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

Percentage Accurate: 99.9% → 99.9%

Time: 17.3s

Alternatives: 15

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 99.8%

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

3. Taylor expanded in x around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. associate--l+ 99.8%

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

   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. +-commutative 99.8%

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

   6. associate-+r- 99.8%

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

   7. fma-neg 99.8%

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

   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%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= x -1.65e+96)
     (- t_1 y)
     (if (<= x 4.8e-15) (- (log t) (+ y z)) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (x <= -1.65e+96) {
		tmp = t_1 - y;
	} else if (x <= 4.8e-15) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1 - 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) :: t_1
    real(8) :: tmp
    t_1 = log(t) + (x * log(y))
    if (x <= (-1.65d+96)) then
        tmp = t_1 - y
    else if (x <= 4.8d-15) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1 - z
    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) + (x * Math.log(y));
	double tmp;
	if (x <= -1.65e+96) {
		tmp = t_1 - y;
	} else if (x <= 4.8e-15) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if x <= -1.65e+96:
		tmp = t_1 - y
	elif x <= 4.8e-15:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (x <= -1.65e+96)
		tmp = Float64(t_1 - y);
	elseif (x <= 4.8e-15)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (x <= -1.65e+96)
		tmp = t_1 - y;
	elseif (x <= 4.8e-15)
		tmp = log(t) - (y + z);
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+96], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 4.8e-15], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.64999999999999992e96

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 88.3%

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

   if -1.64999999999999992e96 < x < 4.7999999999999999e-15

   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 96.0%

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

   if 4.7999999999999999e-15 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 93.4%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.75 \cdot 10^{+96}:\\ \;\;\;\;\left(\log t + t\_1\right) - y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.75e+96)
     (- (+ (log t) t_1) y)
     (if (<= x 4.8e-15) (- (log t) (+ y z)) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.75e+96) {
		tmp = (log(t) + t_1) - y;
	} else if (x <= 4.8e-15) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1 - 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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-3.75d+96)) then
        tmp = (log(t) + t_1) - y
    else if (x <= 4.8d-15) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1 - z
    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 (x <= -3.75e+96) {
		tmp = (Math.log(t) + t_1) - y;
	} else if (x <= 4.8e-15) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.75e+96:
		tmp = (math.log(t) + t_1) - y
	elif x <= 4.8e-15:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.75e+96)
		tmp = Float64(Float64(log(t) + t_1) - y);
	elseif (x <= 4.8e-15)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -3.75e+96)
		tmp = (log(t) + t_1) - y;
	elseif (x <= 4.8e-15)
		tmp = log(t) - (y + z);
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.75e+96], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 4.8e-15], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7499999999999998e96

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 88.3%

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

   if -3.7499999999999998e96 < x < 4.7999999999999999e-15

   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 96.0%

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

   if 4.7999999999999999e-15 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 92.7%

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

      1. neg-mul-1 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in y around inf 92.7%

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

       1. log-rec 92.7%

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

       2. associate-*r* 92.7%

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

       3. neg-mul-1 92.7%

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

       4. *-commutative 92.7%

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

   11. Simplified 92.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{+96}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -z\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.5e+151)
   (fma x (log y) (- z))
   (if (<= x 4.8e-15) (- (log t) (+ y z)) (- (* x (log y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.5e+151) {
		tmp = fma(x, log(y), -z);
	} else if (x <= 4.8e-15) {
		tmp = log(t) - (y + z);
	} else {
		tmp = (x * log(y)) - z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.5e+151)
		tmp = fma(x, log(y), Float64(-z));
	elseif (x <= 4.8e-15)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.5e+151], N[(x * N[Log[y], $MachinePrecision] + (-z)), $MachinePrecision], If[LessEqual[x, 4.8e-15], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999977e151

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 91.9%

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

      1. neg-mul-1 91.9%

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

   8. Simplified 91.9%

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

   if -7.49999999999999977e151 < x < 4.7999999999999999e-15

   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 93.8%

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

   if 4.7999999999999999e-15 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 92.7%

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

      1. neg-mul-1 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in y around inf 92.7%

