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

   6. Taylor expanded in t around 0 68.5%

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

   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%

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

      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 x around 0 71.5%

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

   6. Taylor expanded in a around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in a around 0 71.5%

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

4. Final simplification 70.0%

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

Alternative 7: 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 8: 69.1% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in x around 0 70.5%

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

Alternative 9: 69.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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 x around 0 70.5%

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

6. Final simplification 70.5%

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

Alternative 10: 48.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {t}^{\left(0.5 - a\right)}\\ t_2 := \log t \cdot a\\ \mathbf{if}\;t \leq 7 \cdot 10^{-208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\log \left(\frac{y \cdot z}{t\_1}\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;\log \left(z \cdot \frac{y}{t\_1}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (pow t (- 0.5 a))) (t_2 (* (log t) a)))
   (if (<= t 7e-208)
     t_2
     (if (<= t 1.8e-174)
       (log (/ (* y z) t_1))
       (if (<= t 9.8e-102)
         t_2
         (if (<= t 6.8e-43)
           (log (* z (/ y t_1)))
           (if (<= t 1.35e+26) t_2 (- (+ (log z) (log y)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = pow(t, (0.5 - a));
	double t_2 = log(t) * a;
	double tmp;
	if (t <= 7e-208) {
		tmp = t_2;
	} else if (t <= 1.8e-174) {
		tmp = log(((y * z) / t_1));
	} else if (t <= 9.8e-102) {
		tmp = t_2;
	} else if (t <= 6.8e-43) {
		tmp = log((z * (y / t_1)));
	} else if (t <= 1.35e+26) {
		tmp = t_2;
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t ** (0.5d0 - a)
    t_2 = log(t) * a
    if (t <= 7d-208) then
        tmp = t_2
    else if (t <= 1.8d-174) then
        tmp = log(((y * z) / t_1))
    else if (t <= 9.8d-102) then
        tmp = t_2
    else if (t <= 6.8d-43) then
        tmp = log((z * (y / t_1)))
    else if (t <= 1.35d+26) then
        tmp = t_2
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.pow(t, (0.5 - a));
	double t_2 = Math.log(t) * a;
	double tmp;
	if (t <= 7e-208) {
		tmp = t_2;
	} else if (t <= 1.8e-174) {
		tmp = Math.log(((y * z) / t_1));
	} else if (t <= 9.8e-102) {
		tmp = t_2;
	} else if (t <= 6.8e-43) {
		tmp = Math.log((z * (y / t_1)));
	} else if (t <= 1.35e+26) {
		tmp = t_2;
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.pow(t, (0.5 - a))
	t_2 = math.log(t) * a
	tmp = 0
	if t <= 7e-208:
		tmp = t_2
	elif t <= 1.8e-174:
		tmp = math.log(((y * z) / t_1))
	elif t <= 9.8e-102:
		tmp = t_2
	elif t <= 6.8e-43:
		tmp = math.log((z * (y / t_1)))
	elif t <= 1.35e+26:
		tmp = t_2
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = t ^ Float64(0.5 - a)
	t_2 = Float64(log(t) * a)
	tmp = 0.0
	if (t <= 7e-208)
		tmp = t_2;
	elseif (t <= 1.8e-174)
		tmp = log(Float64(Float64(y * z) / t_1));
	elseif (t <= 9.8e-102)
		tmp = t_2;
	elseif (t <= 6.8e-43)
		tmp = log(Float64(z * Float64(y / t_1)));
	elseif (t <= 1.35e+26)
		tmp = t_2;
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t ^ (0.5 - a);
	t_2 = log(t) * a;
	tmp = 0.0;
	if (t <= 7e-208)
		tmp = t_2;
	elseif (t <= 1.8e-174)
		tmp = log(((y * z) / t_1));
	elseif (t <= 9.8e-102)
		tmp = t_2;
	elseif (t <= 6.8e-43)
		tmp = log((z * (y / t_1)));
	elseif (t <= 1.35e+26)
		tmp = t_2;
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Power[t, N[(0.5 - a), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, 7e-208], t$95$2, If[LessEqual[t, 1.8e-174], N[Log[N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 9.8e-102], t$95$2, If[LessEqual[t, 6.8e-43], N[Log[N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 1.35e+26], t$95$2, N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 6.99999999999999982e-208 or 1.79999999999999999e-174 < t < 9.7999999999999995e-102 or 6.8000000000000001e-43 < t < 1.35e26

