Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 14.2s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.6%

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

Alternative 2: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y + x\right)\\ t_2 := \log t \cdot \left(a - 0.5\right) + \left(\left(t\_1 + \log z\right) - t\right)\\ t_3 := \mathsf{fma}\left(\log t, a - 0.5, -t\right) + t\_1\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 946.3:\\ \;\;\;\;\mathsf{fma}\left(\log t, -0.5, \log \left(\left(y + x\right) \cdot z\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (+ y x)))
        (t_2 (+ (* (log t) (- a 0.5)) (- (+ t_1 (log z)) t)))
        (t_3 (+ (fma (log t) (- a 0.5) (- t)) t_1)))
   (if (<= t_2 -4e+17)
     t_3
     (if (<= t_2 946.3) (fma (log t) -0.5 (- (log (* (+ y x) z)) t)) t_3))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y + x));
	double t_2 = (log(t) * (a - 0.5)) + ((t_1 + log(z)) - t);
	double t_3 = fma(log(t), (a - 0.5), -t) + t_1;
	double tmp;
	if (t_2 <= -4e+17) {
		tmp = t_3;
	} else if (t_2 <= 946.3) {
		tmp = fma(log(t), -0.5, (log(((y + x) * z)) - t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y + x))
	t_2 = Float64(Float64(log(t) * Float64(a - 0.5)) + Float64(Float64(t_1 + log(z)) - t))
	t_3 = Float64(fma(log(t), Float64(a - 0.5), Float64(-t)) + t_1)
	tmp = 0.0
	if (t_2 <= -4e+17)
		tmp = t_3;
	elseif (t_2 <= 946.3)
		tmp = fma(log(t), -0.5, Float64(log(Float64(Float64(y + x) * z)) - t));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision] + (-t)), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+17], t$95$3, If[LessEqual[t$95$2, 946.3], N[(N[Log[t], $MachinePrecision] * -0.5 + N[(N[Log[N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < -4e17 or 946.29999999999995 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t)))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      5. associate--l+ N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

      7. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

      12. lower--.f64 99.8

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

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

      15. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{-1 \cdot t}\right) + \log \left(y + x\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{\mathsf{neg}\left(t\right)}\right) + \log \left(y + x\right) \]

      2. lower-neg.f64 97.1

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

   7. Applied rewrites 97.1%

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

   if -4e17 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < 946.29999999999995

   1. Initial program 98.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      5. associate--l+ N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

      7. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

      12. lower--.f64 98.7

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

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

      15. lower-+.f64 98.7

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

   4. Applied rewrites 98.7%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(\log t, \color{blue}{\frac{-1}{2}}, \log z - t\right) + \log \left(y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 97.6%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, \frac{-1}{2}, \log z - t\right) + \log \left(y + x\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto \color{blue}{\left(\log t \cdot \frac{-1}{2} + \left(\log z - t\right)\right)} + \log \left(y + x\right) \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\log t \cdot \frac{-1}{2} + \left(\left(\log z - t\right) + \log \left(y + x\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \color{blue}{\left(\log \left(y + x\right) + \left(\log z - t\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \left(\log \left(y + x\right) + \color{blue}{\left(\log z - t\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \color{blue}{\left(\left(\log \left(y + x\right) + \log z\right) - t\right)} \]

      7. lift-+.f64 N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \left(\left(\log \color{blue}{\left(y + x\right)} + \log z\right) - t\right) \]

      8. +-commutative N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \left(\left(\log \color{blue}{\left(x + y\right)} + \log z\right) - t\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \log t \cdot \frac{-1}{2} + \left(\left(\log \color{blue}{\left(x + y\right)} + \log z\right) - t\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \log t \cdot \frac{-1}{2} + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      11. lift--.f64 N/A

          \[\leadsto \log t \cdot \frac{-1}{2} + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      12. lower-fma.f64 97.7

