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

Percentage Accurate: 99.9% → 99.9%

Time: 10.7s

Alternatives: 12

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. Add Preprocessing

Alternative 2: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+15} \lor \neg \left(t\_2 \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;t\_1 - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (or (<= t_2 -5e+15) (not (<= t_2 2e-13)))
     (- t_1 (+ y z))
     (- (log t) (+ y z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if ((t_2 <= -5e+15) || !(t_2 <= 2e-13)) {
		tmp = t_1 - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if ((t_2 <= (-5d+15)) .or. (.not. (t_2 <= 2d-13))) then
        tmp = t_1 - (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 t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if ((t_2 <= -5e+15) || !(t_2 <= 2e-13)) {
		tmp = t_1 - (y + z);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if (t_2 <= -5e+15) or not (t_2 <= 2e-13):
		tmp = t_1 - (y + z)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if ((t_2 <= -5e+15) || !(t_2 <= 2e-13))
		tmp = Float64(t_1 - Float64(y + z));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if ((t_2 <= -5e+15) || ~((t_2 <= 2e-13)))
		tmp = t_1 - (y + z);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+15], N[Not[LessEqual[t$95$2, 2e-13]], $MachinePrecision]], N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e15 or 2.0000000000000001e-13 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   if -5e15 < (-.f64 (*.f64 x (log.f64 y)) y) < 2.0000000000000001e-13

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+15} \lor \neg \left(x \cdot \log y - y \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \log y - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 96.0) (- (+ t_1 (log t)) z) (- t_1 (+ y z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 96.0) {
		tmp = (t_1 + log(t)) - z;
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 96.0d0) then
        tmp = (t_1 + log(t)) - z
    else
        tmp = t_1 - (y + 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 (y <= 96.0) {
		tmp = (t_1 + Math.log(t)) - z;
	} else {
		tmp = t_1 - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 96.0:
		tmp = (t_1 + math.log(t)) - z
	else:
		tmp = t_1 - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 96.0)
		tmp = Float64(Float64(t_1 + log(t)) - z);
	else
		tmp = Float64(t_1 - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 96.0)
		tmp = (t_1 + log(t)) - z;
	else
		tmp = t_1 - (y + 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[y, 96.0], N[(N[(t$95$1 + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 96

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.4%

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

   if 96 < y

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 98.8%

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

4. Final simplification 99.1%

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

Alternative 4: 47.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -340000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-111}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-199}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-228}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-267}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+87}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -340000000000.0)
     t_1
     (if (<= x -3.3e-111)
       (- z)
       (if (<= x -1.9e-199)
         (log t)
         (if (<= x -2.15e-228)
           (- z)
           (if (<= x -7.6e-267)
             (- y)
             (if (<= x 3.2e+54) (- z) (if (<= x 4.6e+87) (- y) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -340000000000.0) {
		tmp = t_1;
	} else if (x <= -3.3e-111) {
		tmp = -z;
	} else if (x <= -1.9e-199) {
		tmp = log(t);
	} else if (x <= -2.15e-228) {
		tmp = -z;
	} else if (x <= -7.6e-267) {
		tmp = -y;
	} else if (x <= 3.2e+54) {
		tmp = -z;
	} else if (x <= 4.6e+87) {
		tmp = -y;
	} 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) :: tmp
    t_1 = x * log(y)
    if (x <= (-340000000000.0d0)) then
        tmp = t_1
    else if (x <= (-3.3d-111)) then
        tmp = -z
    else if (x <= (-1.9d-199)) then
        tmp = log(t)
    else if (x <= (-2.15d-228)) then
        tmp = -z
    else if (x <= (-7.6d-267)) then
        tmp = -y
    else if (x <= 3.2d+54) then
        tmp = -z
    else if (x <= 4.6d+87) then
        tmp = -y
    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 = x * Math.log(y);
	double tmp;
	if (x <= -340000000000.0) {
		tmp = t_1;
	} else if (x <= -3.3e-111) {
		tmp = -z;
	} else if (x <= -1.9e-199) {
		tmp = Math.log(t);
	} else if (x <= -2.15e-228) {
		tmp = -z;
	} else if (x <= -7.6e-267) {
		tmp = -y;
	} else if (x <= 3.2e+54) {
		tmp = -z;
	} else if (x <= 4.6e+87) {
		tmp = -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -340000000000.0:
		tmp = t_1
	elif x <= -3.3e-111:
		tmp = -z
	elif x <= -1.9e-199:
		tmp = math.log(t)
	elif x <= -2.15e-228:
		tmp = -z
	elif x <= -7.6e-267:
		tmp = -y
	elif x <= 3.2e+54:
		tmp = -z
	elif x <= 4.6e+87:
		tmp = -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -340000000000.0)
		tmp = t_1;
	elseif (x <= -3.3e-111)
		tmp = Float64(-z);
	elseif (x <= -1.9e-199)
		tmp = log(t);
	elseif (x <= -2.15e-228)
		tmp = Float64(-z);
	elseif (x <= -7.6e-267)
		tmp = Float64(-y);
	elseif (x <= 3.2e+54)
		tmp = Float64(-z);
	elseif (x <= 4.6e+87)
		tmp = Float64(-y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -340000000000.0)
		tmp = t_1;
	elseif (x <= -3.3e-111)
		tmp = -z;
	elseif (x <= -1.9e-199)
		tmp = log(t);
	elseif (x <= -2.15e-228)
		tmp = -z;
	elseif (x <= -7.6e-267)
		tmp = -y;
	elseif (x <= 3.2e+54)
		tmp = -z;
	elseif (x <= 4.6e+87)
		tmp = -y;
	else
		tmp = t_1;
	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, -340000000000.0], t$95$1, If[LessEqual[x, -3.3e-111], (-z), If[LessEqual[x, -1.9e-199], N[Log[t], $MachinePrecision], If[LessEqual[x, -2.15e-228], (-z), If[LessEqual[x, -7.6e-267], (-y), If[LessEqual[x, 3.2e+54], (-z), If[LessEqual[x, 4.6e+87], (-y), t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4e11 or 4.6000000000000003e87 < x

