Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 25.0s

Alternatives: 16

Speedup: N/A×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. associate--l+ 99.6%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. fma-def 99.6%

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

   5. remove-double-neg 99.6%

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

   6. remove-double-neg 99.6%

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

   7. sub-neg 99.6%

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

   8. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -200000000000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \left(\log y + -0.5 \cdot \log t\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -200000000000.0) (not (<= (- a 0.5) -0.4)))
   (- (* a (log t)) t)
   (- (+ (log z) (+ (log y) (* -0.5 (log t)))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -200000000000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = (log(z) + (log(y) + (-0.5 * log(t)))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a - 0.5d0) <= (-200000000000.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (a * log(t)) - t
    else
        tmp = (log(z) + (log(y) + ((-0.5d0) * log(t)))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -200000000000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = (Math.log(z) + (Math.log(y) + (-0.5 * Math.log(t)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -200000000000.0) or not ((a - 0.5) <= -0.4):
		tmp = (a * math.log(t)) - t
	else:
		tmp = (math.log(z) + (math.log(y) + (-0.5 * math.log(t)))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -200000000000.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(Float64(log(z) + Float64(log(y) + Float64(-0.5 * log(t)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -200000000000.0) || ~(((a - 0.5) <= -0.4)))
		tmp = (a * log(t)) - t;
	else
		tmp = (log(z) + (log(y) + (-0.5 * log(t)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -200000000000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] + N[(N[Log[y], $MachinePrecision] + N[(-0.5 * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a 1/2) < -2e11 or -0.40000000000000002 < (-.f64 a 1/2)

   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%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. remove-double-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 76.2%

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

   5. Taylor expanded in a around inf 98.8%

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

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if -2e11 < (-.f64 a 1/2) < -0.40000000000000002

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. remove-double-neg 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 61.4%

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

   5. Taylor expanded in a around 0 60.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -200000000000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \left(\log y + -0.5 \cdot \log t\right)\right) - t\\ \end{array} \]

Alternative 3: 99.6% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 99.6%

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

   1. associate--l+ 99.6%

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

   2. sub-neg 99.6%

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

   3. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 4: 68.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate--l+ 99.6%

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

   2. +-commutative 99.6%

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

   3. associate-+l+ 99.6%

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

   4. +-commutative 99.6%

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

   5. fma-def 99.6%

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

   6. sub-neg 99.6%

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

   7. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around 0 67.8%

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

5. Final simplification 67.8%

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

Alternative 5: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. associate--l+ 99.6%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. fma-def 99.6%

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

   5. remove-double-neg 99.6%

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

   6. remove-double-neg 99.6%

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

   7. sub-neg 99.6%

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

   8. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around 0 67.7%

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

5. Final simplification 67.7%

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

Alternative 6: 72.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \log t + \log \left(y \cdot z\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -1.0) (not (<= (- a 0.5) -0.4)))
   (- (* a (log t)) t)
   (- (+ (* -0.5 (log t)) (log (* y z))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -1.0) || !((a - 0.5) <= -0.4)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = ((-0.5 * log(t)) + log((y * z))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a - 0.5d0) <= (-1.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (a * log(t)) - t
    else
        tmp = (((-0.5d0) * log(t)) + log((y * z))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -1.0) || !((a - 0.5) <= -0.4)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = ((-0.5 * Math.log(t)) + Math.log((y * z))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -1.0) or not ((a - 0.5) <= -0.4):
		tmp = (a * math.log(t)) - t
	else:
		tmp = ((-0.5 * math.log(t)) + math.log((y * z))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -1.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(Float64(Float64(-0.5 * log(t)) + log(Float64(y * z))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -1.0) || ~(((a - 0.5) <= -0.4)))
		tmp = (a * log(t)) - t;
	else
		tmp = ((-0.5 * log(t)) + log((y * z))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -1.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(-0.5 * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a 1/2) < -1 or -0.40000000000000002 < (-.f64 a 1/2)

   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%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. remove-double-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 76.8%

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

   5. Taylor expanded in a around inf 98.1%

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

      1. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   if -1 < (-.f64 a 1/2) < -0.40000000000000002

