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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--r- 99.9%

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

   5. fma-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+r- 99.9%

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

   8. associate-+r- 99.9%

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

   9. +-commutative 99.9%

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

   10. sub-neg 99.9%

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

   11. log-rec 99.9%

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

   12. distribute-neg-in 99.9%

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

   13. +-commutative 99.9%

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

   14. log-rec 99.9%

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

   15. remove-double-neg 99.9%

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

   16. +-commutative 99.9%

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

   17. sub-neg 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $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. Final simplification 99.9%

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

Alternative 3: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e+38)
   (fma x (log y) (- y))
   (if (<= x 2.8e+67) (- (log t) (+ y z)) (- (* x (log y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e+38) {
		tmp = fma(x, log(y), -y);
	} else if (x <= 2.8e+67) {
		tmp = log(t) - (y + z);
	} else {
		tmp = (x * log(y)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e+38)
		tmp = fma(x, log(y), Float64(-y));
	elseif (x <= 2.8e+67)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e+38], N[(x * N[Log[y], $MachinePrecision] + (-y)), $MachinePrecision], If[LessEqual[x, 2.8e+67], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02000000000000006e38

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 91.7%

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

      1. mul-1-neg 91.7%

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

   7. Simplified 91.7%

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

   if -1.02000000000000006e38 < x < 2.7999999999999998e67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.3%

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

   if 2.7999999999999998e67 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.8%

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

      1. mul-1-neg 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in x around 0 92.8%

      \[\leadsto \color{blue}{-1 \cdot y + x \cdot \log y} \]
   9. Step-by-step derivation

      1. +-commutative 92.8%

         \[\leadsto \color{blue}{x \cdot \log y + -1 \cdot y} \]

      2. mul-1-neg 92.8%

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

      3. sub-neg 92.8%

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

   10. Simplified 92.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 4: 83.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+116} \lor \neg \left(x \leq 9.4 \cdot 10^{+69} \lor \neg \left(x \leq 3.5 \cdot 10^{+118}\right) \land x \leq 3.6 \cdot 10^{+170}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e+116)
         (not (or (<= x 9.4e+69) (and (not (<= x 3.5e+118)) (<= x 3.6e+170)))))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+116) || !((x <= 9.4e+69) || (!(x <= 3.5e+118) && (x <= 3.6e+170)))) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - (y + z);
	}
	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 <= (-3.8d+116)) .or. (.not. (x <= 9.4d+69) .or. (.not. (x <= 3.5d+118)) .and. (x <= 3.6d+170))) then
        tmp = x * log(y)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+116) || !((x <= 9.4e+69) || (!(x <= 3.5e+118) && (x <= 3.6e+170)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e+116) or not ((x <= 9.4e+69) or (not (x <= 3.5e+118) and (x <= 3.6e+170))):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e+116) || !((x <= 9.4e+69) || (!(x <= 3.5e+118) && (x <= 3.6e+170))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e+116) || ~(((x <= 9.4e+69) || (~((x <= 3.5e+118)) && (x <= 3.6e+170)))))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e+116], N[Not[Or[LessEqual[x, 9.4e+69], And[N[Not[LessEqual[x, 3.5e+118]], $MachinePrecision], LessEqual[x, 3.6e+170]]]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999999e116 or 9.39999999999999992e69 < x < 3.50000000000000016e118 or 3.6e170 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.6%

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

      1. mul-1-neg 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x around inf 80.2%

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

   if -3.7999999999999999e116 < x < 9.39999999999999992e69 or 3.50000000000000016e118 < x < 3.6e170