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

       1. log-rec 92.7%

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

       2. associate-*r* 92.7%

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

       3. neg-mul-1 92.7%

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

       4. *-commutative 92.7%

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

   11. Simplified 92.7%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -z\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := \log t - y\\ t_3 := x \cdot \log y + z\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+105}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (- (log t) y)) (t_3 (+ (* x (log y)) z)))
   (if (<= x -8.6e+105)
     t_3
     (if (<= x -2.2e+30)
       t_1
       (if (<= x -2.55e-70)
         t_2
         (if (<= x 1.65e-236)
           t_1
           (if (<= x 2.5e-194)
             t_2
             (if (<= x 8.5e-111)
               t_1
               (if (<= x 3.5e-15)
                 t_2
                 (if (<= x 7000000000.0) (- z) t_3))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = log(t) - y;
	double t_3 = (x * log(y)) + z;
	double tmp;
	if (x <= -8.6e+105) {
		tmp = t_3;
	} else if (x <= -2.2e+30) {
		tmp = t_1;
	} else if (x <= -2.55e-70) {
		tmp = t_2;
	} else if (x <= 1.65e-236) {
		tmp = t_1;
	} else if (x <= 2.5e-194) {
		tmp = t_2;
	} else if (x <= 8.5e-111) {
		tmp = t_1;
	} else if (x <= 3.5e-15) {
		tmp = t_2;
	} else if (x <= 7000000000.0) {
		tmp = -z;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log(t) - z
    t_2 = log(t) - y
    t_3 = (x * log(y)) + z
    if (x <= (-8.6d+105)) then
        tmp = t_3
    else if (x <= (-2.2d+30)) then
        tmp = t_1
    else if (x <= (-2.55d-70)) then
        tmp = t_2
    else if (x <= 1.65d-236) then
        tmp = t_1
    else if (x <= 2.5d-194) then
        tmp = t_2
    else if (x <= 8.5d-111) then
        tmp = t_1
    else if (x <= 3.5d-15) then
        tmp = t_2
    else if (x <= 7000000000.0d0) then
        tmp = -z
    else
        tmp = t_3
    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 t_2 = Math.log(t) - y;
	double t_3 = (x * Math.log(y)) + z;
	double tmp;
	if (x <= -8.6e+105) {
		tmp = t_3;
	} else if (x <= -2.2e+30) {
		tmp = t_1;
	} else if (x <= -2.55e-70) {
		tmp = t_2;
	} else if (x <= 1.65e-236) {
		tmp = t_1;
	} else if (x <= 2.5e-194) {
		tmp = t_2;
	} else if (x <= 8.5e-111) {
		tmp = t_1;
	} else if (x <= 3.5e-15) {
		tmp = t_2;
	} else if (x <= 7000000000.0) {
		tmp = -z;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = math.log(t) - y
	t_3 = (x * math.log(y)) + z
	tmp = 0
	if x <= -8.6e+105:
		tmp = t_3
	elif x <= -2.2e+30:
		tmp = t_1
	elif x <= -2.55e-70:
		tmp = t_2
	elif x <= 1.65e-236:
		tmp = t_1
	elif x <= 2.5e-194:
		tmp = t_2
	elif x <= 8.5e-111:
		tmp = t_1
	elif x <= 3.5e-15:
		tmp = t_2
	elif x <= 7000000000.0:
		tmp = -z
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(log(t) - y)
	t_3 = Float64(Float64(x * log(y)) + z)
	tmp = 0.0
	if (x <= -8.6e+105)
		tmp = t_3;
	elseif (x <= -2.2e+30)
		tmp = t_1;
	elseif (x <= -2.55e-70)
		tmp = t_2;
	elseif (x <= 1.65e-236)
		tmp = t_1;
	elseif (x <= 2.5e-194)
		tmp = t_2;
	elseif (x <= 8.5e-111)
		tmp = t_1;
	elseif (x <= 3.5e-15)
		tmp = t_2;
	elseif (x <= 7000000000.0)
		tmp = Float64(-z);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = log(t) - y;
	t_3 = (x * log(y)) + z;
	tmp = 0.0;
	if (x <= -8.6e+105)
		tmp = t_3;
	elseif (x <= -2.2e+30)
		tmp = t_1;
	elseif (x <= -2.55e-70)
		tmp = t_2;
	elseif (x <= 1.65e-236)
		tmp = t_1;
	elseif (x <= 2.5e-194)
		tmp = t_2;
	elseif (x <= 8.5e-111)
		tmp = t_1;
	elseif (x <= 3.5e-15)
		tmp = t_2;
	elseif (x <= 7000000000.0)
		tmp = -z;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -8.6e+105], t$95$3, If[LessEqual[x, -2.2e+30], t$95$1, If[LessEqual[x, -2.55e-70], t$95$2, If[LessEqual[x, 1.65e-236], t$95$1, If[LessEqual[x, 2.5e-194], t$95$2, If[LessEqual[x, 8.5e-111], t$95$1, If[LessEqual[x, 3.5e-15], t$95$2, If[LessEqual[x, 7000000000.0], (-z), t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.6000000000000003e105 or 7e9 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 88.4%