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. +-commutative 65.6%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in x around inf 69.2%

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

   if -3.4e11 < x < -3.3e-111 or -1.8999999999999999e-199 < x < -2.15e-228 or -7.60000000000000006e-267 < x < 3.2e54

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. mul-1-neg 48.8%

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

   7. Simplified 48.8%

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

   if -3.3e-111 < x < -1.8999999999999999e-199

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in y around 0 81.7%

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

   7. Taylor expanded in z around 0 63.7%

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

   if -2.15e-228 < x < -7.60000000000000006e-267 or 3.2e54 < x < 4.6000000000000003e87

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. mul-1-neg 60.8%

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

   7. Simplified 60.8%

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

Alternative 5: 59.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \log t - z\\ \mathbf{if}\;x \leq -2400000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-231}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (* x (log y))) (t_3 (- (log t) z)))
   (if (<= x -2400000000000.0)
     t_2
     (if (<= x -3.9e-231)
       t_3
       (if (<= x -1.05e-266)
         t_1
         (if (<= x 3.7e+55) t_3 (if (<= x 4.8e+86) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = x * log(y);
	double t_3 = log(t) - z;
	double tmp;
	if (x <= -2400000000000.0) {
		tmp = t_2;
	} else if (x <= -3.9e-231) {
		tmp = t_3;
	} else if (x <= -1.05e-266) {
		tmp = t_1;
	} else if (x <= 3.7e+55) {
		tmp = t_3;
	} else if (x <= 4.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) - y
    t_2 = x * log(y)
    t_3 = log(t) - z
    if (x <= (-2400000000000.0d0)) then
        tmp = t_2
    else if (x <= (-3.9d-231)) then
        tmp = t_3
    else if (x <= (-1.05d-266)) then
        tmp = t_1
    else if (x <= 3.7d+55) then
        tmp = t_3
    else if (x <= 4.8d+86) then
        tmp = t_1
    else
        tmp = t_2
    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) - y;
	double t_2 = x * Math.log(y);
	double t_3 = Math.log(t) - z;
	double tmp;
	if (x <= -2400000000000.0) {
		tmp = t_2;
	} else if (x <= -3.9e-231) {
		tmp = t_3;
	} else if (x <= -1.05e-266) {
		tmp = t_1;
	} else if (x <= 3.7e+55) {
		tmp = t_3;
	} else if (x <= 4.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = x * math.log(y)
	t_3 = math.log(t) - z
	tmp = 0
	if x <= -2400000000000.0:
		tmp = t_2
	elif x <= -3.9e-231:
		tmp = t_3
	elif x <= -1.05e-266:
		tmp = t_1
	elif x <= 3.7e+55:
		tmp = t_3
	elif x <= 4.8e+86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(x * log(y))
	t_3 = Float64(log(t) - z)
	tmp = 0.0
	if (x <= -2400000000000.0)
		tmp = t_2;
	elseif (x <= -3.9e-231)
		tmp = t_3;
	elseif (x <= -1.05e-266)
		tmp = t_1;
	elseif (x <= 3.7e+55)
		tmp = t_3;
	elseif (x <= 4.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = x * log(y);
	t_3 = log(t) - z;
	tmp = 0.0;
	if (x <= -2400000000000.0)
		tmp = t_2;
	elseif (x <= -3.9e-231)
		tmp = t_3;
	elseif (x <= -1.05e-266)
		tmp = t_1;
	elseif (x <= 3.7e+55)
		tmp = t_3;
	elseif (x <= 4.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -2400000000000.0], t$95$2, If[LessEqual[x, -3.9e-231], t$95$3, If[LessEqual[x, -1.05e-266], t$95$1, If[LessEqual[x, 3.7e+55], t$95$3, If[LessEqual[x, 4.8e+86], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e12 or 4.8000000000000001e86 < x