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. remove-double-neg 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 60.6%

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

   5. Taylor expanded in a around 0 60.5%

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

      1. associate-+r+ 60.4%

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

      2. log-prod 42.5%

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

      3. +-commutative 42.5%

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

   7. Simplified 42.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \log t + \log \left(y \cdot z\right)\right) - t\\ \end{array} \]

Alternative 7: 87.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1850:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(\left(x + y\right) \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1850.0)
   (- (+ (* (+ a -0.5) (log t)) (log (* (+ x y) z))) t)
   (- (* a (log t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1850.0) {
		tmp = (((a + -0.5) * log(t)) + log(((x + y) * z))) - t;
	} else {
		tmp = (a * log(t)) - 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 <= 1850.0d0) then
        tmp = (((a + (-0.5d0)) * log(t)) + log(((x + y) * z))) - t
    else
        tmp = (a * log(t)) - 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 <= 1850.0) {
		tmp = (((a + -0.5) * Math.log(t)) + Math.log(((x + y) * z))) - t;
	} else {
		tmp = (a * Math.log(t)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1850.0:
		tmp = (((a + -0.5) * math.log(t)) + math.log(((x + y) * z))) - t
	else:
		tmp = (a * math.log(t)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1850.0)
		tmp = Float64(Float64(Float64(Float64(a + -0.5) * log(t)) + log(Float64(Float64(x + y) * z))) - t);
	else
		tmp = Float64(Float64(a * log(t)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1850.0)
		tmp = (((a + -0.5) * log(t)) + log(((x + y) * z))) - t;
	else
		tmp = (a * log(t)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1850.0], N[(N[(N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1850

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. remove-double-neg 99.3%

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

      6. remove-double-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-udef 99.3%

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

      3. associate-+r+ 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-+r- 99.2%

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

      6. associate-+r- 99.2%

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

      7. sum-log 73.3%

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

   5. Applied egg-rr 73.3%

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

   if 1850 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in a around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1850:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(\left(x + y\right) \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 8: 86.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.00086:\\ \;\;\;\;\left(a + -0.5\right) \cdot \log t + \log \left(\left(x + y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 0.00086)
   (+ (* (+ a -0.5) (log t)) (log (* (+ x y) z)))
   (- (* a (log t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 0.00086) {
		tmp = ((a + -0.5) * log(t)) + log(((x + y) * z));
	} else {
		tmp = (a * log(t)) - 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 <= 0.00086d0) then
        tmp = ((a + (-0.5d0)) * log(t)) + log(((x + y) * z))
    else
        tmp = (a * log(t)) - 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 <= 0.00086) {
		tmp = ((a + -0.5) * Math.log(t)) + Math.log(((x + y) * z));
	} else {
		tmp = (a * Math.log(t)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 0.00086:
		tmp = ((a + -0.5) * math.log(t)) + math.log(((x + y) * z))
	else:
		tmp = (a * math.log(t)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 0.00086)
		tmp = Float64(Float64(Float64(a + -0.5) * log(t)) + log(Float64(Float64(x + y) * z)));
	else
		tmp = Float64(Float64(a * log(t)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 0.00086)
		tmp = ((a + -0.5) * log(t)) + log(((x + y) * z));
	else
		tmp = (a * log(t)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 0.00086], N[(N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.59999999999999979e-4

