Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Percentage Accurate: 99.6% → 99.6%

Time: 16.9s

Alternatives: 18

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. +-commutative 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

Alternative 2: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log z \leq 150:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(\left(a + -0.5\right) \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (log z) 150.0)
   (+ (log (* z (+ x y))) (- (* (+ a -0.5) (log t)) t))
   (- (+ (log y) (+ (log z) (* a (log t)))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (log(z) <= 150.0) {
		tmp = log((z * (x + y))) + (((a + -0.5) * log(t)) - t);
	} else {
		tmp = (log(y) + (log(z) + (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 (log(z) <= 150.0d0) then
        tmp = log((z * (x + y))) + (((a + (-0.5d0)) * log(t)) - t)
    else
        tmp = (log(y) + (log(z) + (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 (Math.log(z) <= 150.0) {
		tmp = Math.log((z * (x + y))) + (((a + -0.5) * Math.log(t)) - t);
	} else {
		tmp = (Math.log(y) + (Math.log(z) + (a * Math.log(t)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if math.log(z) <= 150.0:
		tmp = math.log((z * (x + y))) + (((a + -0.5) * math.log(t)) - t)
	else:
		tmp = (math.log(y) + (math.log(z) + (a * math.log(t)))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (log(z) <= 150.0)
		tmp = Float64(log(Float64(z * Float64(x + y))) + Float64(Float64(Float64(a + -0.5) * log(t)) - t));
	else
		tmp = Float64(Float64(log(y) + Float64(log(z) + Float64(a * log(t)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (log(z) <= 150.0)
		tmp = log((z * (x + y))) + (((a + -0.5) * log(t)) - t);
	else
		tmp = (log(y) + (log(z) + (a * log(t)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Log[z], $MachinePrecision], 150.0], N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 z) < 150

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-define 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. associate--l+ 99.4%

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

   3. Simplified 99.4%

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

      1. fma-undefine 99.3%

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

      2. metadata-eval 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+r- 99.3%

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

      6. associate-+l- 99.3%

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

      7. +-commutative 99.3%

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

      8. sum-log 95.8%

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

      9. sub-neg 95.8%

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

      10. metadata-eval 95.8%

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

   6. Applied egg-rr 95.8%

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

   if 150 < (log.f64 z)

   1. Initial program 99.7%

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

      1. 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. +-commutative 99.7%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. fma-define 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.0%

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

   6. Taylor expanded in a around inf 62.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log z \leq 150:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(\left(a + -0.5\right) \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \log t + \left(\log z + \log y\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -50000.0) (not (<= (- a 0.5) -0.4)))
   (- (+ (log y) (+ (log z) (* a (log t)))) t)
   (- (+ (* -0.5 (log t)) (+ (log z) (log y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (log(y) + (log(z) + (a * log(t)))) - t;
	} else {
		tmp = ((-0.5 * log(t)) + (log(z) + log(y))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a - 0.5d0) <= (-50000.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (log(y) + (log(z) + (a * log(t)))) - t
    else
        tmp = (((-0.5d0) * log(t)) + (log(z) + log(y))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (Math.log(y) + (Math.log(z) + (a * Math.log(t)))) - t;
	} else {
		tmp = ((-0.5 * Math.log(t)) + (Math.log(z) + Math.log(y))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -50000.0) or not ((a - 0.5) <= -0.4):
		tmp = (math.log(y) + (math.log(z) + (a * math.log(t)))) - t
	else:
		tmp = ((-0.5 * math.log(t)) + (math.log(z) + math.log(y))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -50000.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(log(y) + Float64(log(z) + Float64(a * log(t)))) - t);
	else
		tmp = Float64(Float64(Float64(-0.5 * log(t)) + Float64(log(z) + log(y))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -50000.0) || ~(((a - 0.5) <= -0.4)))
		tmp = (log(y) + (log(z) + (a * log(t)))) - t;
	else
		tmp = ((-0.5 * log(t)) + (log(z) + log(y))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -50000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(-0.5 * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -5e4 or -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. fma-define 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 77.7%