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

      1. neg-mul-1 88.4%

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

   8. Simplified 88.4%

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

      1. fma-undefine 88.3%

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

      2. add-sqr-sqrt 39.7%

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

      3. sqrt-unprod 66.4%

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

      4. sqr-neg 66.4%

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

      5. sqrt-unprod 40.8%

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

      6. add-sqr-sqrt 72.6%

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

   10. Applied egg-rr 72.6%

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

   if -8.6000000000000003e105 < x < -2.2e30 or -2.55000000000000013e-70 < x < 1.6500000000000001e-236 or 2.5000000000000001e-194 < x < 8.5000000000000003e-111

   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 inf 68.5%

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

      1. neg-mul-1 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in z around 0 68.5%

      \[\leadsto \color{blue}{\log t + -1 \cdot z} \]
   7. Step-by-step derivation

      1. neg-mul-1 68.5%

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

      2. sub-neg 68.5%

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

   8. Simplified 68.5%

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

   if -2.2e30 < x < -2.55000000000000013e-70 or 1.6500000000000001e-236 < x < 2.5000000000000001e-194 or 8.5000000000000003e-111 < x < 3.5000000000000001e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

   5. Simplified 79.3%

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

   if 3.5000000000000001e-15 < x < 7e9

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 100.0%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 100.0%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 100.0%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 100.0%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 100.0%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 100.0%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 100.0%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 100.0%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 100.0%

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

      7. clear-num 100.0%

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

      8. pow-div 100.0%

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

      9. metadata-eval 100.0%

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

      10. pow1 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+30}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-70}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-236}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 7000000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+153} \lor \neg \left(x \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e+153) (not (<= x 2.7e+84)))
   (+ (* x (log y)) z)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e+153) || !(x <= 2.7e+84)) {
		tmp = (x * log(y)) + z;
	} 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 <= (-5.5d+153)) .or. (.not. (x <= 2.7d+84))) then
        tmp = (x * log(y)) + z
    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 <= -5.5e+153) || !(x <= 2.7e+84)) {
		tmp = (x * Math.log(y)) + z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e+153) or not (x <= 2.7e+84):
		tmp = (x * math.log(y)) + z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e+153) || !(x <= 2.7e+84))
		tmp = Float64(Float64(x * log(y)) + z);
	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 <= -5.5e+153) || ~((x <= 2.7e+84)))
		tmp = (x * log(y)) + z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e+153], N[Not[LessEqual[x, 2.7e+84]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e153 or 2.7e84 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 96.2%

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

      1. neg-mul-1 96.2%

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

   8. Simplified 96.2%

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

      1. fma-undefine 96.2%

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

      2. add-sqr-sqrt 41.5%

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

      3. sqrt-unprod 72.5%

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

      4. sqr-neg 72.5%

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

      5. sqrt-unprod 47.0%

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

      6. add-sqr-sqrt 81.8%

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

   10. Applied egg-rr 81.8%

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

   if -5.5000000000000003e153 < x < 2.7e84

   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 90.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+153} \lor \neg \left(x \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+151} \lor \neg \left(x \leq 4.8 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e+151) (not (<= x 4.8e-15)))
   (- (* x (log y)) z)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+151) || !(x <= 4.8e-15)) {
		tmp = (x * log(y)) - z;
	} 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 <= (-9d+151)) .or. (.not. (x <= 4.8d-15))) then
        tmp = (x * log(y)) - z
    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 <= -9e+151) || !(x <= 4.8e-15)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e+151) or not (x <= 4.8e-15):
		tmp = (x * math.log(y)) - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e+151) || !(x <= 4.8e-15))
		tmp = Float64(Float64(x * log(y)) - z);
	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 <= -9e+151) || ~((x <= 4.8e-15)))
		tmp = (x * log(y)) - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e+151], N[Not[LessEqual[x, 4.8e-15]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999997e151 or 4.7999999999999999e-15 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--r- 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-+r- 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. log-rec 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. log-rec 99.6%