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. log-prod 72.6%

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

      3. +-commutative 72.6%

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

   6. Simplified 72.6%

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

   if 8.59999999999999979e-4 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in a around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.00086:\\ \;\;\;\;\left(a + -0.5\right) \cdot \log t + \log \left(\left(x + y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 9: 72.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2500:\\ \;\;\;\;\left(\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2500.0)
   (- (+ (* (log t) (- a 0.5)) (log (* y z))) t)
   (- (* a (log t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2500.0) {
		tmp = ((log(t) * (a - 0.5)) + log((y * z))) - t;
	} else {
		tmp = (a * log(t)) - 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 <= 2500.0d0) then
        tmp = ((log(t) * (a - 0.5d0)) + log((y * z))) - t
    else
        tmp = (a * log(t)) - 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 <= 2500.0) {
		tmp = ((Math.log(t) * (a - 0.5)) + Math.log((y * z))) - t;
	} else {
		tmp = (a * Math.log(t)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2500.0:
		tmp = ((math.log(t) * (a - 0.5)) + math.log((y * z))) - t
	else:
		tmp = (a * math.log(t)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2500.0)
		tmp = Float64(Float64(Float64(log(t) * Float64(a - 0.5)) + log(Float64(y * z))) - t);
	else
		tmp = Float64(Float64(a * log(t)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2500.0)
		tmp = ((log(t) * (a - 0.5)) + log((y * z))) - t;
	else
		tmp = (a * log(t)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2500.0], N[(N[(N[(N[Log[t], $MachinePrecision] * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2500

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. remove-double-neg 99.3%

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

      6. remove-double-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 55.8%

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

   5. Taylor expanded in z around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. log-rec 55.8%

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

      3. remove-double-neg 55.8%

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

      4. log-prod 45.3%

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

   7. Simplified 45.3%

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

   if 2500 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in a around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2500:\\ \;\;\;\;\left(\log t \cdot \left(a - 0.5\right) + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 10: 66.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;t \leq 6.2 \cdot 10^{-166}:\\ \;\;\;\;\log y + t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-39}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* a (log t))))
   (if (<= t 6.2e-166)
     (+ (log y) t_1)
     (if (<= t 3e-39) (log (* y (* z (pow t (+ a -0.5))))) (- t_1 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a * log(t);
	double tmp;
	if (t <= 6.2e-166) {
		tmp = log(y) + t_1;
	} else if (t <= 3e-39) {
		tmp = log((y * (z * pow(t, (a + -0.5)))));
	} else {
		tmp = 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 = a * log(t)
    if (t <= 6.2d-166) then
        tmp = log(y) + t_1
    else if (t <= 3d-39) then
        tmp = log((y * (z * (t ** (a + (-0.5d0))))))
    else
        tmp = 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 = a * Math.log(t);
	double tmp;
	if (t <= 6.2e-166) {
		tmp = Math.log(y) + t_1;
	} else if (t <= 3e-39) {
		tmp = Math.log((y * (z * Math.pow(t, (a + -0.5)))));
	} else {
		tmp = t_1 - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a * math.log(t)
	tmp = 0
	if t <= 6.2e-166:
		tmp = math.log(y) + t_1
	elif t <= 3e-39:
		tmp = math.log((y * (z * math.pow(t, (a + -0.5)))))
	else:
		tmp = t_1 - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a * log(t))
	tmp = 0.0
	if (t <= 6.2e-166)
		tmp = Float64(log(y) + t_1);
	elseif (t <= 3e-39)
		tmp = log(Float64(y * Float64(z * (t ^ Float64(a + -0.5)))));
	else
		tmp = Float64(t_1 - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a * log(t);
	tmp = 0.0;
	if (t <= 6.2e-166)
		tmp = log(y) + t_1;
	elseif (t <= 3e-39)
		tmp = log((y * (z * (t ^ (a + -0.5)))));
	else
		tmp = t_1 - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 6.2e-166], N[(N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3e-39], N[Log[N[(y * N[(z * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(t$95$1 - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < 6.19999999999999968e-166

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. remove-double-neg 99.3%

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

      6. remove-double-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around inf 47.6%

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

      1. *-commutative 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in x around 0 32.4%

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

   if 6.19999999999999968e-166 < t < 3.00000000000000028e-39

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-+l+ 99.2%

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

      3. +-commutative 99.2%

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

      4. fma-def 99.2%

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

      5. remove-double-neg 99.2%

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

      6. remove-double-neg 99.2%

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

      7. sub-neg 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. add-cube-cbrt 97.7%