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

   6. Taylor expanded in a around inf 77.6%

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

   if -5e4 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 65.4%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. +-commutative 65.0%

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

      3. associate-+l+ 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot \log t + \left(\log z + \log y\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \left(\log z + -0.5 \cdot \log t\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -50000.0) (not (<= (- a 0.5) -0.4)))
   (- (+ (log y) (+ (log z) (* a (log t)))) t)
   (- (+ (log y) (+ (log z) (* -0.5 (log t)))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (log(y) + (log(z) + (a * log(t)))) - t;
	} else {
		tmp = (log(y) + (log(z) + (-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) <= (-50000.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (log(y) + (log(z) + (a * log(t)))) - t
    else
        tmp = (log(y) + (log(z) + ((-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) <= -50000.0) || !((a - 0.5) <= -0.4)) {
		tmp = (Math.log(y) + (Math.log(z) + (a * Math.log(t)))) - t;
	} else {
		tmp = (Math.log(y) + (Math.log(z) + (-0.5 * Math.log(t)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -50000.0) or not ((a - 0.5) <= -0.4):
		tmp = (math.log(y) + (math.log(z) + (a * math.log(t)))) - t
	else:
		tmp = (math.log(y) + (math.log(z) + (-0.5 * math.log(t)))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -50000.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(log(y) + Float64(log(z) + Float64(a * log(t)))) - t);
	else
		tmp = Float64(Float64(log(y) + Float64(log(z) + 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) <= -50000.0) || ~(((a - 0.5) <= -0.4)))
		tmp = (log(y) + (log(z) + (a * log(t)))) - t;
	else
		tmp = (log(y) + (log(z) + (-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], -50000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] + N[(N[Log[z], $MachinePrecision] + N[(-0.5 * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -5e4 or -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. fma-define 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 77.7%

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

   6. Taylor expanded in a around inf 77.6%

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

   if -5e4 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 65.4%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. +-commutative 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;\left(\log y + \left(\log z + a \cdot \log t\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y + \left(\log z + -0.5 \cdot \log t\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. sub-neg 99.5%

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

   3. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 6: 69.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. +-commutative 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 71.4%

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

Alternative 7: 69.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. sub-neg 99.5%

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

   3. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 71.4%

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

   1. remove-double-neg 71.4%

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

   2. log-rec 71.4%

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

   3. mul-1-neg 71.4%

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

   4. +-commutative 71.4%

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

   5. associate--l+ 71.4%

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

   6. mul-1-neg 71.4%

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

   7. log-rec 71.4%

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

   8. remove-double-neg 71.4%

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

7. Simplified 71.4%

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

8. Final simplification 71.4%

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

Alternative 8: 86.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq 2\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(-0.5 \cdot \log t - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -50000.0) (not (<= (- a 0.5) 2.0)))
   (- (* a (log t)) t)
   (+ (log (* z (+ x 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) <= -50000.0) || !((a - 0.5) <= 2.0)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = log((z * (x + 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) <= (-50000.0d0)) .or. (.not. ((a - 0.5d0) <= 2.0d0))) then
        tmp = (a * log(t)) - t
    else
        tmp = log((z * (x + 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) <= -50000.0) || !((a - 0.5) <= 2.0)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = Math.log((z * (x + y))) + ((-0.5 * Math.log(t)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -50000.0) or not ((a - 0.5) <= 2.0):
		tmp = (a * math.log(t)) - t
	else:
		tmp = math.log((z * (x + 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) <= -50000.0) || !(Float64(a - 0.5) <= 2.0))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(log(Float64(z * Float64(x + y))) + Float64(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) <= -50000.0) || ~(((a - 0.5) <= 2.0)))
		tmp = (a * log(t)) - t;
	else
		tmp = log((z * (x + 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], -50000.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[(-0.5 * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -5e4 or 2 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 53.2%