   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 6.99999999999999982e-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%

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

      2. associate--l+ 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

      7. fma-undefine 99.3%

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

      8. sub-neg 99.3%

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

      9. +-commutative 99.3%

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

      10. distribute-neg-in 99.3%

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

      11. metadata-eval 99.3%

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

      12. metadata-eval 99.3%

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

      13. unsub-neg 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 70.6%

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

   6. Taylor expanded in t around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. log-prod 51.6%

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

      3. add-log-exp 51.6%

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

      4. diff-log 51.6%

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

      5. exp-to-pow 51.7%

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

   8. Applied egg-rr 51.7%

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

   if 9.7999999999999995e-102 < t < 6.8000000000000001e-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%

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

      2. associate--l+ 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. distribute-rgt-neg-in 99.2%

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

      7. fma-undefine 99.2%

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

      8. sub-neg 99.2%

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

      9. +-commutative 99.2%

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

      10. distribute-neg-in 99.2%

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

      11. metadata-eval 99.2%

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

      12. metadata-eval 99.2%

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

      13. unsub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 59.6%

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

   6. Taylor expanded in t around 0 59.6%

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

      1. *-un-lft-identity 59.6%

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

      2. +-commutative 59.6%

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

      3. log-prod 41.9%

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

      4. add-log-exp 30.6%

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

      5. diff-log 30.8%

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

      6. exp-to-pow 30.8%

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

   8. Applied egg-rr 30.8%

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

      1. *-lft-identity 30.8%

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

      2. associate-/l* 33.8%

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

   10. Simplified 33.8%

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

   if 1.35e26 < 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 x around 0 73.5%

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

   6. Taylor expanded in a around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. *-commutative 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in a around 0 54.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-208}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\log \left(\frac{y \cdot z}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-102}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;\log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ t_2 := \log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{if}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)) (t_2 (log (* z (/ y (pow t (- 0.5 a)))))))
   (if (<= t 8e-208)
     t_1
     (if (<= t 5.9e-173)
       t_2
       (if (<= t 5e-102)
         t_1
         (if (<= t 2.7e-43)
           t_2
           (if (<= t 1.9e+23) t_1 (- (+ (log z) (log y)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double t_2 = log((z * (y / pow(t, (0.5 - a)))));
	double tmp;
	if (t <= 8e-208) {
		tmp = t_1;
	} else if (t <= 5.9e-173) {
		tmp = t_2;
	} else if (t <= 5e-102) {
		tmp = t_1;
	} else if (t <= 2.7e-43) {
		tmp = t_2;
	} else if (t <= 1.9e+23) {
		tmp = t_1;
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) * a
    t_2 = log((z * (y / (t ** (0.5d0 - a)))))
    if (t <= 8d-208) then
        tmp = t_1
    else if (t <= 5.9d-173) then
        tmp = t_2
    else if (t <= 5d-102) then
        tmp = t_1
    else if (t <= 2.7d-43) then
        tmp = t_2
    else if (t <= 1.9d+23) then
        tmp = t_1
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log(t) * a;
	double t_2 = Math.log((z * (y / Math.pow(t, (0.5 - a)))));
	double tmp;
	if (t <= 8e-208) {
		tmp = t_1;
	} else if (t <= 5.9e-173) {
		tmp = t_2;
	} else if (t <= 5e-102) {
		tmp = t_1;
	} else if (t <= 2.7e-43) {
		tmp = t_2;
	} else if (t <= 1.9e+23) {
		tmp = t_1;
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	t_2 = math.log((z * (y / math.pow(t, (0.5 - a)))))
	tmp = 0
	if t <= 8e-208:
		tmp = t_1
	elif t <= 5.9e-173:
		tmp = t_2
	elif t <= 5e-102:
		tmp = t_1
	elif t <= 2.7e-43:
		tmp = t_2
	elif t <= 1.9e+23:
		tmp = t_1
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	t_2 = log(Float64(z * Float64(y / (t ^ Float64(0.5 - a)))))
	tmp = 0.0
	if (t <= 8e-208)
		tmp = t_1;
	elseif (t <= 5.9e-173)
		tmp = t_2;
	elseif (t <= 5e-102)
		tmp = t_1;
	elseif (t <= 2.7e-43)
		tmp = t_2;
	elseif (t <= 1.9e+23)
		tmp = t_1;
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	t_2 = log((z * (y / (t ^ (0.5 - a)))));
	tmp = 0.0;
	if (t <= 8e-208)
		tmp = t_1;
	elseif (t <= 5.9e-173)
		tmp = t_2;
	elseif (t <= 5e-102)
		tmp = t_1;
	elseif (t <= 2.7e-43)
		tmp = t_2;
	elseif (t <= 1.9e+23)
		tmp = t_1;
	else
		tmp = (log(z) + log(y)) - 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[(z * N[(y / N[Power[t, N[(0.5 - a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 8e-208], t$95$1, If[LessEqual[t, 5.9e-173], t$95$2, If[LessEqual[t, 5e-102], t$95$1, If[LessEqual[t, 2.7e-43], t$95$2, If[LessEqual[t, 1.9e+23], t$95$1, N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 8.0000000000000008e-208 or 5.89999999999999995e-173 < t < 5.00000000000000026e-102 or 2.69999999999999991e-43 < t < 1.89999999999999987e23