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

      2. pow3 97.7%

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

      3. +-commutative 97.7%

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

      4. fma-udef 97.7%

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

      5. associate-+r+ 97.9%

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

      6. +-commutative 97.9%

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

      7. fma-def 97.9%

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

      8. associate-+r- 97.9%

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

      9. sum-log 73.7%

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

   5. Applied egg-rr 73.7%

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

   6. Taylor expanded in z around 0 97.9%

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

   7. Taylor expanded in y around inf 54.2%

      \[\leadsto {\left(\sqrt[3]{\left(\left(a - 0.5\right) \cdot \log t + \color{blue}{\left(\log z + -1 \cdot \log \left(\frac{1}{y}\right)\right)}\right) - t}\right)}^{3} \]
   8. Step-by-step derivation

      1. mul-1-neg 54.2%

         \[\leadsto {\left(\sqrt[3]{\left(\left(a - 0.5\right) \cdot \log t + \left(\log z + \color{blue}{\left(-\log \left(\frac{1}{y}\right)\right)}\right)\right) - t}\right)}^{3} \]

      2. log-rec 54.2%

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

      3. remove-double-neg 54.2%

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

   9. Simplified 54.2%

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

   10. Taylor expanded in t around 0 54.8%

       \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot \log t + \left(\log z + \log y\right)\right) \cdot {1}^{0.3333333333333333}} \]
   11. Step-by-step derivation

       1. pow-base-1 54.8%

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

       2. *-rgt-identity 54.8%

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

       3. log-pow 36.9%

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

       4. associate-+r+ 36.9%

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

       5. log-prod 28.7%

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

       6. *-commutative 28.7%

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

       7. sub-neg 28.7%

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

       8. metadata-eval 28.7%

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

       9. log-prod 26.7%

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

       10. *-commutative 26.7%

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

       11. +-commutative 26.7%

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

   12. Simplified 26.7%

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

   if 3.00000000000000028e-39 < t

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. fma-def 99.8%

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

      5. remove-double-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 76.8%

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

   5. Taylor expanded in a around inf 95.9%

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

      1. *-commutative 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{-166}:\\ \;\;\;\;\log y + a \cdot \log t\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-39}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 11: 70.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;t \leq 210:\\ \;\;\;\;\log y + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* a (log t)))) (if (<= t 210.0) (+ (log y) t_1) (- t_1 t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a * log(t);
	double tmp;
	if (t <= 210.0) {
		tmp = log(y) + t_1;
	} else {
		tmp = 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 = a * log(t)
    if (t <= 210.0d0) then
        tmp = log(y) + t_1
    else
        tmp = 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 = a * Math.log(t);
	double tmp;
	if (t <= 210.0) {
		tmp = Math.log(y) + t_1;
	} else {
		tmp = t_1 - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a * math.log(t)
	tmp = 0
	if t <= 210.0:
		tmp = math.log(y) + t_1
	else:
		tmp = t_1 - t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a * log(t))
	tmp = 0.0
	if (t <= 210.0)
		tmp = Float64(log(y) + t_1);
	else
		tmp = Float64(t_1 - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a * log(t);
	tmp = 0.0;
	if (t <= 210.0)
		tmp = log(y) + t_1;
	else
		tmp = t_1 - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 210.0], N[(N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 210

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. remove-double-neg 99.3%

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

      6. remove-double-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

   6. Simplified 45.8%

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

   7. Taylor expanded in x around 0 31.5%

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

   if 210 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in a around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 69.2%

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

Alternative 12: 69.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -220000 \lor \neg \left(a \leq 2.9\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -220000.0) (not (<= a 2.9))) (- (* a (log t)) t) (- (log y) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -220000.0) || !(a <= 2.9)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = log(y) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-220000.0d0)) .or. (.not. (a <= 2.9d0))) then
        tmp = (a * log(t)) - t
    else
        tmp = log(y) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -220000.0) || !(a <= 2.9)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -220000.0) or not (a <= 2.9):
		tmp = (a * math.log(t)) - t
	else:
		tmp = math.log(y) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -220000.0) || !(a <= 2.9))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(log(y) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -220000.0) || ~((a <= 2.9)))
		tmp = (a * log(t)) - t;
	else
		tmp = log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -220000.0], N[Not[LessEqual[a, 2.9]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e5 or 2.89999999999999991 < a

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. remove-double-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 76.2%