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

      2. pow2 53.2%

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

   6. Applied egg-rr 53.2%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 53.2%

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

      2. unpow2 53.2%

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

      3. add-sqr-sqrt 99.6%

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

      4. fma-define 99.6%

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

      5. associate-+r- 99.6%

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

      6. sum-log 77.8%

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

      7. +-commutative 77.8%

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

   8. Applied egg-rr 77.8%

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

   9. Taylor expanded in y around 0 54.5%

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

   10. Taylor expanded in a around inf 99.0%

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

   if -5e4 < (-.f64 a #s(literal 1/2 binary64)) < 2

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. add-sqr-sqrt 1.5%

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

      2. pow2 1.5%

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

   6. Applied egg-rr 1.5%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 1.5%

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

      2. unpow2 1.5%

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

      3. add-sqr-sqrt 99.4%

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

      4. fma-define 99.4%

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

      5. associate-+r- 99.3%

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

      6. sum-log 78.1%

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

      7. +-commutative 78.1%

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

   8. Applied egg-rr 78.1%

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

   9. Taylor expanded in a around 0 76.2%

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

       1. associate--l+ 76.2%

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

       2. +-commutative 76.2%

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

       3. *-commutative 76.2%

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

   11. Simplified 76.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -50000 \lor \neg \left(a - 0.5 \leq 2\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(-0.5 \cdot \log t - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.5000005 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -0.5000005) (not (<= (- a 0.5) -0.4)))
   (- (* a (log t)) t)
   (- (log (* y (* z (pow t (+ a -0.5))))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -0.5000005) || !((a - 0.5) <= -0.4)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = log((y * (z * pow(t, (a + -0.5))))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a - 0.5d0) <= (-0.5000005d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = (a * log(t)) - t
    else
        tmp = log((y * (z * (t ** (a + (-0.5d0)))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -0.5000005) || !((a - 0.5) <= -0.4)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = Math.log((y * (z * Math.pow(t, (a + -0.5))))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -0.5000005) or not ((a - 0.5) <= -0.4):
		tmp = (a * math.log(t)) - t
	else:
		tmp = math.log((y * (z * math.pow(t, (a + -0.5))))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -0.5000005) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(log(Float64(y * Float64(z * (t ^ Float64(a + -0.5))))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -0.5000005) || ~(((a - 0.5) <= -0.4)))
		tmp = (a * log(t)) - t;
	else
		tmp = log((y * (z * (t ^ (a + -0.5))))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5000005], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(y * N[(z * N[Power[t, N[(a + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -0.500000499999999959 or -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 52.7%

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

      2. pow2 52.7%

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

   6. Applied egg-rr 52.7%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 52.7%

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

      2. unpow2 52.7%

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

      3. add-sqr-sqrt 99.6%

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

      4. fma-define 99.6%

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

      5. associate-+r- 99.6%

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

      6. sum-log 78.6%

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

      7. +-commutative 78.6%

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

   8. Applied egg-rr 78.6%

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

   9. Taylor expanded in y around 0 54.1%

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

   10. Taylor expanded in a around inf 97.6%

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

   if -0.500000499999999959 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   1. Initial program 99.3%