   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 < 5.89999999999999995e-173 or 5.00000000000000026e-102 < t < 2.69999999999999991e-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%

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

      2. associate--l+ 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

      7. fma-undefine 99.3%

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

      8. sub-neg 99.3%

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

      9. +-commutative 99.3%

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

      10. distribute-neg-in 99.3%

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

      11. metadata-eval 99.3%

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

      12. metadata-eval 99.3%

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

      13. unsub-neg 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 62.7%

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

   6. Taylor expanded in t around 0 62.7%

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

      1. *-un-lft-identity 62.7%

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

      2. +-commutative 62.7%

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

      3. log-prod 44.7%

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

      4. add-log-exp 36.6%

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

      5. diff-log 36.7%

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

      6. exp-to-pow 36.8%

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

   8. Applied egg-rr 36.8%

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

      1. *-lft-identity 36.8%

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

      2. associate-/l* 38.9%

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

   10. Simplified 38.9%

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

   if 1.89999999999999987e23 < 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 x around 0 73.5%

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

   6. Taylor expanded in a around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. *-commutative 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in a around 0 54.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-208}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-173}:\\ \;\;\;\;\log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-102}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;\log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ t_2 := \log \left(y \cdot z\right) + \left(t\_1 - t\right)\\ \mathbf{if}\;a \leq -780000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-70}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;a \leq 0.32:\\ \;\;\;\;\log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)) (t_2 (+ (log (* y z)) (- t_1 t))))
   (if (<= a -780000.0)
     t_2
     (if (<= a 1.6e-70)
       (- (+ (log z) (log y)) t)
       (if (<= a 0.32)
         (log (* z (/ y (pow t (- 0.5 a)))))
         (if (<= a 9.2e+53) 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)) + (t_1 - t);
	double tmp;
	if (a <= -780000.0) {
		tmp = t_2;
	} else if (a <= 1.6e-70) {
		tmp = (log(z) + log(y)) - t;
	} else if (a <= 0.32) {
		tmp = log((z * (y / pow(t, (0.5 - a)))));
	} else if (a <= 9.2e+53) {
		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) :: tmp
    t_1 = log(t) * a
    t_2 = log((y * z)) + (t_1 - t)
    if (a <= (-780000.0d0)) then
        tmp = t_2
    else if (a <= 1.6d-70) then
        tmp = (log(z) + log(y)) - t
    else if (a <= 0.32d0) then
        tmp = log((z * (y / (t ** (0.5d0 - a)))))
    else if (a <= 9.2d+53) 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)) + (t_1 - t);
	double tmp;
	if (a <= -780000.0) {
		tmp = t_2;
	} else if (a <= 1.6e-70) {
		tmp = (Math.log(z) + Math.log(y)) - t;
	} else if (a <= 0.32) {
		tmp = Math.log((z * (y / Math.pow(t, (0.5 - a)))));
	} else if (a <= 9.2e+53) {
		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)) + (t_1 - t)
	tmp = 0
	if a <= -780000.0:
		tmp = t_2
	elif a <= 1.6e-70:
		tmp = (math.log(z) + math.log(y)) - t
	elif a <= 0.32:
		tmp = math.log((z * (y / math.pow(t, (0.5 - a)))))
	elif a <= 9.2e+53:
		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 * z)) + Float64(t_1 - t))
	tmp = 0.0
	if (a <= -780000.0)
		tmp = t_2;
	elseif (a <= 1.6e-70)
		tmp = Float64(Float64(log(z) + log(y)) - t);
	elseif (a <= 0.32)
		tmp = log(Float64(z * Float64(y / (t ^ Float64(0.5 - a)))));
	elseif (a <= 9.2e+53)
		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_1 - t);
	tmp = 0.0;
	if (a <= -780000.0)
		tmp = t_2;
	elseif (a <= 1.6e-70)
		tmp = (log(z) + log(y)) - t;
	elseif (a <= 0.32)
		tmp = log((z * (y / (t ^ (0.5 - a)))));
	elseif (a <= 9.2e+53)