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

   5. Taylor expanded in a around inf 98.8%

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

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if -2.2e5 < a < 2.89999999999999991

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. remove-double-neg 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 58.1%

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

      1. neg-mul-1 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in x around 0 42.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -220000 \lor \neg \left(a \leq 2.9\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \]

Alternative 13: 53.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+120} \lor \neg \left(a \leq 7.8 \cdot 10^{+108}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.55e+120) (not (<= a 7.8e+108))) (* a (log t)) (- (log y) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e+120) || !(a <= 7.8e+108)) {
		tmp = a * log(t);
	} else {
		tmp = log(y) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.55d+120)) .or. (.not. (a <= 7.8d+108))) then
        tmp = a * log(t)
    else
        tmp = log(y) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e+120) || !(a <= 7.8e+108)) {
		tmp = a * Math.log(t);
	} else {
		tmp = Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.55e+120) or not (a <= 7.8e+108):
		tmp = a * math.log(t)
	else:
		tmp = math.log(y) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.55e+120) || !(a <= 7.8e+108))
		tmp = Float64(a * log(t));
	else
		tmp = Float64(log(y) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.55e+120) || ~((a <= 7.8e+108)))
		tmp = a * log(t);
	else
		tmp = log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.55e+120], N[Not[LessEqual[a, 7.8e+108]], $MachinePrecision]], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.54999999999999987e120 or 7.79999999999999969e108 < 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%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. remove-double-neg 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 83.5%

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

      1. *-commutative 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around 0 67.0%

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

   8. Taylor expanded in a around inf 83.5%

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

   if -1.54999999999999987e120 < a < 7.79999999999999969e108

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. remove-double-neg 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 59.9%

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

      1. neg-mul-1 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in x around 0 43.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+120} \lor \neg \left(a \leq 7.8 \cdot 10^{+108}\right):\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \]

Alternative 14: 62.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.4 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3.4e+63) (* a (log t)) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.4e+63) {
		tmp = a * log(t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 3.4d+63) then
        tmp = a * log(t)
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.4e+63) {
		tmp = a * Math.log(t);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 3.4e+63:
		tmp = a * math.log(t)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.4e+63)
		tmp = Float64(a * log(t));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 3.4e+63)
		tmp = a * log(t);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3.4e+63], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 3.3999999999999999e63

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. fma-def 99.4%

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

      5. remove-double-neg 99.4%

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

      6. remove-double-neg 99.4%

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

      7. sub-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around inf 48.5%

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

      1. *-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in x around 0 35.0%

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

   8. Taylor expanded in a around inf 42.2%

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

   if 3.3999999999999999e63 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in t around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   9. Simplified 83.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.4 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 15: 39.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 450:\\ \;\;\;\;\log y\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 450.0) (log y) (- t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 450.0) {
		tmp = log(y);
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 450.0d0) then
        tmp = log(y)
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 450.0) {
		tmp = Math.log(y);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 450.0:
		tmp = math.log(y)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 450.0)
		tmp = log(y);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 450.0)
		tmp = log(y);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 450.0], N[Log[y], $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if t < 450

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. remove-double-neg 99.3%

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

      6. remove-double-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

   6. Simplified 45.8%

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

   7. Taylor expanded in x around 0 31.5%

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

   8. Taylor expanded in a around 0 6.9%

      \[\leadsto \color{blue}{\log y} \]

   if 450 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. remove-double-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 76.4%

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

      1. neg-mul-1 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in t around inf 76.4%

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

      1. neg-mul-1 76.4%

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

   9. Simplified 76.4%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 450:\\ \;\;\;\;\log y\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 16: 38.1% 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%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. fma-def 99.6%

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

   5. remove-double-neg 99.6%

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

   6. remove-double-neg 99.6%

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

   7. sub-neg 99.6%

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

   8. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in t around inf 47.3%

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

   1. neg-mul-1 47.3%

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

6. Simplified 47.3%

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

7. Taylor expanded in t around inf 43.6%

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

   1. neg-mul-1 43.6%

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

9. Simplified 43.6%

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

10. Final simplification 43.6%

    \[\leadsto -t \]

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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