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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

Alternatives: 11

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. Final simplification 99.9%

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

Alternative 2: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+55} \lor \neg \left(z \leq 3.1 \cdot 10^{+63}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e+55) (not (<= z 3.1e+63)))
   (- (- z) y)
   (- (+ (* x (log y)) (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+55) || !(z <= 3.1e+63)) {
		tmp = -z - y;
	} 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 <= (-1.1d+55)) .or. (.not. (z <= 3.1d+63))) then
        tmp = -z - y
    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 <= -1.1e+55) || !(z <= 3.1e+63)) {
		tmp = -z - y;
	} else {
		tmp = ((x * Math.log(y)) + Math.log(t)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e+55) or not (z <= 3.1e+63):
		tmp = -z - y
	else:
		tmp = ((x * math.log(y)) + math.log(t)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e+55) || !(z <= 3.1e+63))
		tmp = Float64(Float64(-z) - y);
	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 <= -1.1e+55) || ~((z <= 3.1e+63)))
		tmp = -z - y;
	else
		tmp = ((x * log(y)) + log(t)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e+55], N[Not[LessEqual[z, 3.1e+63]], $MachinePrecision]], N[((-z) - y), $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 < -1.10000000000000005e55 or 3.1000000000000001e63 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. add-sqr-sqrt 54.8%

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

      6. associate-*r* 54.8%

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

      7. fma-def 54.8%

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

   3. Applied egg-rr 54.8%

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

   4. Taylor expanded in z around inf 54.8%

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

   5. Taylor expanded in x around 0 91.3%

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

      1. distribute-lft-in 91.3%

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

      2. neg-mul-1 91.3%

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

      3. unsub-neg 91.3%

         \[\leadsto \color{blue}{-1 \cdot y - z} \]

      4. mul-1-neg 91.3%

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

   7. Simplified 91.3%

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

   if -1.10000000000000005e55 < z < 3.1000000000000001e63

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 96.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+55} \lor \neg \left(z \leq 3.1 \cdot 10^{+63}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \]

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 20000000:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 20000000.0) (- (+ (* 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 <= 20000000.0) {
		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 <= 20000000.0d0) 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 <= 20000000.0) {
		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 <= 20000000.0:
		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 <= 20000000.0)
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - 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 (y <= 20000000.0)
		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, 20000000.0], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2e7

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.2%

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

   if 2e7 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 20000000:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 4: 70.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+46} \lor \neg \left(x \leq 7.5 \cdot 10^{+73} \lor \neg \left(x \leq 3.7 \cdot 10^{+94}\right) \land x \leq 1.02 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6e+46)
         (not (or (<= x 7.5e+73) (and (not (<= x 3.7e+94)) (<= x 1.02e+138)))))
   (* x (log y))
   (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e+46) || !((x <= 7.5e+73) || (!(x <= 3.7e+94) && (x <= 1.02e+138)))) {
		tmp = x * log(y);
	} else {
		tmp = -z - 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 ((x <= (-6d+46)) .or. (.not. (x <= 7.5d+73) .or. (.not. (x <= 3.7d+94)) .and. (x <= 1.02d+138))) then
        tmp = x * log(y)
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e+46) || !((x <= 7.5e+73) || (!(x <= 3.7e+94) && (x <= 1.02e+138)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6e+46) or not ((x <= 7.5e+73) or (not (x <= 3.7e+94) and (x <= 1.02e+138))):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6e+46) || !((x <= 7.5e+73) || (!(x <= 3.7e+94) && (x <= 1.02e+138))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6e+46) || ~(((x <= 7.5e+73) || (~((x <= 3.7e+94)) && (x <= 1.02e+138)))))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6e+46], N[Not[Or[LessEqual[x, 7.5e+73], And[N[Not[LessEqual[x, 3.7e+94]], $MachinePrecision], LessEqual[x, 1.02e+138]]]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000047e46 or 7.5e73 < x < 3.7000000000000001e94 or 1.02e138 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 71.2%

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

   if -6.00000000000000047e46 < x < 7.5e73 or 3.7000000000000001e94 < x < 1.02e138

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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-sqr-sqrt 56.1%

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

      6. associate-*r* 56.1%

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

      7. fma-def 56.1%

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

   3. Applied egg-rr 56.1%

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

   4. Taylor expanded in z around inf 44.4%

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

   5. Taylor expanded in x around 0 75.5%

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

      1. distribute-lft-in 75.5%

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

      2. neg-mul-1 75.5%

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

      3. unsub-neg 75.5%

         \[\leadsto \color{blue}{-1 \cdot y - z} \]