		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 * z), $MachinePrecision]], $MachinePrecision] + N[(t$95$1 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -780000.0], t$95$2, If[LessEqual[a, 1.6e-70], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[a, 0.32], N[Log[N[(z * N[(y / N[Power[t, N[(0.5 - a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[a, 9.2e+53], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.8e5 or 0.320000000000000007 < a < 9.20000000000000079e53

   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 99.8%

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

      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 x around 0 77.7%

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

   6. Taylor expanded in a around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. *-commutative 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

   8. Simplified 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. sum-log 61.3%

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

      4. +-commutative 61.3%

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

      5. fma-define 61.3%

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

   10. Applied egg-rr 61.3%

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

       1. neg-sub0 61.3%

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

       2. fma-define 61.3%

          \[\leadsto \log \left(z \cdot y\right) + \left(0 - \color{blue}{\left(\log t \cdot \left(-a\right) + t\right)}\right) \]

       3. associate--r+ 61.3%

          \[\leadsto \log \left(z \cdot y\right) + \color{blue}{\left(\left(0 - \log t \cdot \left(-a\right)\right) - t\right)} \]

       4. neg-sub0 61.3%

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

       5. distribute-rgt-neg-in 61.3%

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

       6. remove-double-neg 61.3%

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

   12. Simplified 61.3%

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

   if -7.8e5 < a < 1.5999999999999999e-70

   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+ 99.6%

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

      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 x around 0 65.4%

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

   6. Taylor expanded in a around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. *-commutative 43.9%

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

      3. distribute-rgt-neg-in 43.9%

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

   8. Simplified 43.9%

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

   9. Taylor expanded in a around 0 43.5%

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

   if 1.5999999999999999e-70 < a < 0.320000000000000007

   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%

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

      2. associate--l+ 99.0%

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

      3. sub-neg 99.0%

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

      4. +-commutative 99.0%

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

      5. *-commutative 99.0%

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

      6. distribute-rgt-neg-in 99.0%

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

      7. fma-undefine 99.0%

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

      8. sub-neg 99.0%

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

      9. +-commutative 99.0%

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

      10. distribute-neg-in 99.0%

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

      11. metadata-eval 99.0%

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

      12. metadata-eval 99.0%

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

      13. unsub-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0 69.5%

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

   6. Taylor expanded in t around 0 52.1%

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

      1. *-un-lft-identity 52.1%

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

      2. +-commutative 52.1%

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

      3. log-prod 36.1%

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

      4. add-log-exp 36.1%

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

      5. diff-log 36.0%

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

      6. exp-to-pow 36.5%

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

   8. Applied egg-rr 36.5%

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

      1. *-lft-identity 36.5%

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

      2. associate-/l* 45.0%

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

   10. Simplified 45.0%

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

   if 9.20000000000000079e53 < a

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. associate--l+ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-undefine 99.6%