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

      1. associate--l+ 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 64.6%

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

      1. *-un-lft-identity 64.6%

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

      2. add-log-exp 59.7%

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

      3. sum-log 50.8%

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

      4. exp-sum 50.9%

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

      5. add-exp-log 51.0%

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

      6. sub-neg 51.0%

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

      7. metadata-eval 51.0%

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

      8. exp-to-pow 51.1%

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

   7. Applied egg-rr 51.1%

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

      1. *-lft-identity 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.5000005 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.5 \lor \neg \left(a - 0.5 \leq 2\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(\left(z \cdot y\right) \cdot {t}^{-0.5}\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- a 0.5) -0.5) (not (<= (- a 0.5) 2.0)))
   (- (* a (log t)) t)
   (- (log (* (* z y) (pow t -0.5))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -0.5) || !((a - 0.5) <= 2.0)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = log(((z * y) * pow(t, -0.5))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a - 0.5d0) <= (-0.5d0)) .or. (.not. ((a - 0.5d0) <= 2.0d0))) then
        tmp = (a * log(t)) - t
    else
        tmp = log(((z * y) * (t ** (-0.5d0)))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a - 0.5) <= -0.5) || !((a - 0.5) <= 2.0)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = Math.log(((z * y) * Math.pow(t, -0.5))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a - 0.5) <= -0.5) or not ((a - 0.5) <= 2.0):
		tmp = (a * math.log(t)) - t
	else:
		tmp = math.log(((z * y) * math.pow(t, -0.5))) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -0.5) || !(Float64(a - 0.5) <= 2.0))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(log(Float64(Float64(z * y) * (t ^ -0.5))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a - 0.5) <= -0.5) || ~(((a - 0.5) <= 2.0)))
		tmp = (a * log(t)) - t;
	else
		tmp = log(((z * y) * (t ^ -0.5))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[N[(N[(z * y), $MachinePrecision] * N[Power[t, -0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   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. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. add-sqr-sqrt 26.2%

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

      2. pow2 26.2%

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

   6. Applied egg-rr 26.2%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 26.2%

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

      2. unpow2 26.2%

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

      3. add-sqr-sqrt 99.5%

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

      4. fma-define 99.5%

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

      5. associate-+r- 99.5%

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

      6. sum-log 77.4%

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

      7. +-commutative 77.4%

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

   8. Applied egg-rr 77.4%

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

   9. Taylor expanded in y around 0 50.5%

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

   10. Taylor expanded in a around inf 71.2%

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

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

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-define 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 59.9%

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

      1. *-un-lft-identity 59.9%

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

      2. add-log-exp 59.9%

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

      3. sum-log 43.3%

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

      4. exp-sum 43.3%

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

      5. add-exp-log 43.3%

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

      6. sub-neg 43.3%

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

      7. metadata-eval 43.3%

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

      8. exp-to-pow 43.3%

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

   7. Applied egg-rr 43.3%

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

      1. *-lft-identity 43.3%

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

      2. associate-*r* 40.6%

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

   9. Simplified 40.6%

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

   10. Taylor expanded in a around 0 57.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -0.5 \lor \neg \left(a - 0.5 \leq 2\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(\left(z \cdot y\right) \cdot {t}^{-0.5}\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(\left(a + -0.5\right) \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.7e+14)
   (+ (log (* z (+ x y))) (- (* (+ a -0.5) (log t)) t))
   (- (* a (log t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.7e+14) {
		tmp = log((z * (x + y))) + (((a + -0.5) * log(t)) - 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 <= 1.7d+14) then
        tmp = log((z * (x + y))) + (((a + (-0.5d0)) * log(t)) - 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 <= 1.7e+14) {
		tmp = Math.log((z * (x + y))) + (((a + -0.5) * Math.log(t)) - t);
	} else {
		tmp = (a * Math.log(t)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.7e+14:
		tmp = math.log((z * (x + y))) + (((a + -0.5) * math.log(t)) - t)
	else:
		tmp = (a * math.log(t)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.7e+14)
		tmp = Float64(log(Float64(z * Float64(x + y))) + Float64(Float64(Float64(a + -0.5) * log(t)) - 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 <= 1.7e+14)
		tmp = log((z * (x + y))) + (((a + -0.5) * log(t)) - t);
	else
		tmp = (a * log(t)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.7e+14], N[(N[Log[N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.7e14