      4. mul-1-neg 75.5%

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

   7. Simplified 75.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+46} \lor \neg \left(x \leq 7.5 \cdot 10^{+73} \lor \neg \left(x \leq 3.7 \cdot 10^{+94}\right) \land x \leq 1.02 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 5: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+95} \lor \neg \left(x \leq 2.2 \cdot 10^{+136}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -7.2e+53)
     t_1
     (if (<= x 4e+73)
       (- (log t) (+ y z))
       (if (or (<= x 8.8e+95) (not (<= x 2.2e+136))) t_1 (- (- z) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -7.2e+53) {
		tmp = t_1;
	} else if (x <= 4e+73) {
		tmp = log(t) - (y + z);
	} else if ((x <= 8.8e+95) || !(x <= 2.2e+136)) {
		tmp = t_1;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-7.2d+53)) then
        tmp = t_1
    else if (x <= 4d+73) then
        tmp = log(t) - (y + z)
    else if ((x <= 8.8d+95) .or. (.not. (x <= 2.2d+136))) then
        tmp = t_1
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -7.2e+53) {
		tmp = t_1;
	} else if (x <= 4e+73) {
		tmp = Math.log(t) - (y + z);
	} else if ((x <= 8.8e+95) || !(x <= 2.2e+136)) {
		tmp = t_1;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -7.2e+53:
		tmp = t_1
	elif x <= 4e+73:
		tmp = math.log(t) - (y + z)
	elif (x <= 8.8e+95) or not (x <= 2.2e+136):
		tmp = t_1
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -7.2e+53)
		tmp = t_1;
	elseif (x <= 4e+73)
		tmp = Float64(log(t) - Float64(y + z));
	elseif ((x <= 8.8e+95) || !(x <= 2.2e+136))
		tmp = t_1;
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -7.2e+53)
		tmp = t_1;
	elseif (x <= 4e+73)
		tmp = log(t) - (y + z);
	elseif ((x <= 8.8e+95) || ~((x <= 2.2e+136)))
		tmp = t_1;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+53], t$95$1, If[LessEqual[x, 4e+73], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.8e+95], N[Not[LessEqual[x, 2.2e+136]], $MachinePrecision]], t$95$1, N[((-z) - y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2e53 or 3.99999999999999993e73 < x < 8.7999999999999996e95 or 2.1999999999999999e136 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 71.2%

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

   if -7.2e53 < x < 3.99999999999999993e73

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.9%

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

   if 8.7999999999999996e95 < x < 2.1999999999999999e136

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. add-sqr-sqrt 99.9%

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

      6. associate-*r* 99.5%

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

      7. fma-def 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in z around inf 99.5%

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

   5. Taylor expanded in x around 0 73.8%

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

      1. distribute-lft-in 73.8%

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

      2. neg-mul-1 73.8%

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

      3. unsub-neg 73.8%

         \[\leadsto \color{blue}{-1 \cdot y - z} \]

      4. mul-1-neg 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+95} \lor \neg \left(x \leq 2.2 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 6: 66.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) - y\\ t_2 := x \cdot \log y\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- z) y)) (t_2 (* x (log y))))
   (if (<= z -1.02e+55)
     t_1
     (if (<= z -1.65e-131)
       t_2
       (if (<= z 7.2e-22) (- (log t) y) (if (<= z 4.7e+32) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double t_2 = x * log(y);
	double tmp;
	if (z <= -1.02e+55) {
		tmp = t_1;
	} else if (z <= -1.65e-131) {
		tmp = t_2;
	} else if (z <= 7.2e-22) {
		tmp = log(t) - y;
	} else if (z <= 4.7e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = -z - y
    t_2 = x * log(y)
    if (z <= (-1.02d+55)) then
        tmp = t_1
    else if (z <= (-1.65d-131)) then
        tmp = t_2
    else if (z <= 7.2d-22) then
        tmp = log(t) - y
    else if (z <= 4.7d+32) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -z - y;
	double t_2 = x * Math.log(y);
	double tmp;
	if (z <= -1.02e+55) {
		tmp = t_1;
	} else if (z <= -1.65e-131) {
		tmp = t_2;
	} else if (z <= 7.2e-22) {
		tmp = Math.log(t) - y;
	} else if (z <= 4.7e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z - y
	t_2 = x * math.log(y)
	tmp = 0
	if z <= -1.02e+55:
		tmp = t_1
	elif z <= -1.65e-131:
		tmp = t_2
	elif z <= 7.2e-22:
		tmp = math.log(t) - y
	elif z <= 4.7e+32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) - y)
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -1.02e+55)
		tmp = t_1;
	elseif (z <= -1.65e-131)
		tmp = t_2;
	elseif (z <= 7.2e-22)
		tmp = Float64(log(t) - y);
	elseif (z <= 4.7e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z - y;
	t_2 = x * log(y);
	tmp = 0.0;
	if (z <= -1.02e+55)
		tmp = t_1;
	elseif (z <= -1.65e-131)
		tmp = t_2;
	elseif (z <= 7.2e-22)
		tmp = log(t) - y;
	elseif (z <= 4.7e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+55], t$95$1, If[LessEqual[z, -1.65e-131], t$95$2, If[LessEqual[z, 7.2e-22], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[z, 4.7e+32], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02000000000000002e55 or 4.70000000000000023e32 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. add-sqr-sqrt 54.0%