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

      8. sub-neg 99.6%

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

      9. +-commutative 99.6%

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

      10. distribute-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around inf 81.8%

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

      1. *-commutative 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -780000:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-70}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;a \leq 0.32:\\ \;\;\;\;\log \left(z \cdot \frac{y}{{t}^{\left(0.5 - a\right)}}\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3.8e+99)
   (- (+ (log (* (+ x y) z)) (* (log t) (- a 0.5))) t)
   (if (<= t 1.9e+167)
     (- t)
     (if (<= t 1.12e+229)
       (+ (log (* y z)) (- (* (log t) a) t))
       (- (+ (log z) (log y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.8e+99) {
		tmp = (log(((x + y) * z)) + (log(t) * (a - 0.5))) - t;
	} else if (t <= 1.9e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = log((y * z)) + ((log(t) * a) - t);
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 3.8d+99) then
        tmp = (log(((x + y) * z)) + (log(t) * (a - 0.5d0))) - t
    else if (t <= 1.9d+167) then
        tmp = -t
    else if (t <= 1.12d+229) then
        tmp = log((y * z)) + ((log(t) * a) - t)
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.8e+99) {
		tmp = (Math.log(((x + y) * z)) + (Math.log(t) * (a - 0.5))) - t;
	} else if (t <= 1.9e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = Math.log((y * z)) + ((Math.log(t) * a) - t);
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 3.8e+99:
		tmp = (math.log(((x + y) * z)) + (math.log(t) * (a - 0.5))) - t
	elif t <= 1.9e+167:
		tmp = -t
	elif t <= 1.12e+229:
		tmp = math.log((y * z)) + ((math.log(t) * a) - t)
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.8e+99)
		tmp = Float64(Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a - 0.5))) - t);
	elseif (t <= 1.9e+167)
		tmp = Float64(-t);
	elseif (t <= 1.12e+229)
		tmp = Float64(log(Float64(y * z)) + Float64(Float64(log(t) * a) - t));
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 3.8e+99)
		tmp = (log(((x + y) * z)) + (log(t) * (a - 0.5))) - t;
	elseif (t <= 1.9e+167)
		tmp = -t;
	elseif (t <= 1.12e+229)
		tmp = log((y * z)) + ((log(t) * a) - t);
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3.8e+99], N[(N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t, 1.9e+167], (-t), If[LessEqual[t, 1.12e+229], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < 3.8e99

   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 3.8e99 < t < 1.89999999999999997e167

   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 1.89999999999999997e167 < 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%

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

      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 x around 0 88.2%

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

   6. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-neg-in 88.2%

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

   8. Simplified 88.2%

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

      1. sub-neg 88.2%

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

      2. +-commutative 88.2%

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

      3. sum-log 73.7%

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

      4. +-commutative 73.7%

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

      5. fma-define 73.7%

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

   10. Applied egg-rr 73.7%

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

       1. neg-sub0 73.7%

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

       2. fma-define 73.7%

          \[\leadsto \log \left(z \cdot y\right) + \left(0 - \color{blue}{\left(\log t \cdot \left(-a\right) + t\right)}\right) \]

       3. associate--r+ 73.7%

          \[\leadsto \log \left(z \cdot y\right) + \color{blue}{\left(\left(0 - \log t \cdot \left(-a\right)\right) - t\right)} \]