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

   9. Applied rewrites 86.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right) \leq -4 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a - 0.5, -t\right) + \log \left(y + x\right)\\ \mathbf{elif}\;\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right) \leq 946.3:\\ \;\;\;\;\mathsf{fma}\left(\log t, -0.5, \log \left(\left(y + x\right) \cdot z\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a - 0.5, -t\right) + \log \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y + x\right)\\ t_2 := \log t \cdot \left(a - 0.5\right) + \left(\left(t\_1 + \log z\right) - t\right)\\ t_3 := \log t \cdot a + \left(-t\right)\\ \mathbf{if}\;t\_2 \leq -1016.2:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2000:\\ \;\;\;\;\left(-t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (+ y x)))
        (t_2 (+ (* (log t) (- a 0.5)) (- (+ t_1 (log z)) t)))
        (t_3 (+ (* (log t) a) (- t))))
   (if (<= t_2 -1016.2) t_3 (if (<= t_2 2000.0) (+ (- t) t_1) t_3))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y + x));
	double t_2 = (log(t) * (a - 0.5)) + ((t_1 + log(z)) - t);
	double t_3 = (log(t) * a) + -t;
	double tmp;
	if (t_2 <= -1016.2) {
		tmp = t_3;
	} else if (t_2 <= 2000.0) {
		tmp = -t + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log((y + x))
    t_2 = (log(t) * (a - 0.5d0)) + ((t_1 + log(z)) - t)
    t_3 = (log(t) * a) + -t
    if (t_2 <= (-1016.2d0)) then
        tmp = t_3
    else if (t_2 <= 2000.0d0) then
        tmp = -t + t_1
    else
        tmp = t_3
    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 + x));
	double t_2 = (Math.log(t) * (a - 0.5)) + ((t_1 + Math.log(z)) - t);
	double t_3 = (Math.log(t) * a) + -t;
	double tmp;
	if (t_2 <= -1016.2) {
		tmp = t_3;
	} else if (t_2 <= 2000.0) {
		tmp = -t + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log((y + x))
	t_2 = (math.log(t) * (a - 0.5)) + ((t_1 + math.log(z)) - t)
	t_3 = (math.log(t) * a) + -t
	tmp = 0
	if t_2 <= -1016.2:
		tmp = t_3
	elif t_2 <= 2000.0:
		tmp = -t + t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y + x))
	t_2 = Float64(Float64(log(t) * Float64(a - 0.5)) + Float64(Float64(t_1 + log(z)) - t))
	t_3 = Float64(Float64(log(t) * a) + Float64(-t))
	tmp = 0.0
	if (t_2 <= -1016.2)
		tmp = t_3;
	elseif (t_2 <= 2000.0)
		tmp = Float64(Float64(-t) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log((y + x));
	t_2 = (log(t) * (a - 0.5)) + ((t_1 + log(z)) - t);
	t_3 = (log(t) * a) + -t;
	tmp = 0.0;
	if (t_2 <= -1016.2)
		tmp = t_3;
	elseif (t_2 <= 2000.0)
		tmp = -t + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] + (-t)), $MachinePrecision]}, If[LessEqual[t$95$2, -1016.2], t$95$3, If[LessEqual[t$95$2, 2000.0], N[((-t) + t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < -1016.2 or 2e3 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t)))

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} + \left(a - \frac{1}{2}\right) \cdot \log t \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot \log t \]

      2. lower-neg.f64 98.2

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 98.3

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

   8. Applied rewrites 98.3%

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

   if -1016.2 < (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a #s(literal 1/2 binary64)) (log.f64 t))) < 2e3

   1. Initial program 98.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      5. associate--l+ N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

