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

Percentage Accurate: 99.9% → 99.9%

Time: 11.4s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+141} \lor \neg \left(z \leq 3.8 \cdot 10^{+50}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e+141) (not (<= z 3.8e+50)))
   (- (- (log t) y) z)
   (- (+ (* x (log y)) (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e+141) || !(z <= 3.8e+50)) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = ((x * log(y)) + 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 ((z <= (-1.02d+141)) .or. (.not. (z <= 3.8d+50))) then
        tmp = (log(t) - y) - z
    else
        tmp = ((x * log(y)) + 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 ((z <= -1.02e+141) || !(z <= 3.8e+50)) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = ((x * Math.log(y)) + Math.log(t)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e+141) or not (z <= 3.8e+50):
		tmp = (math.log(t) - y) - z
	else:
		tmp = ((x * math.log(y)) + math.log(t)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e+141) || !(z <= 3.8e+50))
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e+141) || ~((z <= 3.8e+50)))
		tmp = (log(t) - y) - z;
	else
		tmp = ((x * log(y)) + log(t)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e+141], N[Not[LessEqual[z, 3.8e+50]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e141 or 3.79999999999999987e50 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. associate--r+ 85.2%

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

   5. Simplified 85.2%

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

   if -1.02e141 < z < 3.79999999999999987e50

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 94.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+141} \lor \neg \left(z \leq 3.8 \cdot 10^{+50}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+92}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.1e+92) (- (+ (* x (log y)) (log t)) z) (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.1e+92) {
		tmp = ((x * log(y)) + log(t)) - 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 (y <= 5.1d+92) then
        tmp = ((x * log(y)) + log(t)) - 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 (y <= 5.1e+92) {
		tmp = ((x * Math.log(y)) + Math.log(t)) - z;
	} else {
		tmp = (Math.log(t) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.1e+92:
		tmp = ((x * math.log(y)) + math.log(t)) - z
	else:
		tmp = (math.log(t) - y) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.1e+92)
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - z);
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 5.1e+92)
		tmp = ((x * log(y)) + log(t)) - z;
	else
		tmp = (log(t) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.1e+92], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.1000000000000003e92

   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 0 93.2%

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

   if 5.1000000000000003e92 < y

   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%

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

      1. associate--r+ 90.7%

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

   5. Simplified 90.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+92}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-249}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e+150)
   (- z)
   (if (<= z -1.25e-21)
     (- y)
     (if (<= z -2.9e-249)
       (log t)
       (if (<= z 2.9e-227)
         (- y)
         (if (<= z 1.35e+69)
           (* x (log y))
           (if (<= z 1.3e+154) (- y) (- z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+150) {
		tmp = -z;
	} else if (z <= -1.25e-21) {
		tmp = -y;
	} else if (z <= -2.9e-249) {
		tmp = log(t);
	} else if (z <= 2.9e-227) {
		tmp = -y;
	} else if (z <= 1.35e+69) {
		tmp = x * log(y);
	} else if (z <= 1.3e+154) {
		tmp = -y;
	} else {
		tmp = -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 (z <= (-6d+150)) then
        tmp = -z
    else if (z <= (-1.25d-21)) then
        tmp = -y
    else if (z <= (-2.9d-249)) then
        tmp = log(t)
    else if (z <= 2.9d-227) then
        tmp = -y
    else if (z <= 1.35d+69) then
        tmp = x * log(y)
    else if (z <= 1.3d+154) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+150) {
		tmp = -z;
	} else if (z <= -1.25e-21) {
		tmp = -y;
	} else if (z <= -2.9e-249) {
		tmp = Math.log(t);
	} else if (z <= 2.9e-227) {
		tmp = -y;
	} else if (z <= 1.35e+69) {
		tmp = x * Math.log(y);
	} else if (z <= 1.3e+154) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e+150:
		tmp = -z
	elif z <= -1.25e-21:
		tmp = -y
	elif z <= -2.9e-249:
		tmp = math.log(t)
	elif z <= 2.9e-227:
		tmp = -y
	elif z <= 1.35e+69:
		tmp = x * math.log(y)
	elif z <= 1.3e+154:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e+150)
		tmp = Float64(-z);
	elseif (z <= -1.25e-21)
		tmp = Float64(-y);
	elseif (z <= -2.9e-249)
		tmp = log(t);
	elseif (z <= 2.9e-227)
		tmp = Float64(-y);
	elseif (z <= 1.35e+69)
		tmp = Float64(x * log(y));
	elseif (z <= 1.3e+154)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e+150)
		tmp = -z;
	elseif (z <= -1.25e-21)
		tmp = -y;
	elseif (z <= -2.9e-249)
		tmp = log(t);
	elseif (z <= 2.9e-227)
		tmp = -y;
	elseif (z <= 1.35e+69)
		tmp = x * log(y);
	elseif (z <= 1.3e+154)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e+150], (-z), If[LessEqual[z, -1.25e-21], (-y), If[LessEqual[z, -2.9e-249], N[Log[t], $MachinePrecision], If[LessEqual[z, 2.9e-227], (-y), If[LessEqual[z, 1.35e+69], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+154], (-y), (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.00000000000000025e150 or 1.29999999999999994e154 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. mul-1-neg 83.1%