       4. neg-sub0 73.7%

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

       5. distribute-rgt-neg-in 73.7%

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

       6. remove-double-neg 73.7%

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

   12. Simplified 73.7%

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

   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 x around 0 59.1%

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

   6. Taylor expanded in a around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in a around 0 55.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y \cdot z\right)\\ \mathbf{if}\;t \leq 3.7 \cdot 10^{+97}:\\ \;\;\;\;\left(t\_1 + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;t\_1 + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (* y z))))
   (if (<= t 3.7e+97)
     (- (+ t_1 (* (log t) (- a 0.5))) t)
     (if (<= t 1.9e+167)
       (- t)
       (if (<= t 1.12e+229)
         (+ t_1 (- (* (log t) a) t))
         (- (+ (log z) (log y)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y * z));
	double tmp;
	if (t <= 3.7e+97) {
		tmp = (t_1 + (log(t) * (a - 0.5))) - t;
	} else if (t <= 1.9e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = t_1 + ((log(t) * a) - t);
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log((y * z))
    if (t <= 3.7d+97) then
        tmp = (t_1 + (log(t) * (a - 0.5d0))) - t
    else if (t <= 1.9d+167) then
        tmp = -t
    else if (t <= 1.12d+229) then
        tmp = t_1 + ((log(t) * a) - t)
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log((y * z));
	double tmp;
	if (t <= 3.7e+97) {
		tmp = (t_1 + (Math.log(t) * (a - 0.5))) - t;
	} else if (t <= 1.9e+167) {
		tmp = -t;
	} else if (t <= 1.12e+229) {
		tmp = t_1 + ((Math.log(t) * a) - t);
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log((y * z))
	tmp = 0
	if t <= 3.7e+97:
		tmp = (t_1 + (math.log(t) * (a - 0.5))) - t
	elif t <= 1.9e+167:
		tmp = -t
	elif t <= 1.12e+229:
		tmp = t_1 + ((math.log(t) * a) - t)
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y * z))
	tmp = 0.0
	if (t <= 3.7e+97)
		tmp = Float64(Float64(t_1 + Float64(log(t) * Float64(a - 0.5))) - t);
	elseif (t <= 1.9e+167)
		tmp = Float64(-t);
	elseif (t <= 1.12e+229)
		tmp = Float64(t_1 + Float64(Float64(log(t) * a) - t));
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log((y * z));
	tmp = 0.0;
	if (t <= 3.7e+97)
		tmp = (t_1 + (log(t) * (a - 0.5))) - t;
	elseif (t <= 1.9e+167)
		tmp = -t;
	elseif (t <= 1.12e+229)
		tmp = t_1 + ((log(t) * a) - t);
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 3.7e+97], N[(N[(t$95$1 + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t, 1.9e+167], (-t), If[LessEqual[t, 1.12e+229], N[(t$95$1 + N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 3.70000000000000001e97

   1. Initial program 99.4%

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

      1. add-cube-cbrt 98.0%

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

      2. pow3 98.0%

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

      3. +-commutative 98.0%

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

      4. *-commutative 98.0%

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

      5. fma-define 98.0%

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

      6. sub-neg 98.0%

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

      7. metadata-eval 98.0%

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

      8. sum-log 74.4%

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

   4. Applied egg-rr 74.4%

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

   5. 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 3.70000000000000001e97 < t < 1.89999999999999997e167

   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 1.89999999999999997e167 < 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%

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

      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 x around 0 88.2%

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

   6. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-neg-in 88.2%

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

   8. Simplified 88.2%

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

      1. sub-neg 88.2%

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

      2. +-commutative 88.2%

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

      3. sum-log 73.7%

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

      4. +-commutative 73.7%

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

      5. fma-define 73.7%

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

   10. Applied egg-rr 73.7%

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

       1. neg-sub0 73.7%

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

       2. fma-define 73.7%

          \[\leadsto \log \left(z \cdot y\right) + \left(0 - \color{blue}{\left(\log t \cdot \left(-a\right) + t\right)}\right) \]

       3. associate--r+ 73.7%

          \[\leadsto \log \left(z \cdot y\right) + \color{blue}{\left(\left(0 - \log t \cdot \left(-a\right)\right) - t\right)} \]