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. fma-define 99.2%

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

      3. sub-neg 99.2%

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

      4. metadata-eval 99.2%

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

      5. associate--l+ 99.2%

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

   3. Simplified 99.2%

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

      1. fma-undefine 99.2%

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

      2. metadata-eval 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-+r- 99.2%

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

      6. associate-+l- 99.2%

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

      7. +-commutative 99.2%

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

      8. sum-log 78.5%

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

      9. sub-neg 78.5%

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

      10. metadata-eval 78.5%

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

   6. Applied egg-rr 78.5%

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

   if 1.7e14 < 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. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 26.7%

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

      2. pow2 26.7%

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

   6. Applied egg-rr 26.7%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 26.7%

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

      2. unpow2 26.7%

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

      3. add-sqr-sqrt 99.9%

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

      4. fma-define 99.9%

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

      5. associate-+r- 99.9%

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

      6. sum-log 77.2%

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

      7. +-commutative 77.2%

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

   8. Applied egg-rr 77.2%

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

   9. Taylor expanded in y around 0 60.0%

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

   10. Taylor expanded in a around inf 99.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;\log \left(z \cdot \left(x + y\right)\right) + \left(\left(a + -0.5\right) \cdot \log t - t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \lor \neg \left(a \leq 2.1\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1) (not (<= a 2.1)))
   (- (* a (log t)) t)
   (+ (- (log z) t) (log (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1) || !(a <= 2.1)) {
		tmp = (a * log(t)) - t;
	} else {
		tmp = (log(z) - t) + log((x + y));
	}
	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 <= (-1.1d0)) .or. (.not. (a <= 2.1d0))) then
        tmp = (a * log(t)) - t
    else
        tmp = (log(z) - t) + log((x + y))
    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 <= -1.1) || !(a <= 2.1)) {
		tmp = (a * Math.log(t)) - t;
	} else {
		tmp = (Math.log(z) - t) + Math.log((x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1) or not (a <= 2.1):
		tmp = (a * math.log(t)) - t
	else:
		tmp = (math.log(z) - t) + math.log((x + y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1) || !(a <= 2.1))
		tmp = Float64(Float64(a * log(t)) - t);
	else
		tmp = Float64(Float64(log(z) - t) + log(Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1) || ~((a <= 2.1)))
		tmp = (a * log(t)) - t;
	else
		tmp = (log(z) - t) + log((x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1], N[Not[LessEqual[a, 2.1]], $MachinePrecision]], N[(N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1000000000000001 or 2.10000000000000009 < 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. 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. Add Preprocessing
   5. Step-by-step derivation