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. +-commutative 65.6%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in x around inf 69.2%

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

   if -2.4e12 < x < -3.8999999999999998e-231 or -1.04999999999999998e-266 < x < 3.7000000000000002e55

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 96.5%

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

   6. Taylor expanded in y around 0 69.8%

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

   if -3.8999999999999998e-231 < x < -1.04999999999999998e-266 or 3.7000000000000002e55 < x < 4.8000000000000001e86

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 96.1%

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

   6. Taylor expanded in z around 0 77.7%

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

Alternative 6: 59.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-116}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -1.15e+63)
     t_1
     (if (<= x -6.8e-43)
       t_2
       (if (<= x -3.6e-116) (- z) (if (<= x 1.5e+88) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -1.15e+63) {
		tmp = t_1;
	} else if (x <= -6.8e-43) {
		tmp = t_2;
	} else if (x <= -3.6e-116) {
		tmp = -z;
	} else if (x <= 1.5e+88) {
		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 = x * log(y)
    t_2 = log(t) - y
    if (x <= (-1.15d+63)) then
        tmp = t_1
    else if (x <= (-6.8d-43)) then
        tmp = t_2
    else if (x <= (-3.6d-116)) then
        tmp = -z
    else if (x <= 1.5d+88) 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 = x * Math.log(y);
	double t_2 = Math.log(t) - y;
	double tmp;
	if (x <= -1.15e+63) {
		tmp = t_1;
	} else if (x <= -6.8e-43) {
		tmp = t_2;
	} else if (x <= -3.6e-116) {
		tmp = -z;
	} else if (x <= 1.5e+88) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -1.15e+63:
		tmp = t_1
	elif x <= -6.8e-43:
		tmp = t_2
	elif x <= -3.6e-116:
		tmp = -z
	elif x <= 1.5e+88:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -1.15e+63)
		tmp = t_1;
	elseif (x <= -6.8e-43)
		tmp = t_2;
	elseif (x <= -3.6e-116)
		tmp = Float64(-z);
	elseif (x <= 1.5e+88)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = log(t) - y;
	tmp = 0.0;
	if (x <= -1.15e+63)
		tmp = t_1;
	elseif (x <= -6.8e-43)
		tmp = t_2;
	elseif (x <= -3.6e-116)
		tmp = -z;
	elseif (x <= 1.5e+88)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -1.15e+63], t$95$1, If[LessEqual[x, -6.8e-43], t$95$2, If[LessEqual[x, -3.6e-116], (-z), If[LessEqual[x, 1.5e+88], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.14999999999999997e63 or 1.50000000000000003e88 < 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. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. +-commutative 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in x around inf 73.7%

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

   if -1.14999999999999997e63 < x < -6.8000000000000001e-43 or -3.59999999999999975e-116 < x < 1.50000000000000003e88

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.8%

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

   6. Taylor expanded in z around 0 59.9%

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

   if -6.8000000000000001e-43 < x < -3.59999999999999975e-116

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 69.7%

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

      1. mul-1-neg 69.7%

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

   7. Simplified 69.7%

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

Alternative 7: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+26} \lor \neg \left(x \leq 7.5 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.5e+26) (not (<= x 7.5e+85)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.5e+26) || !(x <= 7.5e+85)) {
		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 <= (-3.5d+26)) .or. (.not. (x <= 7.5d+85))) 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 <= -3.5e+26) || !(x <= 7.5e+85)) {
		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 <= -3.5e+26) or not (x <= 7.5e+85):
		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 <= -3.5e+26) || !(x <= 7.5e+85))
		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 <= -3.5e+26) || ~((x <= 7.5e+85)))
		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, -3.5e+26], N[Not[LessEqual[x, 7.5e+85]], $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 < -3.4999999999999999e26 or 7.49999999999999942e85 < x