      7. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

      12. lower--.f64 98.7

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

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

      15. lower-+.f64 98.7

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

   4. Applied rewrites 98.7%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 16.0

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

   7. Applied rewrites 16.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right) \leq -1016.2:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \mathbf{elif}\;\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right) \leq 2000:\\ \;\;\;\;\left(-t\right) + \log \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(y + x\right)\\ t_2 := t\_1 + \log z\\ t_3 := \mathsf{fma}\left(\log t, a - 0.5, -t\right) + t\_1\\ \mathbf{if}\;t\_2 \leq -750:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 700:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(\left(y + x\right) \cdot z\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (log (+ y x)))
        (t_2 (+ t_1 (log z)))
        (t_3 (+ (fma (log t) (- a 0.5) (- t)) t_1)))
   (if (<= t_2 -750.0)
     t_3
     (if (<= t_2 700.0)
       (fma (- a 0.5) (log t) (- (log (* (+ y x) z)) t))
       t_3))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log((y + x));
	double t_2 = t_1 + log(z);
	double t_3 = fma(log(t), (a - 0.5), -t) + t_1;
	double tmp;
	if (t_2 <= -750.0) {
		tmp = t_3;
	} else if (t_2 <= 700.0) {
		tmp = fma((a - 0.5), log(t), (log(((y + x) * z)) - t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = log(Float64(y + x))
	t_2 = Float64(t_1 + log(z))
	t_3 = Float64(fma(log(t), Float64(a - 0.5), Float64(-t)) + t_1)
	tmp = 0.0
	if (t_2 <= -750.0)
		tmp = t_3;
	elseif (t_2 <= 700.0)
		tmp = fma(Float64(a - 0.5), log(t), Float64(log(Float64(Float64(y + x) * z)) - t));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[Log[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision] + (-t)), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -750.0], t$95$3, If[LessEqual[t$95$2, 700.0], N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + N[(N[Log[N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) < -750 or 700 < (+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      5. associate--l+ N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

      7. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

      12. lower--.f64 99.7

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

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

      15. lower-+.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{-1 \cdot t}\right) + \log \left(y + x\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{\mathsf{neg}\left(t\right)}\right) + \log \left(y + x\right) \]

      2. lower-neg.f64 85.1

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

   7. Applied rewrites 85.1%

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

   if -750 < (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) < 700

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\left(\log \left(x + y\right) + \log z\right) - t\right) \]

      4. lower-fma.f64 99.5

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

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      6. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \left(\color{blue}{\log \left(x + y\right)} + \log z\right) - t\right) \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \left(\log \left(x + y\right) + \color{blue}{\log z}\right) - t\right) \]

      8. sum-log N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \color{blue}{\log \left(\left(x + y\right) \cdot z\right)} - t\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \color{blue}{\log \left(\left(x + y\right) \cdot z\right)} - t\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \color{blue}{\left(z \cdot \left(x + y\right)\right)} - t\right) \]

      11. lower-*.f64 99.6

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

      12. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \left(z \cdot \color{blue}{\left(x + y\right)}\right) - t\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \left(z \cdot \color{blue}{\left(y + x\right)}\right) - t\right) \]

      14. lower-+.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log \left(y + x\right) + \log z \leq -750:\\ \;\;\;\;\mathsf{fma}\left(\log t, a - 0.5, -t\right) + \log \left(y + x\right)\\ \mathbf{elif}\;\log \left(y + x\right) + \log z \leq 700:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(\left(y + x\right) \cdot z\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log t, a - 0.5, -t\right) + \log \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1000000:\\ \;\;\;\;\frac{\log t}{\frac{1}{a - 0.5}} + \left(-t\right)\\ \mathbf{elif}\;a - 0.5 \leq -0.5:\\ \;\;\;\;\left(\mathsf{fma}\left(-0.5, \log t, \log z\right) - t\right) + \log y\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- a 0.5) -1000000.0)
   (+ (/ (log t) (/ 1.0 (- a 0.5))) (- t))
   (if (<= (- a 0.5) -0.5)
     (+ (- (fma -0.5 (log t) (log z)) t) (log y))
     (+ (* (log t) a) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a - 0.5) <= -1000000.0) {
		tmp = (log(t) / (1.0 / (a - 0.5))) + -t;
	} else if ((a - 0.5) <= -0.5) {
		tmp = (fma(-0.5, log(t), log(z)) - t) + log(y);
	} else {
		tmp = (log(t) * a) + -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a - 0.5) <= -1000000.0)
		tmp = Float64(Float64(log(t) / Float64(1.0 / Float64(a - 0.5))) + Float64(-t));
	elseif (Float64(a - 0.5) <= -0.5)
		tmp = Float64(Float64(fma(-0.5, log(t), log(z)) - t) + log(y));
	else
		tmp = Float64(Float64(log(t) * a) + Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a - 0.5), $MachinePrecision], -1000000.0], N[(N[(N[Log[t], $MachinePrecision] / N[(1.0 / N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-t)), $MachinePrecision], If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5], N[(N[(N[(-0.5 * N[Log[t], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] + (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -1e6

   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. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log t \cdot \color{blue}{\left(a - \frac{1}{2}\right)} \]