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+116} \lor \neg \left(x \leq 9.4 \cdot 10^{+69} \lor \neg \left(x \leq 3.5 \cdot 10^{+118}\right) \land x \leq 3.6 \cdot 10^{+170}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 5: 47.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.05 \cdot 10^{-255}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 1.05e-255)
     (- z)
     (if (<= y 5.6e-92)
       t_1
       (if (<= y 8e-39) (- z) (if (<= y 4.6e+19) t_1 (- y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 1.05e-255) {
		tmp = -z;
	} else if (y <= 5.6e-92) {
		tmp = t_1;
	} else if (y <= 8e-39) {
		tmp = -z;
	} else if (y <= 4.6e+19) {
		tmp = t_1;
	} else {
		tmp = -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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 1.05d-255) then
        tmp = -z
    else if (y <= 5.6d-92) then
        tmp = t_1
    else if (y <= 8d-39) then
        tmp = -z
    else if (y <= 4.6d+19) then
        tmp = t_1
    else
        tmp = -y
    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);
	double tmp;
	if (y <= 1.05e-255) {
		tmp = -z;
	} else if (y <= 5.6e-92) {
		tmp = t_1;
	} else if (y <= 8e-39) {
		tmp = -z;
	} else if (y <= 4.6e+19) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 1.05e-255:
		tmp = -z
	elif y <= 5.6e-92:
		tmp = t_1
	elif y <= 8e-39:
		tmp = -z
	elif y <= 4.6e+19:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.05e-255)
		tmp = Float64(-z);
	elseif (y <= 5.6e-92)
		tmp = t_1;
	elseif (y <= 8e-39)
		tmp = Float64(-z);
	elseif (y <= 4.6e+19)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 1.05e-255)
		tmp = -z;
	elseif (y <= 5.6e-92)
		tmp = t_1;
	elseif (y <= 8e-39)
		tmp = -z;
	elseif (y <= 4.6e+19)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.05e-255], (-z), If[LessEqual[y, 5.6e-92], t$95$1, If[LessEqual[y, 8e-39], (-z), If[LessEqual[y, 4.6e+19], t$95$1, (-y)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.05e-255 or 5.6e-92 < y < 7.99999999999999943e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. neg-mul-1 57.2%

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

   4. Simplified 57.2%

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

   if 1.05e-255 < y < 5.6e-92 or 7.99999999999999943e-39 < y < 4.6e19

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. mul-1-neg 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in x around inf 49.8%

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

   if 4.6e19 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 87.3%

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

      1. mul-1-neg 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 68.4%

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

      1. mul-1-neg 68.4%

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

   10. Simplified 68.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{-255}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 6: 59.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 3.1 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 3.1e-214)
     t_1
     (if (<= y 8.4e-185) (* x (log y)) (if (<= y 8.5e+18) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 3.1e-214) {
		tmp = t_1;
	} else if (y <= 8.4e-185) {
		tmp = x * log(y);
	} else if (y <= 8.5e+18) {
		tmp = t_1;
	} else {
		tmp = -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) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (y <= 3.1d-214) then
        tmp = t_1
    else if (y <= 8.4d-185) then
        tmp = x * log(y)
    else if (y <= 8.5d+18) then
        tmp = t_1
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double tmp;
	if (y <= 3.1e-214) {
		tmp = t_1;
	} else if (y <= 8.4e-185) {
		tmp = x * Math.log(y);
	} else if (y <= 8.5e+18) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if y <= 3.1e-214:
		tmp = t_1
	elif y <= 8.4e-185:
		tmp = x * math.log(y)
	elif y <= 8.5e+18:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (y <= 3.1e-214)
		tmp = t_1;
	elseif (y <= 8.4e-185)
		tmp = Float64(x * log(y));
	elseif (y <= 8.5e+18)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (y <= 3.1e-214)
		tmp = t_1;
	elseif (y <= 8.4e-185)
		tmp = x * log(y);
	elseif (y <= 8.5e+18)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 3.1e-214], t$95$1, If[LessEqual[y, 8.4e-185], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+18], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.10000000000000004e-214 or 8.4000000000000001e-185 < y < 8.5e18