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

      15. remove-double-neg 99.6%

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

      16. +-commutative 99.6%

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

      17. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 92.4%

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

      1. neg-mul-1 92.4%

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

   8. Simplified 92.4%

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

   9. Taylor expanded in y around inf 92.4%

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

       1. log-rec 92.4%

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

       2. associate-*r* 92.4%

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

       3. neg-mul-1 92.4%

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

       4. *-commutative 92.4%

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

   11. Simplified 92.4%

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

   if -8.9999999999999997e151 < x < 4.7999999999999999e-15

   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 93.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+151} \lor \neg \left(x \leq 4.8 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;\log t + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.8e-49)
   (- z)
   (if (<= y 2.1e-13) (+ (log t) z) (if (<= y 2e+59) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.8e-49) {
		tmp = -z;
	} else if (y <= 2.1e-13) {
		tmp = log(t) + z;
	} else if (y <= 2e+59) {
		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 <= 3.8d-49) then
        tmp = -z
    else if (y <= 2.1d-13) then
        tmp = log(t) + z
    else if (y <= 2d+59) 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 <= 3.8e-49) {
		tmp = -z;
	} else if (y <= 2.1e-13) {
		tmp = Math.log(t) + z;
	} else if (y <= 2e+59) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.8e-49:
		tmp = -z
	elif y <= 2.1e-13:
		tmp = math.log(t) + z
	elif y <= 2e+59:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.8e-49)
		tmp = Float64(-z);
	elseif (y <= 2.1e-13)
		tmp = Float64(log(t) + z);
	elseif (y <= 2e+59)
		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 <= 3.8e-49)
		tmp = -z;
	elseif (y <= 2.1e-13)
		tmp = log(t) + z;
	elseif (y <= 2e+59)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.8e-49], (-z), If[LessEqual[y, 2.1e-13], N[(N[Log[t], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2e+59], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.7999999999999997e-49 or 2.09999999999999989e-13 < y < 1.99999999999999994e59

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 37.8%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 37.8%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 37.8%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 37.8%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 37.8%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 37.8%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 37.8%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 37.8%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 37.8%

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

      7. clear-num 37.8%

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

      8. pow-div 99.7%

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

      9. metadata-eval 99.7%

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

      10. pow1 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 41.1%

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

      1. neg-mul-1 41.1%

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

   9. Simplified 41.1%

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

   if 3.7999999999999997e-49 < y < 2.09999999999999989e-13

   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 inf 60.3%

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

      1. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

      1. *-un-lft-identity 60.3%

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

      2. add-sqr-sqrt 48.3%

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

      3. sqrt-unprod 55.3%

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

      4. sqr-neg 55.3%

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

      5. sqrt-unprod 12.4%

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

      6. add-sqr-sqrt 47.5%

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

   7. Applied egg-rr 47.5%

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

      1. *-lft-identity 47.5%

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

      2. +-commutative 47.5%

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

   9. Simplified 47.5%

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

   if 1.99999999999999994e59 < y

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 40.9%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 40.9%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 40.9%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 40.9%

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

      7. clear-num 40.9%

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

      8. pow-div 99.8%

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

      9. metadata-eval 99.8%

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

      10. pow1 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 61.6%

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

      1. neg-mul-1 61.6%

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

   9. Simplified 61.6%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;\log t + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.8e-49)
   (- z)
   (if (<= y 6.2e-13) (log t) (if (<= y 1.02e+57) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.8e-49) {
		tmp = -z;
	} else if (y <= 6.2e-13) {
		tmp = log(t);
	} else if (y <= 1.02e+57) {
		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 <= 1.8d-49) then
        tmp = -z
    else if (y <= 6.2d-13) then
        tmp = log(t)
    else if (y <= 1.02d+57) 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 <= 1.8e-49) {
		tmp = -z;
	} else if (y <= 6.2e-13) {
		tmp = Math.log(t);
	} else if (y <= 1.02e+57) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.8e-49:
		tmp = -z
	elif y <= 6.2e-13:
		tmp = math.log(t)
	elif y <= 1.02e+57:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.8e-49)
		tmp = Float64(-z);
	elseif (y <= 6.2e-13)
		tmp = log(t);
	elseif (y <= 1.02e+57)
		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 <= 1.8e-49)
		tmp = -z;
	elseif (y <= 6.2e-13)
		tmp = log(t);
	elseif (y <= 1.02e+57)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.8e-49], (-z), If[LessEqual[y, 6.2e-13], N[Log[t], $MachinePrecision], If[LessEqual[y, 1.02e+57], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.79999999999999985e-49 or 6.1999999999999998e-13 < y < 1.02e57