      4. flip3-- N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log t \cdot \color{blue}{\frac{{a}^{3} - {\frac{1}{2}}^{3}}{a \cdot a + \left(\frac{1}{2} \cdot \frac{1}{2} + a \cdot \frac{1}{2}\right)}} \]

      5. clear-num N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log t \cdot \color{blue}{\frac{1}{\frac{a \cdot a + \left(\frac{1}{2} \cdot \frac{1}{2} + a \cdot \frac{1}{2}\right)}{{a}^{3} - {\frac{1}{2}}^{3}}}} \]

      6. un-div-inv N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\frac{\log t}{\frac{a \cdot a + \left(\frac{1}{2} \cdot \frac{1}{2} + a \cdot \frac{1}{2}\right)}{{a}^{3} - {\frac{1}{2}}^{3}}}} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\frac{\log t}{\frac{a \cdot a + \left(\frac{1}{2} \cdot \frac{1}{2} + a \cdot \frac{1}{2}\right)}{{a}^{3} - {\frac{1}{2}}^{3}}}} \]

      8. clear-num N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\color{blue}{\frac{1}{\frac{{a}^{3} - {\frac{1}{2}}^{3}}{a \cdot a + \left(\frac{1}{2} \cdot \frac{1}{2} + a \cdot \frac{1}{2}\right)}}}} \]

      9. flip3-- N/A

         \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\frac{1}{\color{blue}{a - \frac{1}{2}}}} \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\frac{1}{\color{blue}{a - \frac{1}{2}}}} \]

      11. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} + \frac{\log t}{\frac{1}{a - \frac{1}{2}}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \frac{\log t}{\frac{1}{a - \frac{1}{2}}} \]

      2. lower-neg.f64 97.8

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

   7. Applied rewrites 97.8%

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

   if -1e6 < (-.f64 a #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(\log z + \left(\log \left(x + y\right) + \frac{-1}{2} \cdot \log t\right)\right) - t} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\log z + \left(\left(\log \left(x + y\right) + \frac{-1}{2} \cdot \log t\right) - t\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \frac{-1}{2} \cdot \log t\right) - t\right) + \log z} \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \frac{-1}{2} \cdot \log t\right) - \left(t - \log z\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \frac{-1}{2} \cdot \log t\right) - \left(t - \log z\right)} \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{2} \cdot \log t + \log \left(x + y\right)\right)} - \left(t - \log z\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\color{blue}{\log t \cdot \frac{-1}{2}} + \log \left(x + y\right)\right) - \left(t - \log z\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, \frac{-1}{2}, \log \left(x + y\right)\right)} - \left(t - \log z\right) \]

      8. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log t}, \frac{-1}{2}, \log \left(x + y\right)\right) - \left(t - \log z\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log t, \frac{-1}{2}, \color{blue}{\log \left(x + y\right)}\right) - \left(t - \log z\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, \frac{-1}{2}, \log \color{blue}{\left(y + x\right)}\right) - \left(t - \log z\right) \]

      11. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, \frac{-1}{2}, \log \color{blue}{\left(y + x\right)}\right) - \left(t - \log z\right) \]

      12. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, \frac{-1}{2}, \log \left(y + x\right)\right) - \color{blue}{\left(t - \log z\right)} \]

      13. lower-log.f64 98.7

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(\log y + \left(\log z + \frac{-1}{2} \cdot \log t\right)\right) - \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.6%

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

   if -0.5 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} + \left(a - \frac{1}{2}\right) \cdot \log t \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot \log t \]

      2. lower-neg.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 99.8

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

   8. Applied rewrites 99.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1000000:\\ \;\;\;\;\frac{\log t}{\frac{1}{a - 0.5}} + \left(-t\right)\\ \mathbf{elif}\;a - 0.5 \leq -0.5:\\ \;\;\;\;\left(\mathsf{fma}\left(-0.5, \log t, \log z\right) - t\right) + \log y\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(y + x\right)\right) + \log z\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 7.6e-7)
   (+ (fma (- a 0.5) (log t) (log (+ y x))) (log z))
   (+ (* (log t) a) (- t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7.6e-7) {
		tmp = fma((a - 0.5), log(t), log((y + x))) + log(z);
	} else {
		tmp = (log(t) * a) + -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7.6e-7)
		tmp = Float64(fma(Float64(a - 0.5), log(t), log(Float64(y + x))) + log(z));
	else
		tmp = Float64(Float64(log(t) * a) + Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7.6e-7], N[(N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision] + N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision] + (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.60000000000000029e-7