       4. neg-sub0 73.7%

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

       5. distribute-rgt-neg-in 73.7%

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

       6. remove-double-neg 73.7%

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

   12. Simplified 73.7%

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

   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 x around 0 59.1%

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

   6. Taylor expanded in a around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in a around 0 55.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{+97}:\\ \;\;\;\;\left(\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\right) - t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+229}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+95}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.43)
   (+ (log (* (+ x y) z)) (* (log t) (+ a -0.5)))
   (if (<= t 9.4e+95)
     (+ (log (* y z)) (- (* (log t) a) t))
     (- (+ (log z) (log y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.43) {
		tmp = log(((x + y) * z)) + (log(t) * (a + -0.5));
	} else if (t <= 9.4e+95) {
		tmp = log((y * z)) + ((log(t) * a) - t);
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 0.43d0) then
        tmp = log(((x + y) * z)) + (log(t) * (a + (-0.5d0)))
    else if (t <= 9.4d+95) then
        tmp = log((y * z)) + ((log(t) * a) - t)
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.43) {
		tmp = Math.log(((x + y) * z)) + (Math.log(t) * (a + -0.5));
	} else if (t <= 9.4e+95) {
		tmp = Math.log((y * z)) + ((Math.log(t) * a) - t);
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 0.43:
		tmp = math.log(((x + y) * z)) + (math.log(t) * (a + -0.5))
	elif t <= 9.4e+95:
		tmp = math.log((y * z)) + ((math.log(t) * a) - t)
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 0.43)
		tmp = Float64(log(Float64(Float64(x + y) * z)) + Float64(log(t) * Float64(a + -0.5)));
	elseif (t <= 9.4e+95)
		tmp = Float64(log(Float64(y * z)) + Float64(Float64(log(t) * a) - t));
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 0.43)
		tmp = log(((x + y) * z)) + (log(t) * (a + -0.5));
	elseif (t <= 9.4e+95)
		tmp = log((y * z)) + ((log(t) * a) - t);
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 0.43], N[(N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.4e+95], N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] + N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

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

      2. pow3 98.0%

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

      3. +-commutative 98.0%

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

      4. *-commutative 98.0%

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

      5. fma-define 98.0%

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

      6. sub-neg 98.0%

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

      7. metadata-eval 98.0%

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

      8. sum-log 71.6%

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

   4. Applied egg-rr 71.6%

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

   5. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. +-commutative 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   7. Simplified 71.7%

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

   if 0.429999999999999993 < t < 9.39999999999999945e95

   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+ 99.6%

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

      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 x around 0 77.2%

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

   6. Taylor expanded in a around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

   8. Simplified 77.1%

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

      1. sub-neg 77.1%

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

      2. +-commutative 77.1%

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

      3. sum-log 58.6%

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

      4. +-commutative 58.6%

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

      5. fma-define 58.6%

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

   10. Applied egg-rr 58.6%

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

       1. neg-sub0 58.6%

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

       2. fma-define 58.6%

          \[\leadsto \log \left(z \cdot y\right) + \left(0 - \color{blue}{\left(\log t \cdot \left(-a\right) + t\right)}\right) \]

       3. associate--r+ 58.6%

          \[\leadsto \log \left(z \cdot y\right) + \color{blue}{\left(\left(0 - \log t \cdot \left(-a\right)\right) - t\right)} \]

       4. neg-sub0 58.6%

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

       5. distribute-rgt-neg-in 58.6%

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

       6. remove-double-neg 58.6%

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

   12. Simplified 58.6%

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

   if 9.39999999999999945e95 < 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 x around 0 69.8%

