Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. *-rgt-identity N/A

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

   4. *-inverses N/A

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

   5. fp-cancel-sign-sub N/A

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

   6. mul-1-neg N/A

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

   7. associate-/l* N/A

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

   8. associate-*l/ N/A

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

   9. associate-*r/ N/A

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

   10. *-commutative N/A

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

   11. remove-double-neg N/A

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

   12. fp-cancel-sign-sub N/A

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

   13. *-commutative N/A

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

   14. mul-1-neg N/A

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

   15. lower-fma.f64 N/A

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

5. Applied rewrites 99.9%

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

Alternative 2: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+29}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;t\_1 \leq 10^{+68}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -1e+29)
     (- (log t) y)
     (if (<= t_1 1e+68) (- (log t) z) (* (log y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -1e+29) {
		tmp = log(t) - y;
	} else if (t_1 <= 1e+68) {
		tmp = log(t) - z;
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-1d+29)) then
        tmp = log(t) - y
    else if (t_1 <= 1d+68) then
        tmp = log(t) - z
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (t_1 <= -1e+29) {
		tmp = Math.log(t) - y;
	} else if (t_1 <= 1e+68) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -1e+29:
		tmp = math.log(t) - y
	elif t_1 <= 1e+68:
		tmp = math.log(t) - z
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -1e+29)
		tmp = Float64(log(t) - y);
	elseif (t_1 <= 1e+68)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (t_1 <= -1e+29)
		tmp = log(t) - y;
	elseif (t_1 <= 1e+68)
		tmp = log(t) - z;
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+29], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$1, 1e+68], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -9.99999999999999914e28

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   7. Step-by-step derivation

   8. Applied rewrites 59.1%

      \[\leadsto \log t - y \]

   if -9.99999999999999914e28 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999953e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-log.f64 96.2

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

   8. Applied rewrites 96.2%

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

   9. Taylor expanded in x around 0

      \[\leadsto \log t - \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 89.6%

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

   if 9.99999999999999953e67 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 82.7

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

   8. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\log y \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq 10^{+68}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x (log y)) y) 1e+68)
   (- (- (log t) y) z)
   (fma (log y) x (log t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * log(y)) - y) <= 1e+68) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = fma(log(y), x, log(t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * log(y)) - y) <= 1e+68)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = fma(log(y), x, log(t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], 1e+68], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999953e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. lower--.f64 N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if 9.99999999999999953e67 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-log.f64 97.6

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

   8. Applied rewrites 97.6%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\log y, x, \log t\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 82.7%

       \[\leadsto \mathsf{fma}\left(\log y, x, \log t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+60} \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;t\_1 - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)))
   (if (or (<= z -8.8e+60) (not (<= z 4e+59))) (- t_1 z) (fma (log y) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double tmp;
	if ((z <= -8.8e+60) || !(z <= 4e+59)) {
		tmp = t_1 - z;
	} else {
		tmp = fma(log(y), x, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	tmp = 0.0
	if ((z <= -8.8e+60) || !(z <= 4e+59))
		tmp = Float64(t_1 - z);
	else
		tmp = fma(log(y), x, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[z, -8.8e+60], N[Not[LessEqual[z, 4e+59]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999984e60 or 3.99999999999999989e59 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. lower--.f64 N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 89.4

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

   5. Applied rewrites 89.4%

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

   if -8.79999999999999984e60 < z < 3.99999999999999989e59

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 96.4

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

   5. Applied rewrites 96.4%

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

   7. Applied rewrites 96.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+60} \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+60} \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e+60) (not (<= z 4e+59)))
   (- (- (log t) y) z)
   (- (fma (log y) x (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e+60) || !(z <= 4e+59)) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = fma(log(y), x, log(t)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e+60) || !(z <= 4e+59))
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(fma(log(y), x, log(t)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e+60], N[Not[LessEqual[z, 4e+59]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999984e60 or 3.99999999999999989e59 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. lower--.f64 N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 89.4

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

   5. Applied rewrites 89.4%

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

   if -8.79999999999999984e60 < z < 3.99999999999999989e59

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 96.4

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

   5. Applied rewrites 96.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+60} \lor \neg \left(z \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq 10^{+68}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x (log y)) y) 1e+68) (- (- (log t) y) z) (* (log y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * log(y)) - y) <= 1e+68) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x * log(y)) - y) <= 1d+68) then
        tmp = (log(t) - y) - z
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * Math.log(y)) - y) <= 1e+68) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * math.log(y)) - y) <= 1e+68:
		tmp = (math.log(t) - y) - z
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * log(y)) - y) <= 1e+68)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * log(y)) - y) <= 1e+68)
		tmp = (log(t) - y) - z;
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], 1e+68], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < 9.99999999999999953e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. lower--.f64 N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if 9.99999999999999953e67 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 82.7

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

   8. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\log y \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 60.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.5e+28) (- (log t) z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e+28) {
		tmp = log(t) - z;
	} else {
		tmp = log(t) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 9.5d+28) then
        tmp = log(t) - z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e+28) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.5e+28:
		tmp = math.log(t) - z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.5e+28)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 9.5e+28)
		tmp = log(t) - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.5e+28], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.49999999999999927e28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-log.f64 97.4

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in x around 0

      \[\leadsto \log t - \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 65.3%

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

   if 9.49999999999999927e28 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 82.5

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

   5. Applied rewrites 82.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   7. Step-by-step derivation

   8. Applied rewrites 62.1%

      \[\leadsto \log t - y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 60.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.5e+28) (- (log t) z) (* -1.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e+28) {
		tmp = log(t) - z;
	} else {
		tmp = -1.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 9.5d+28) then
        tmp = log(t) - z
    else
        tmp = (-1.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e+28) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -1.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.5e+28:
		tmp = math.log(t) - z
	else:
		tmp = -1.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.5e+28)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(-1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 9.5e+28)
		tmp = log(t) - z;
	else
		tmp = -1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.5e+28], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(-1.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.49999999999999927e28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-rgt-identity N/A

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

      4. *-inverses N/A

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

      5. fp-cancel-sign-sub N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. remove-double-neg N/A

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

      12. fp-cancel-sign-sub N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-log.f64 97.4

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in x around 0

      \[\leadsto \log t - \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 65.3%

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

   if 9.49999999999999927e28 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 62.1%

      \[\leadsto -1 \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 48.6% accurate, 17.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 65000000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 65000000000000.0) (- z) (* -1.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 65000000000000.0) {
		tmp = -z;
	} else {
		tmp = -1.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 65000000000000.0d0) then
        tmp = -z
    else
        tmp = (-1.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 65000000000000.0) {
		tmp = -z;
	} else {
		tmp = -1.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 65000000000000.0:
		tmp = -z
	else:
		tmp = -1.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 65000000000000.0)
		tmp = Float64(-z);
	else
		tmp = Float64(-1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 65000000000000.0)
		tmp = -z;
	else
		tmp = -1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 65000000000000.0], (-z), N[(-1.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5e13

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 35.6

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

   5. Applied rewrites 35.6%

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

   if 6.5e13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.6%

      \[\leadsto -1 \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 30.3% accurate, 71.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 27.1

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

5. Applied rewrites 27.1%

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))