      1. add-sqr-sqrt 53.2%

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

      2. pow2 53.2%

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

   6. Applied egg-rr 53.2%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 53.2%

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

      2. unpow2 53.2%

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

      3. add-sqr-sqrt 99.6%

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

      4. fma-define 99.6%

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

      5. associate-+r- 99.6%

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

      6. sum-log 77.8%

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

      7. +-commutative 77.8%

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

   8. Applied egg-rr 77.8%

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

   9. Taylor expanded in y around 0 54.5%

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

   10. Taylor expanded in a around inf 99.0%

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

   if -1.1000000000000001 < a < 2.10000000000000009

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

      7. fma-undefine 99.3%

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

      8. sub-neg 99.3%

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

      9. +-commutative 99.3%

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

      10. distribute-neg-in 99.3%

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

      11. metadata-eval 99.3%

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

      12. metadata-eval 99.3%

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

      13. unsub-neg 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf 53.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \lor \neg \left(a \leq 2.1\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z - t\right) + \log \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(z \cdot y\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.26e+14)
   (- (+ (* (+ a -0.5) (log t)) (log (* z y))) t)
   (- (* a (log t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.26e+14) {
		tmp = (((a + -0.5) * log(t)) + log((z * y))) - 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 <= 1.26d+14) then
        tmp = (((a + (-0.5d0)) * log(t)) + log((z * y))) - 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 <= 1.26e+14) {
		tmp = (((a + -0.5) * Math.log(t)) + Math.log((z * y))) - t;
	} else {
		tmp = (a * Math.log(t)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.26e+14:
		tmp = (((a + -0.5) * math.log(t)) + math.log((z * y))) - t
	else:
		tmp = (a * math.log(t)) - t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.26e+14)
		tmp = Float64(Float64(Float64(Float64(a + -0.5) * log(t)) + log(Float64(z * y))) - 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 <= 1.26e+14)
		tmp = (((a + -0.5) * log(t)) + log((z * y))) - t;
	else
		tmp = (a * log(t)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.26e+14], N[(N[(N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision] + N[Log[N[(z * y), $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 < 1.26e14

   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. +-commutative 99.2%

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

      3. associate-+l+ 99.2%

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

      4. +-commutative 99.2%

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

      5. fma-define 99.2%

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

      6. sub-neg 99.2%

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

      7. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 66.1%

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

      1. *-un-lft-identity 66.1%

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

      2. add-log-exp 28.5%

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

      3. sum-log 23.6%

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

      4. exp-sum 23.7%

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

      5. add-exp-log 23.7%

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

      6. sub-neg 23.7%

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

      7. metadata-eval 23.7%

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

      8. exp-to-pow 23.9%

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

   7. Applied egg-rr 23.9%

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

      1. *-lft-identity 23.9%

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

      2. associate-*r* 23.7%

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

   9. Simplified 23.7%

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

       1. *-commutative 23.7%

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

       2. log-prod 26.2%

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

       3. log-pow 55.9%

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

   11. Applied egg-rr 55.9%

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

   if 1.26e14 < 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. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-sqr-sqrt 26.7%

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

      2. pow2 26.7%

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

   6. Applied egg-rr 26.7%

      \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
   7. Step-by-step derivation

      1. +-commutative 26.7%

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

      2. unpow2 26.7%

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

      3. add-sqr-sqrt 99.9%

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

      4. fma-define 99.9%

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

      5. associate-+r- 99.9%

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

      6. sum-log 77.2%

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

      7. +-commutative 77.2%

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

   8. Applied egg-rr 77.2%

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

   9. Taylor expanded in y around 0 60.0%

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

   10. Taylor expanded in a around inf 99.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(z \cdot y\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{1}{t} + -1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.4e+26) (* a (log t)) (+ (* t (+ (/ 1.0 t) -1.0)) -1.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.4e+26) {
		tmp = a * log(t);
	} else {
		tmp = (t * ((1.0 / t) + -1.0)) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.4d+26) then
        tmp = a * log(t)
    else
        tmp = (t * ((1.0d0 / t) + (-1.0d0))) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.4e+26) {
		tmp = a * Math.log(t);
	} else {
		tmp = (t * ((1.0 / t) + -1.0)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.4e+26:
		tmp = a * math.log(t)
	else:
		tmp = (t * ((1.0 / t) + -1.0)) + -1.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.4e+26)
		tmp = Float64(a * log(t));
	else
		tmp = Float64(Float64(t * Float64(Float64(1.0 / t) + -1.0)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.4e+26)
		tmp = a * log(t);
	else
		tmp = (t * ((1.0 / t) + -1.0)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.4e+26], N[(a * N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4e26

   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. +-commutative 99.2%

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

      3. associate-+l+ 99.2%

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

      4. +-commutative 99.2%

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

      5. fma-define 99.2%

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

      6. sub-neg 99.2%

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

      7. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 50.3%

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

      1. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if 1.4e26 < t

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-define 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.2%

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

      1. neg-mul-1 77.2%

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

   7. Simplified 77.2%

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

      1. expm1-log1p-u 0.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

      2. expm1-undefine 0.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

   9. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
   10. Step-by-step derivation