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

   6. Taylor expanded in a around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

   8. Simplified 69.8%

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

   9. Taylor expanded in a around 0 56.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+95}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y \cdot z\right)\\ \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;t\_1 + \log t \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+98}:\\ \;\;\;\;t\_1 + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (* y z))))
   (if (<= t 0.43)
     (+ t_1 (* (log t) (- a 0.5)))
     (if (<= t 4.1e+98)
       (+ t_1 (- (* (log t) a) t))
       (- (+ (log z) (log y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y * z));
	double tmp;
	if (t <= 0.43) {
		tmp = t_1 + (log(t) * (a - 0.5));
	} else if (t <= 4.1e+98) {
		tmp = t_1 + ((log(t) * a) - t);
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log((y * z))
    if (t <= 0.43d0) then
        tmp = t_1 + (log(t) * (a - 0.5d0))
    else if (t <= 4.1d+98) then
        tmp = t_1 + ((log(t) * a) - t)
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.log((y * z));
	double tmp;
	if (t <= 0.43) {
		tmp = t_1 + (Math.log(t) * (a - 0.5));
	} else if (t <= 4.1e+98) {
		tmp = t_1 + ((Math.log(t) * a) - t);
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log((y * z))
	tmp = 0
	if t <= 0.43:
		tmp = t_1 + (math.log(t) * (a - 0.5))
	elif t <= 4.1e+98:
		tmp = t_1 + ((math.log(t) * a) - t)
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y * z))
	tmp = 0.0
	if (t <= 0.43)
		tmp = Float64(t_1 + Float64(log(t) * Float64(a - 0.5)));
	elseif (t <= 4.1e+98)
		tmp = Float64(t_1 + Float64(Float64(log(t) * a) - t));
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log((y * z));
	tmp = 0.0;
	if (t <= 0.43)
		tmp = t_1 + (log(t) * (a - 0.5));
	elseif (t <= 4.1e+98)
		tmp = t_1 + ((log(t) * a) - t);
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 0.43], N[(t$95$1 + N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+98], N[(t$95$1 + N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 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%

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

      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 x around 0 69.3%

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

   6. Taylor expanded in t around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. log-prod 46.8%

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

   8. Applied egg-rr 46.8%

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

   if 0.429999999999999993 < t < 4.1e98

   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+ 99.6%

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

      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 x around 0 77.2%

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

   6. Taylor expanded in a around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

   8. Simplified 77.1%

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

      1. sub-neg 77.1%

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

      2. +-commutative 77.1%

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

      3. sum-log 58.6%

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

      4. +-commutative 58.6%

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

      5. fma-define 58.6%

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

   10. Applied egg-rr 58.6%

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

       1. neg-sub0 58.6%

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

       2. fma-define 58.6%

          \[\leadsto \log \left(z \cdot y\right) + \left(0 - \color{blue}{\left(\log t \cdot \left(-a\right) + t\right)}\right) \]

       3. associate--r+ 58.6%

          \[\leadsto \log \left(z \cdot y\right) + \color{blue}{\left(\left(0 - \log t \cdot \left(-a\right)\right) - t\right)} \]

       4. neg-sub0 58.6%

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

       5. distribute-rgt-neg-in 58.6%

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

       6. remove-double-neg 58.6%

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

   12. Simplified 58.6%

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

   if 4.1e98 < 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 x around 0 69.8%

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

   6. Taylor expanded in a around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

   8. Simplified 69.8%

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

   9. Taylor expanded in a around 0 56.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.43:\\ \;\;\;\;\log \left(y \cdot z\right) + \log t \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+98}:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot a - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.6e+22) (* (log t) a) (- (+ (log z) (log y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.6e+22) {
		tmp = log(t) * a;
	} else {
		tmp = (log(z) + log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.6d+22) then
        tmp = log(t) * a
    else
        tmp = (log(z) + log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.6e+22) {
		tmp = Math.log(t) * a;
	} else {
		tmp = (Math.log(z) + Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.6e+22:
		tmp = math.log(t) * a
	else:
		tmp = (math.log(z) + math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.6e+22)
		tmp = Float64(log(t) * a);
	else
		tmp = Float64(Float64(log(z) + log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.6e+22)
		tmp = log(t) * a;
	else
		tmp = (log(z) + log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.6e+22], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.6e22

   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 1.6e22 < 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 x around 0 73.5%

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

   6. Taylor expanded in a around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. *-commutative 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in a around 0 54.8%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{+21}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 7.6e+21) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7.6e+21) {
		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 <= 7.6d+21) 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 <= 7.6e+21) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 7.6e+21:
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7.6e+21)
		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 <= 7.6e+21)
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7.6e+21], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 7.6e21

   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 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 7.6e21 < 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%

      \[\leadsto \color{blue}{-1 \cdot t} \]
   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 19: 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))))