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

      6. associate-*r* 54.0%

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

      7. fma-def 54.0%

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

   3. Applied egg-rr 54.0%

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

   4. Taylor expanded in z around inf 54.0%

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

   5. Taylor expanded in x around 0 89.2%

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

      1. distribute-lft-in 89.2%

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

      2. neg-mul-1 89.2%

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

      3. unsub-neg 89.2%

         \[\leadsto \color{blue}{-1 \cdot y - z} \]

      4. mul-1-neg 89.2%

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

   7. Simplified 89.2%

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

   if -1.02000000000000002e55 < z < -1.6500000000000001e-131 or 7.1999999999999996e-22 < z < 4.70000000000000023e32

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 62.5%

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

   if -1.6500000000000001e-131 < z < 7.1999999999999996e-22

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 69.3%

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

   3. Taylor expanded in z around 0 69.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 7: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+52} \lor \neg \left(x \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e+52) (not (<= x 8e+71)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e+52) || !(x <= 8e+71)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.7d+52)) .or. (.not. (x <= 8d+71))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e+52) || !(x <= 8e+71)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e+52) or not (x <= 8e+71):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e+52) || !(x <= 8e+71))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e+52) || ~((x <= 8e+71)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e+52], N[Not[LessEqual[x, 8e+71]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e52 or 8.0000000000000003e71 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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-sqr-sqrt 57.9%

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

      6. associate-*r* 57.8%

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

      7. fma-def 57.8%

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

   3. Applied egg-rr 57.8%

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

   4. Taylor expanded in z around inf 57.8%

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

   5. Taylor expanded in z around 0 80.1%

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

      1. *-commutative 80.1%

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

   7. Simplified 80.1%

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

   if -1.7e52 < x < 8.0000000000000003e71

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+52} \lor \neg \left(x \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 8: 89.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+46} \lor \neg \left(x \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e+46) (not (<= x 5e+56)))
   (- (* x (log y)) z)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e+46) || !(x <= 5e+56)) {
		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 <= (-2.6d+46)) .or. (.not. (x <= 5d+56))) 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 <= -2.6e+46) || !(x <= 5e+56)) {
		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 <= -2.6e+46) or not (x <= 5e+56):
		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 <= -2.6e+46) || !(x <= 5e+56))
		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 <= -2.6e+46) || ~((x <= 5e+56)))
		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, -2.6e+46], N[Not[LessEqual[x, 5e+56]], $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 < -2.60000000000000013e46 or 5.00000000000000024e56 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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-sqr-sqrt 59.9%

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

      6. associate-*r* 59.8%

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

      7. fma-def 59.8%

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

   3. Applied egg-rr 59.8%

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

   4. Taylor expanded in z around inf 59.8%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. *-commutative 85.3%

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

   7. Simplified 85.3%

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

   if -2.60000000000000013e46 < x < 5.00000000000000024e56

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+46} \lor \neg \left(x \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 9: 48.7% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+61}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -350000.0) (- z) (if (<= z 1.05e+61) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -350000.0) {
		tmp = -z;
	} else if (z <= 1.05e+61) {
		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 <= (-350000.0d0)) then
        tmp = -z
    else if (z <= 1.05d+61) 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 <= -350000.0) {
		tmp = -z;
	} else if (z <= 1.05e+61) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -350000.0:
		tmp = -z
	elif z <= 1.05e+61:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -350000.0)
		tmp = Float64(-z);
	elseif (z <= 1.05e+61)
		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 <= -350000.0)
		tmp = -z;
	elseif (z <= 1.05e+61)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -350000.0], (-z), If[LessEqual[z, 1.05e+61], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e5 or 1.0500000000000001e61 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. neg-mul-1 71.1%

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

   4. Simplified 71.1%

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

   if -3.5e5 < z < 1.0500000000000001e61

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 38.1%

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

      1. neg-mul-1 38.1%

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

   4. Simplified 38.1%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+61}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 58.0% accurate, 52.3× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) - y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-z) - y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
2. 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-sqr-sqrt 54.9%

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

   6. associate-*r* 54.9%

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

   7. fma-def 54.9%

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

3. Applied egg-rr 54.9%

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

4. Taylor expanded in z around inf 47.2%

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

5. Taylor expanded in x around 0 60.1%

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

   1. distribute-lft-in 60.1%

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

   2. neg-mul-1 60.1%

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

   3. unsub-neg 60.1%

      \[\leadsto \color{blue}{-1 \cdot y - z} \]

   4. mul-1-neg 60.1%

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

7. Simplified 60.1%

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

8. Final simplification 60.1%

   \[\leadsto \left(-z\right) - y \]

Alternative 11: 29.5% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around inf 27.6%

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

   1. neg-mul-1 27.6%

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

4. Simplified 27.6%

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

5. Final simplification 27.6%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023290 
(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)))