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

   5. Simplified 83.1%

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

   if -6.00000000000000025e150 < z < -1.24999999999999993e-21 or -2.90000000000000022e-249 < z < 2.90000000000000011e-227 or 1.3499999999999999e69 < z < 1.29999999999999994e154

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      3. associate--l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. add-cube-cbrt 99.5%

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

      6. associate-*r* 99.5%

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

      7. fma-define 99.5%

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

      8. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

   4. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

   5. Taylor expanded in y around inf 52.3%

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

      1. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

   if -1.24999999999999993e-21 < z < -2.90000000000000022e-249

   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 65.8%

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

      1. associate--r+ 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around 0 43.5%

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

   7. Taylor expanded in z around 0 43.5%

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

   if 2.90000000000000011e-227 < z < 1.3499999999999999e69

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. add-cube-cbrt 98.9%

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

      6. associate-*r* 99.0%

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

      7. fma-define 99.0%

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

      8. pow2 99.0%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

   4. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

   5. Taylor expanded in x around inf 41.2%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-249}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-20}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-250}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-214}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 10500000000000:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+150)
   (- z)
   (if (<= z -6e-20)
     (- y)
     (if (<= z -6.6e-250)
       (log t)
       (if (<= z 1.8e-214)
         (- y)
         (if (<= z 10500000000000.0)
           (log t)
           (if (<= z 1.3e+154) (- y) (- z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+150) {
		tmp = -z;
	} else if (z <= -6e-20) {
		tmp = -y;
	} else if (z <= -6.6e-250) {
		tmp = log(t);
	} else if (z <= 1.8e-214) {
		tmp = -y;
	} else if (z <= 10500000000000.0) {
		tmp = log(t);
	} else if (z <= 1.3e+154) {
		tmp = -y;
	} else {
		tmp = -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 (z <= (-5.5d+150)) then
        tmp = -z
    else if (z <= (-6d-20)) then
        tmp = -y
    else if (z <= (-6.6d-250)) then
        tmp = log(t)
    else if (z <= 1.8d-214) then
        tmp = -y
    else if (z <= 10500000000000.0d0) then
        tmp = log(t)
    else if (z <= 1.3d+154) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+150) {
		tmp = -z;
	} else if (z <= -6e-20) {
		tmp = -y;
	} else if (z <= -6.6e-250) {
		tmp = Math.log(t);
	} else if (z <= 1.8e-214) {
		tmp = -y;
	} else if (z <= 10500000000000.0) {
		tmp = Math.log(t);
	} else if (z <= 1.3e+154) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+150:
		tmp = -z
	elif z <= -6e-20:
		tmp = -y
	elif z <= -6.6e-250:
		tmp = math.log(t)
	elif z <= 1.8e-214:
		tmp = -y
	elif z <= 10500000000000.0:
		tmp = math.log(t)
	elif z <= 1.3e+154:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+150)
		tmp = Float64(-z);
	elseif (z <= -6e-20)
		tmp = Float64(-y);
	elseif (z <= -6.6e-250)
		tmp = log(t);
	elseif (z <= 1.8e-214)
		tmp = Float64(-y);
	elseif (z <= 10500000000000.0)
		tmp = log(t);
	elseif (z <= 1.3e+154)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+150)
		tmp = -z;
	elseif (z <= -6e-20)
		tmp = -y;
	elseif (z <= -6.6e-250)
		tmp = log(t);
	elseif (z <= 1.8e-214)
		tmp = -y;
	elseif (z <= 10500000000000.0)
		tmp = log(t);
	elseif (z <= 1.3e+154)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+150], (-z), If[LessEqual[z, -6e-20], (-y), If[LessEqual[z, -6.6e-250], N[Log[t], $MachinePrecision], If[LessEqual[z, 1.8e-214], (-y), If[LessEqual[z, 10500000000000.0], N[Log[t], $MachinePrecision], If[LessEqual[z, 1.3e+154], (-y), (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000017e150 or 1.29999999999999994e154 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. mul-1-neg 83.1%

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

   5. Simplified 83.1%

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

   if -5.50000000000000017e150 < z < -6.00000000000000057e-20 or -6.6e-250 < z < 1.8e-214 or 1.05e13 < z < 1.29999999999999994e154