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.2%

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

      1. remove-double-neg 99.2%

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

      2. log-rec 99.2%

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

      3. mul-1-neg 99.2%

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

      4. mul-1-neg 99.2%

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

      5. log-rec 99.2%

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

      6. remove-double-neg 99.2%

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

      7. log-pow 56.9%

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

      8. log-prod 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in x around 0 64.5%

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

   if 3.10000000000000004e-214 < y < 8.4000000000000001e-185

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+r- 99.9%

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

      8. associate-+r- 99.9%

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

      9. +-commutative 99.9%

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

      10. sub-neg 99.9%

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

      11. log-rec 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. +-commutative 99.9%

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

      14. log-rec 99.9%

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

      15. remove-double-neg 99.9%

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

      16. +-commutative 99.9%

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

      17. sub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. mul-1-neg 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in x around inf 72.4%

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

   if 8.5e18 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 87.4%

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

      1. mul-1-neg 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{-214}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7: 89.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+37} \lor \neg \left(x \leq 8 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.05e+37) (not (<= x 8e+66)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.05e+37) || !(x <= 8e+66)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	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 <= (-2.05d+37)) .or. (.not. (x <= 8d+66))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.05e+37) || !(x <= 8e+66)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.05e+37) or not (x <= 8e+66):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.05e+37) || !(x <= 8e+66))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.05e+37) || ~((x <= 8e+66)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.05e+37], N[Not[LessEqual[x, 8e+66]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0499999999999999e37 or 7.99999999999999956e66 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.2%

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

      1. mul-1-neg 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in x around 0 92.1%

      \[\leadsto \color{blue}{-1 \cdot y + x \cdot \log y} \]
   9. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{x \cdot \log y + -1 \cdot y} \]

      2. mul-1-neg 92.1%

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

      3. sub-neg 92.1%

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

   10. Simplified 92.1%

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

   if -2.0499999999999999e37 < x < 7.99999999999999956e66

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.3%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+37} \lor \neg \left(x \leq 8 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 8: 48.2% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.7e+18) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.7e+18) {
		tmp = -z;
	} else {
		tmp = -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 <= 1.7d+18) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.7e+18) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.7e+18:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.7e+18)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.7e+18)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.7e+18], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e18

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 36.4%

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

      1. neg-mul-1 36.4%

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

   4. Simplified 36.4%

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

   if 1.7e18 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 87.4%

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

      1. mul-1-neg 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9: 30.0% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

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 = -y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--r- 99.9%

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

   5. fma-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+r- 99.9%

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

   8. associate-+r- 99.9%

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

   9. +-commutative 99.9%

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

   10. sub-neg 99.9%

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

   11. log-rec 99.9%

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

   12. distribute-neg-in 99.9%

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

   13. +-commutative 99.9%

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

   14. log-rec 99.9%

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

   15. remove-double-neg 99.9%

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

   16. +-commutative 99.9%

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

   17. sub-neg 99.9%

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

4. Simplified 99.9%

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

5. Taylor expanded in y around inf 64.5%

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

   1. mul-1-neg 64.5%

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

7. Simplified 64.5%

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

8. Taylor expanded in x around 0 35.4%

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

   1. mul-1-neg 35.4%

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

10. Simplified 35.4%

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

11. Final simplification 35.4%

    \[\leadsto -y \]

Alternative 10: 2.2% accurate, 209.0× 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 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. Taylor expanded in y around 0 66.2%

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

3. Taylor expanded in x around inf 53.9%

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

   1. sub-neg 53.9%

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

   2. *-commutative 53.9%

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

   3. add-sqr-sqrt 25.0%

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

   4. associate-*r* 25.0%

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

   5. add-sqr-sqrt 13.8%

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

   6. sqrt-unprod 16.9%

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

   7. sqr-neg 16.9%

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

   8. sqrt-unprod 6.9%

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

   9. add-sqr-sqrt 13.6%

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

   10. fma-def 13.6%

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

5. Applied egg-rr 13.6%

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

6. Taylor expanded in x around 0 2.2%

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

7. Final simplification 2.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023312 
(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)))