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\log z + \left(\log \left(x + y\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right) + \log z} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right) + \log z} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\log t \cdot \left(a - \frac{1}{2}\right) + \log \left(x + y\right)\right)} + \log z \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \log \left(x + y\right)\right) + \log z \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \left(x + y\right)\right)} + \log z \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a - \frac{1}{2}}, \log t, \log \left(x + y\right)\right) + \log z \]

      7. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \color{blue}{\log t}, \log \left(x + y\right)\right) + \log z \]

      8. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \color{blue}{\log \left(x + y\right)}\right) + \log z \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \color{blue}{\left(y + x\right)}\right) + \log z \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a - \frac{1}{2}, \log t, \log \color{blue}{\left(y + x\right)}\right) + \log z \]

      11. lower-log.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if 7.60000000000000029e-7 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} + \left(a - \frac{1}{2}\right) \cdot \log t \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot \log t \]

      2. lower-neg.f64 98.5

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 98.5

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

   8. Applied rewrites 98.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, \log t, \log \left(y + x\right)\right) + \log z\\ \mathbf{else}:\\ \;\;\;\;\log t \cdot a + \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

   3. lift--.f64 N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

   4. lift-+.f64 N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

   5. associate--l+ N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

   6. +-commutative N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

   7. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

   8. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

   10. *-commutative N/A

       \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

   12. lower--.f64 99.5

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

   13. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

   14. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

   15. lower-+.f64 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

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

Alternative 8: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\left(\log z + \left(-1 \cdot \log \left(\frac{1}{y}\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right) - t} \]
4. Step-by-step derivation

   1. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(\left(\log z + -1 \cdot \log \left(\frac{1}{y}\right)\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right)} - t \]

   2. associate--l+ N/A

      \[\leadsto \color{blue}{\left(\log z + -1 \cdot \log \left(\frac{1}{y}\right)\right) + \left(\log t \cdot \left(a - \frac{1}{2}\right) - t\right)} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{y}\right) + \log z\right)} + \left(\log t \cdot \left(a - \frac{1}{2}\right) - t\right) \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)} + \log z\right) + \left(\log t \cdot \left(a - \frac{1}{2}\right) - t\right) \]

   5. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right)\right) + \log z\right) + \left(\log t \cdot \left(a - \frac{1}{2}\right) - t\right) \]

   6. remove-double-neg N/A

      \[\leadsto \left(\color{blue}{\log y} + \log z\right) + \left(\log t \cdot \left(a - \frac{1}{2}\right) - t\right) \]

   7. associate--l+ N/A

      \[\leadsto \color{blue}{\left(\left(\log y + \log z\right) + \log t \cdot \left(a - \frac{1}{2}\right)\right) - t} \]

   8. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right)} - t \]

   9. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\log y + \left(\log z + \log t \cdot \left(a - \frac{1}{2}\right)\right)\right) - t} \]

5. Applied rewrites 70.0%

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

6. Final simplification 70.0%

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

Alternative 9: 77.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

   3. lift--.f64 N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

   4. lift-+.f64 N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

   5. associate--l+ N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

   6. +-commutative N/A

      \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

   7. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

   8. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

   10. *-commutative N/A

       \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

   12. lower--.f64 99.5

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

   13. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

   14. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

   15. lower-+.f64 99.5

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

4. Applied rewrites 99.5%

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

5. Taylor expanded in t around inf

   \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{-1 \cdot t}\right) + \log \left(y + x\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \color{blue}{\mathsf{neg}\left(t\right)}\right) + \log \left(y + x\right) \]