       1. sub-neg 0.0%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

       2. log1p-undefine 0.0%

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

       3. rem-exp-log 77.2%

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

       4. unsub-neg 77.2%

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

       5. metadata-eval 77.2%

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

   11. Simplified 77.2%

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

   12. Taylor expanded in t around inf 77.2%

       \[\leadsto \color{blue}{t \cdot \left(\frac{1}{t} - 1\right)} + -1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{1}{t} + -1\right) + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ a \cdot \log t - t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. sub-neg 99.5%

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

   3. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. add-sqr-sqrt 26.3%

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

   2. pow2 26.3%

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

6. Applied egg-rr 26.3%

   \[\leadsto \left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \color{blue}{{\left(\sqrt{a + -0.5}\right)}^{2}} \cdot \log t \]
7. Step-by-step derivation

   1. +-commutative 26.3%

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

   2. unpow2 26.3%

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

   3. add-sqr-sqrt 99.5%

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

   4. fma-define 99.5%

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

   5. associate-+r- 99.5%

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

   6. sum-log 78.0%

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

   7. +-commutative 78.0%

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

8. Applied egg-rr 78.0%

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

9. Taylor expanded in y around 0 50.5%

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

10. Taylor expanded in a around inf 70.8%

    \[\leadsto \color{blue}{a \cdot \log t} - t \]
11. Add Preprocessing

Alternative 16: 38.3% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(\frac{1}{t} + -1\right) + -1 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ (* t (+ (/ 1.0 t) -1.0)) -1.0))

C

double code(double x, double y, double z, double t, double a) {
	return (t * ((1.0 / t) + -1.0)) + -1.0;
}

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 * ((1.0d0 / t) + (-1.0d0))) + (-1.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (t * ((1.0 / t) + -1.0)) + -1.0;
}

Python

def code(x, y, z, t, a):
	return (t * ((1.0 / t) + -1.0)) + -1.0

Julia

function code(x, y, z, t, a)
	return Float64(Float64(t * Float64(Float64(1.0 / t) + -1.0)) + -1.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (t * ((1.0 / t) + -1.0)) + -1.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(t * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. +-commutative 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in t around inf 33.5%

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

   1. neg-mul-1 33.5%

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

7. Simplified 33.5%

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

   1. expm1-log1p-u 1.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

   2. expm1-undefine 1.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

9. Applied egg-rr 1.6%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
10. Step-by-step derivation

    1. sub-neg 1.6%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

    2. log1p-undefine 1.6%

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

    3. rem-exp-log 33.4%

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

    4. unsub-neg 33.4%

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

    5. metadata-eval 33.4%

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

11. Simplified 33.4%

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

12. Taylor expanded in t around inf 33.5%

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

13. Final simplification 33.5%

    \[\leadsto t \cdot \left(\frac{1}{t} + -1\right) + -1 \]
14. Add Preprocessing

Alternative 17: 38.3% accurate, 156.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = -t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -t;
}

Python

def code(x, y, z, t, a):
	return -t

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := (-t)

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. +-commutative 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in t around inf 33.5%

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

   1. neg-mul-1 33.5%

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

7. Simplified 33.5%

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

Alternative 18: 2.4% accurate, 313.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. +-commutative 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in t around inf 33.5%

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

   1. neg-mul-1 33.5%

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

7. Simplified 33.5%

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

   1. expm1-log1p-u 1.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

   2. expm1-undefine 1.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

9. Applied egg-rr 1.6%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
10. Step-by-step derivation

    1. sub-neg 1.6%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

    2. log1p-undefine 1.6%

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

    3. rem-exp-log 33.4%

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

    4. unsub-neg 33.4%

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

    5. metadata-eval 33.4%

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

11. Simplified 33.4%

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

12. Taylor expanded in t around 0 2.5%

    \[\leadsto \color{blue}{1} + -1 \]
13. Step-by-step derivation

    1. metadata-eval 2.5%

       \[\leadsto \color{blue}{0} \]

14. Applied egg-rr 2.5%

    \[\leadsto \color{blue}{0} \]
15. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024141 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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