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 37.8%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 37.8%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 37.8%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 37.8%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 37.8%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 37.8%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 37.8%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 37.8%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 37.8%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 37.8%

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

      7. clear-num 37.8%

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

      8. pow-div 99.7%

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

      9. metadata-eval 99.7%

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

      10. pow1 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 41.1%

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

      1. neg-mul-1 41.1%

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

   9. Simplified 41.1%

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

   if 1.79999999999999985e-49 < y < 6.1999999999999998e-13

   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 inf 60.3%

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

      1. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in z around 0 47.4%

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

   if 1.02e57 < y

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 40.9%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 40.9%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 40.9%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 40.9%

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

      7. clear-num 40.9%

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

      8. pow-div 99.8%

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

      9. metadata-eval 99.8%

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

      10. pow1 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 61.6%

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

      1. neg-mul-1 61.6%

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

   9. Simplified 61.6%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.3 \cdot 10^{+57}:\\ \;\;\;\;\log t + \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.3e+57) (+ (log t) (- y z)) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.3e+57) {
		tmp = log(t) + (y - 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 <= 5.3d+57) then
        tmp = log(t) + (y - 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 <= 5.3e+57) {
		tmp = Math.log(t) + (y - z);
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.3e+57:
		tmp = math.log(t) + (y - z)
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.3e+57)
		tmp = Float64(log(t) + Float64(y - 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 <= 5.3e+57)
		tmp = log(t) + (y - z);
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.3e+57], N[(N[Log[t], $MachinePrecision] + N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.29999999999999986e57

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-log-exp 25.0%

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

      3. sum-log 25.0%

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

      4. sub-neg 25.0%

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

      5. sub-neg 25.0%

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

      6. associate-+r+ 25.0%

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

      7. sub-neg 25.0%

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

      8. exp-sum 23.6%

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

      9. *-commutative 23.6%

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

      10. exp-to-pow 23.6%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 23.7%

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

      13. sqr-neg 23.7%

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

      14. sqrt-unprod 23.7%

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

      15. add-sqr-sqrt 23.7%

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

   4. Applied egg-rr 23.7%

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

   5. Taylor expanded in x around 0 23.9%

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

      1. log-prod 23.9%

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

      2. rem-log-exp 57.4%

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

   7. Simplified 57.4%

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

   if 5.29999999999999986e57 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. mul-1-neg 61.6%

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

   5. Simplified 61.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.3 \cdot 10^{+57}:\\ \;\;\;\;\log t + \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.35 \cdot 10^{+122}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.35e+122) (- (log t) z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.35e+122) {
		tmp = log(t) - 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 <= 2.35d+122) then
        tmp = log(t) - 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 <= 2.35e+122) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.35e+122:
		tmp = math.log(t) - z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.35e+122)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.35e+122)
		tmp = log(t) - z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.35e+122], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.35000000000000012e122

   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 53.4%

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

      1. neg-mul-1 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around 0 53.4%

      \[\leadsto \color{blue}{\log t + -1 \cdot z} \]
   7. Step-by-step derivation

      1. neg-mul-1 53.4%

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

      2. sub-neg 53.4%

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

   8. Simplified 53.4%

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

   if 2.35000000000000012e122 < y

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 44.5%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 44.5%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 44.5%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 44.5%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 44.5%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 44.5%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 44.5%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 44.5%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 44.5%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 44.5%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 44.5%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 44.5%

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

      7. clear-num 44.5%

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

      8. pow-div 99.8%

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

      9. metadata-eval 99.8%

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

      10. pow1 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 72.4%

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

      1. neg-mul-1 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.35 \cdot 10^{+122}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.15e+57) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.15e+57) {
		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 <= 2.15d+57) 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 <= 2.15e+57) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.15e+57:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.15e+57)
		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 <= 2.15e+57)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.15e+57], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.15000000000000016e57

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 38.9%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 38.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 38.9%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 38.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 38.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 38.9%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 38.9%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 38.9%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 38.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 38.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 38.9%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 38.9%

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

      7. clear-num 38.9%

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

      8. pow-div 99.7%

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

      9. metadata-eval 99.7%

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

      10. pow1 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 38.1%

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

      1. neg-mul-1 38.1%

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

   9. Simplified 38.1%

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

   if 2.15000000000000016e57 < y

   1. Initial program 99.8%

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

      1. add0 99.8%

         \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

      2. flip3-+ 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

      3. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      4. add0 40.9%

         \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      5. pow2 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