   2. lower-neg.f64 77.2

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

7. Applied rewrites 77.2%

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

Alternative 10: 64.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot a\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;\left(-t\right) + \log \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (log t) a)))
   (if (<= a -2.2e+60) t_1 (if (<= a 1.42e+17) (+ (- t) (log (+ y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = log(t) * a;
	double tmp;
	if (a <= -2.2e+60) {
		tmp = t_1;
	} else if (a <= 1.42e+17) {
		tmp = -t + log((y + x));
	} 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) :: tmp
    t_1 = log(t) * a
    if (a <= (-2.2d+60)) then
        tmp = t_1
    else if (a <= 1.42d+17) then
        tmp = -t + log((y + x))
    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 tmp;
	if (a <= -2.2e+60) {
		tmp = t_1;
	} else if (a <= 1.42e+17) {
		tmp = -t + Math.log((y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = math.log(t) * a
	tmp = 0
	if a <= -2.2e+60:
		tmp = t_1
	elif a <= 1.42e+17:
		tmp = -t + math.log((y + x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(log(t) * a)
	tmp = 0.0
	if (a <= -2.2e+60)
		tmp = t_1;
	elseif (a <= 1.42e+17)
		tmp = Float64(Float64(-t) + log(Float64(y + x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = log(t) * a;
	tmp = 0.0;
	if (a <= -2.2e+60)
		tmp = t_1;
	elseif (a <= 1.42e+17)
		tmp = -t + log((y + x));
	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]}, If[LessEqual[a, -2.2e+60], t$95$1, If[LessEqual[a, 1.42e+17], N[((-t) + N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.19999999999999996e60 or 1.42e17 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 79.8

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

   5. Applied rewrites 79.8%

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

   if -2.19999999999999996e60 < a < 1.42e17

   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. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \left(\color{blue}{\left(\log \left(x + y\right) + \log z\right)} - t\right) \]

      5. associate--l+ N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(a - \frac{1}{2}\right) \cdot \log t + \color{blue}{\left(\left(\log z - t\right) + \log \left(x + y\right)\right)} \]

      7. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot \log t + \left(\log z - t\right)\right) + \log \left(x + y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\log t \cdot \left(a - \frac{1}{2}\right)} + \left(\log z - t\right)\right) + \log \left(x + y\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right)} + \log \left(x + y\right) \]

      12. lower--.f64 99.4

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

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(x + y\right)} \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\log t, a - \frac{1}{2}, \log z - t\right) + \log \color{blue}{\left(y + x\right)} \]

      15. lower-+.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 55.0

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

   7. Applied rewrites 55.0%

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

Alternative 11: 76.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[((-t) + 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. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-1 \cdot t} + \left(a - \frac{1}{2}\right) \cdot \log t \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot \log t \]

   2. lower-neg.f64 76.7

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

5. Applied rewrites 76.7%

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

6. Final simplification 76.7%

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

Alternative 12: 60.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{+84}:\\ \;\;\;\;\log t \cdot a\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 6.2e+84) (* (log t) a) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 6.2e+84) {
		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 <= 6.2d+84) 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 <= 6.2e+84) {
		tmp = Math.log(t) * a;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 6.2e+84:
		tmp = math.log(t) * a
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 6.2e+84)
		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 <= 6.2e+84)
		tmp = log(t) * a;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 6.2e+84], N[(N[Log[t], $MachinePrecision] * a), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 6.20000000000000006e84

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 50.7

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

   5. Applied rewrites 50.7%

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

   if 6.20000000000000006e84 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t\right)} \]

      2. lower-neg.f64 82.0

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

   5. Applied rewrites 82.0%

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

Alternative 13: 76.5% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   \[\leadsto \color{blue}{-1 \cdot t} + \left(a - \frac{1}{2}\right) \cdot \log t \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot \log t \]

   2. lower-neg.f64 76.7

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

5. Applied rewrites 76.7%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(-t\right) + \left(a - \frac{1}{2}\right) \cdot \log t} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t + \left(-t\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(a - \frac{1}{2}\right) \cdot \log t} + \left(-t\right) \]

   4. lower-fma.f64 76.7

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

7. Applied rewrites 76.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a - 0.5, \log t, -t\right)} \]
8. Add Preprocessing

Alternative 14: 37.8% accurate, 107.0× 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. Add Preprocessing

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(t\right)} \]

   2. lower-neg.f64 36.0

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

5. Applied rewrites 36.0%

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

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024276 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (log (+ x y)) (+ (- (log z) t) (* (- a 1/2) (log t)))))

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