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. add-cube-cbrt 99.4%

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

      6. associate-*r* 99.4%

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

      7. fma-define 99.4%

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

      8. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

   5. Taylor expanded in y around inf 50.5%

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

      1. neg-mul-1 50.5%

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

   7. Simplified 50.5%

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

   if -6.00000000000000057e-20 < z < -6.6e-250 or 1.8e-214 < z < 1.05e13

   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 62.3%

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

      1. associate--r+ 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 40.7%

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

   7. Taylor expanded in z around 0 40.7%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-20}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-250}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-214}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 10500000000000:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+154}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+167} \lor \neg \left(x \leq 1.92 \cdot 10^{+115}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.12e+167) (not (<= x 1.92e+115)))
   (* x (log y))
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.12e+167) || !(x <= 1.92e+115)) {
		tmp = x * log(y);
	} else {
		tmp = (log(t) - y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.12d+167)) .or. (.not. (x <= 1.92d+115))) then
        tmp = x * log(y)
    else
        tmp = (log(t) - y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.12e+167) || !(x <= 1.92e+115)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (Math.log(t) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.12e+167) or not (x <= 1.92e+115):
		tmp = x * math.log(y)
	else:
		tmp = (math.log(t) - y) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.12e+167) || !(x <= 1.92e+115))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.12e+167) || ~((x <= 1.92e+115)))
		tmp = x * log(y);
	else
		tmp = (log(t) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.12e+167], N[Not[LessEqual[x, 1.92e+115]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999999e167 or 1.92e115 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. associate--l+ 99.7%

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

      4. *-commutative 99.7%

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

      5. add-cube-cbrt 98.4%

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

      6. associate-*r* 98.5%

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

      7. fma-define 98.5%

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

      8. pow2 98.5%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

   5. Taylor expanded in x around inf 78.2%

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

   if -1.11999999999999999e167 < x < 1.92e115

   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 92.1%

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

      1. associate--r+ 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+167} \lor \neg \left(x \leq 1.92 \cdot 10^{+115}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150} \lor \neg \left(z \leq 1.3 \cdot 10^{+154}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+150) (not (<= z 1.3e+154))) (- z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+150) || !(z <= 1.3e+154)) {
		tmp = -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 ((z <= (-5.5d+150)) .or. (.not. (z <= 1.3d+154))) then
        tmp = -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 ((z <= -5.5e+150) || !(z <= 1.3e+154)) {
		tmp = -z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+150) or not (z <= 1.3e+154):
		tmp = -z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+150) || !(z <= 1.3e+154))
		tmp = Float64(-z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+150) || ~((z <= 1.3e+154)))
		tmp = -z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+150], N[Not[LessEqual[z, 1.3e+154]], $MachinePrecision]], (-z), N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000017e150 or 1.29999999999999994e154 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. mul-1-neg 83.1%

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

   5. Simplified 83.1%

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

   if -5.50000000000000017e150 < z < 1.29999999999999994e154

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.5%

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

   4. Taylor expanded in x around 0 56.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150} \lor \neg \left(z \leq 1.3 \cdot 10^{+154}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.0% accurate, 17.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150} \lor \neg \left(z \leq 1.3 \cdot 10^{+154}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+150) (not (<= z 1.3e+154))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+150) || !(z <= 1.3e+154)) {
		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 ((z <= (-5.5d+150)) .or. (.not. (z <= 1.3d+154))) 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 ((z <= -5.5e+150) || !(z <= 1.3e+154)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+150) or not (z <= 1.3e+154):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+150) || !(z <= 1.3e+154))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+150) || ~((z <= 1.3e+154)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+150], N[Not[LessEqual[z, 1.3e+154]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000017e150 or 1.29999999999999994e154 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. mul-1-neg 83.1%

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

   5. Simplified 83.1%

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

   if -5.50000000000000017e150 < z < 1.29999999999999994e154

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. add-cube-cbrt 99.2%

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

      6. associate-*r* 99.2%

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

      7. fma-define 99.2%

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

      8. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

   5. Taylor expanded in y around inf 37.8%

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

      1. neg-mul-1 37.8%

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

   7. Simplified 37.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+150} \lor \neg \left(z \leq 1.3 \cdot 10^{+154}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 30.6% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. associate--l+ 99.9%

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

   4. *-commutative 99.9%

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

   5. add-cube-cbrt 99.4%

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

   6. associate-*r* 99.4%

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

   7. fma-define 99.4%

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

   8. pow2 99.4%

      \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right) \]

4. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(-y\right) - \left(z - \log t\right)\right)} \]

5. Taylor expanded in y around inf 29.2%

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

   1. neg-mul-1 29.2%

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

7. Simplified 29.2%

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

8. Final simplification 29.2%

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

Reproduce

herbie shell --seed 2024115 
(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)))