      6. metadata-eval 40.9%

         \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 40.9%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
   5. Step-by-step derivation

      1. clear-num 40.9%

         \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

      2. inv-pow 40.9%

         \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

      3. sub0-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      4. mul0-rgt 40.9%

         \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      5. sub-neg 40.9%

         \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

      6. --rgt-identity 40.9%

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

      7. clear-num 40.9%

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

      8. pow-div 99.8%

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

      9. metadata-eval 99.8%

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

      10. pow1 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 61.6%

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

      1. neg-mul-1 61.6%

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

   9. Simplified 61.6%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% 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 99.8%

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

   1. add0 99.8%

      \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log y + 0\right)} - y\right) - z\right) + \log t \]

   2. flip3-+ 39.7%

      \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3} + {0}^{3}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]

   3. metadata-eval 39.7%

      \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3} + \color{blue}{0}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   4. add0 39.7%

      \[\leadsto \left(\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{3}}}{\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right) + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   5. pow2 39.7%

      \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} + \left(0 \cdot 0 - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

   6. metadata-eval 39.7%

      \[\leadsto \left(\left(\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(\color{blue}{0} - \left(x \cdot \log y\right) \cdot 0\right)} - y\right) - z\right) + \log t \]

4. Applied egg-rr 39.7%

   \[\leadsto \left(\left(\color{blue}{\frac{{\left(x \cdot \log y\right)}^{3}}{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}} - y\right) - z\right) + \log t \]
5. Step-by-step derivation

   1. clear-num 39.7%

      \[\leadsto \left(\left(\color{blue}{\frac{1}{\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}}} - y\right) - z\right) + \log t \]

   2. inv-pow 39.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(0 - \left(x \cdot \log y\right) \cdot 0\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1}} - y\right) - z\right) + \log t \]

   3. sub0-neg 39.7%

      \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \color{blue}{\left(-\left(x \cdot \log y\right) \cdot 0\right)}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

   4. mul0-rgt 39.7%

      \[\leadsto \left(\left({\left(\frac{{\left(x \cdot \log y\right)}^{2} + \left(-\color{blue}{0}\right)}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

   5. sub-neg 39.7%

      \[\leadsto \left(\left({\left(\frac{\color{blue}{{\left(x \cdot \log y\right)}^{2} - 0}}{{\left(x \cdot \log y\right)}^{3}}\right)}^{-1} - y\right) - z\right) + \log t \]

   6. --rgt-identity 39.7%

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

   7. clear-num 39.7%

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

   8. pow-div 99.8%

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

   9. metadata-eval 99.8%

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

   10. pow1 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in y around inf 27.8%

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

   1. neg-mul-1 27.8%

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

9. Simplified 27.8%

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

10. Final simplification 27.8%

    \[\leadsto -y \]
11. Add Preprocessing

Alternative 15: 2.3% 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 99.8%

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

   1. +-commutative 99.8%

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

   2. add-log-exp 17.4%

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

   3. sum-log 17.4%

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

   4. sub-neg 17.4%

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

   5. sub-neg 17.4%

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

   6. associate-+r+ 17.4%

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

   7. sub-neg 17.4%

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

   8. exp-sum 16.1%

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

   9. *-commutative 16.1%

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

   10. exp-to-pow 16.1%

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

   11. add-sqr-sqrt 0.0%

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

   12. sqrt-unprod 14.6%

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

   13. sqr-neg 14.6%

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

   14. sqrt-unprod 14.6%

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

   15. add-sqr-sqrt 14.6%

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

4. Applied egg-rr 14.6%

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

5. Taylor expanded in x around 0 14.8%

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

   1. log-prod 14.8%

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

   2. add-log-exp 40.0%

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

   3. sub-neg 40.0%

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

   4. add-sqr-sqrt 21.9%

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

   5. sqrt-unprod 16.7%

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

   6. sqr-neg 16.7%

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

   7. sqrt-unprod 5.0%

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

   8. add-sqr-sqrt 12.5%

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

7. Applied egg-rr 12.5%

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

   1. associate-+r+ 12.5%

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

   2. +-commutative 12.5%

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

9. Simplified 12.5%

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

10. Taylor expanded in z around inf 2.4%

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

11. Final simplification 2.4%

    \[\leadsto z \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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)))