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.5%

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

   if -3.4999999999999999e26 < x < 7.49999999999999942e85

   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. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 96.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+26} \lor \neg \left(x \leq 7.5 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+63} \lor \neg \left(x \leq 1.15 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e+63) (not (<= x 1.15e+158)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+63) || !(x <= 1.15e+158)) {
		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 <= (-1.35d+63)) .or. (.not. (x <= 1.15d+158))) 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 <= -1.35e+63) || !(x <= 1.15e+158)) {
		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 <= -1.35e+63) or not (x <= 1.15e+158):
		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 <= -1.35e+63) || !(x <= 1.15e+158))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.35e+63) || ~((x <= 1.15e+158)))
		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, -1.35e+63], N[Not[LessEqual[x, 1.15e+158]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000009e63 or 1.14999999999999993e158 < 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. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. +-commutative 64.2%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in x around inf 77.7%

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

   if -1.35000000000000009e63 < x < 1.14999999999999993e158

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+63} \lor \neg \left(x \leq 1.15 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-99}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-69}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.25e-99)
   (- z)
   (if (<= y 1.35e-69) (log t) (if (<= y 1.18e+42) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.25e-99) {
		tmp = -z;
	} else if (y <= 1.35e-69) {
		tmp = log(t);
	} else if (y <= 1.18e+42) {
		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 <= 1.25d-99) then
        tmp = -z
    else if (y <= 1.35d-69) then
        tmp = log(t)
    else if (y <= 1.18d+42) 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 <= 1.25e-99) {
		tmp = -z;
	} else if (y <= 1.35e-69) {
		tmp = Math.log(t);
	} else if (y <= 1.18e+42) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.25e-99:
		tmp = -z
	elif y <= 1.35e-69:
		tmp = math.log(t)
	elif y <= 1.18e+42:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.25e-99)
		tmp = Float64(-z);
	elseif (y <= 1.35e-69)
		tmp = log(t);
	elseif (y <= 1.18e+42)
		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 <= 1.25e-99)
		tmp = -z;
	elseif (y <= 1.35e-69)
		tmp = log(t);
	elseif (y <= 1.18e+42)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.25e-99], (-z), If[LessEqual[y, 1.35e-69], N[Log[t], $MachinePrecision], If[LessEqual[y, 1.18e+42], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.24999999999999992e-99 or 1.3499999999999999e-69 < y < 1.18e42

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 40.7%

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

      1. mul-1-neg 40.7%

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

   7. Simplified 40.7%

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

   if 1.24999999999999992e-99 < y < 1.3499999999999999e-69

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 62.4%

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

   6. Taylor expanded in y around 0 62.4%

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

   7. Taylor expanded in z around 0 54.7%

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

   if 1.18e42 < y

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.1%

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

      1. mul-1-neg 64.1%

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

   7. Simplified 64.1%

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

Alternative 10: 48.4% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+42}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.45e+42) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.45e+42) {
		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 <= 2.45d+42) 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 <= 2.45e+42) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.45e+42:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.45e+42)
		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 <= 2.45e+42)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.45e+42], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.4500000000000001e42

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   2. 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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 38.2%

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

      1. mul-1-neg 38.2%

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

   7. Simplified 38.2%

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

   if 2.4500000000000001e42 < y

   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. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.1%

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

      1. mul-1-neg 64.1%

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

   7. Simplified 64.1%

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

Alternative 11: 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. 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. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 27.8%

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

   1. mul-1-neg 27.8%

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

7. Simplified 27.8%

   \[\leadsto \color{blue}{-y} \]
8. Add Preprocessing

Alternative 12: 2.2% accurate, 209.0× 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 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. 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. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 84.5%

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

6. Taylor expanded in y around inf 21.6%

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

   1. associate-*r/ 21.6%

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

   2. mul-1-neg 21.6%

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

8. Simplified 21.6%

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

   1. clear-num 21.5%

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

   2. un-div-inv 21.7%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.2%

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

   5. sqr-neg 2.2%

      \[\leadsto \frac{x}{\frac{x}{\sqrt{\color{blue}{y \cdot y}}}} \]

   6. sqrt-unprod 2.3%

      \[\leadsto \frac{x}{\frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}} \]

   7. add-sqr-sqrt 2.3%

      \[\leadsto \frac{x}{\frac{x}{\color{blue}{y}}} \]

10. Applied egg-rr 2.3%

    \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]
11. Step-by-step derivation

    1. associate-/r/ 2.3%

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

    2. *-inverses 2.3%

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

    3. *-lft-identity 2.3%

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

12. Simplified 2.3%

    \[\leadsto \color{blue}{y} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024101 
(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)))