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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 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: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(\log t - y\right) - z\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+59}:\\ \;\;\;\;\log t + t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- (log t) y) z)))
   (if (<= x -1.32e+79)
     t_1
     (if (<= x 5.1e+17)
       t_2
       (if (<= x 1.75e+59) (+ (log t) t_1) (if (<= x 1.2e+119) 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) - z;
	double tmp;
	if (x <= -1.32e+79) {
		tmp = t_1;
	} else if (x <= 5.1e+17) {
		tmp = t_2;
	} else if (x <= 1.75e+59) {
		tmp = log(t) + t_1;
	} else if (x <= 1.2e+119) {
		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) - z
    if (x <= (-1.32d+79)) then
        tmp = t_1
    else if (x <= 5.1d+17) then
        tmp = t_2
    else if (x <= 1.75d+59) then
        tmp = log(t) + t_1
    else if (x <= 1.2d+119) 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) - z;
	double tmp;
	if (x <= -1.32e+79) {
		tmp = t_1;
	} else if (x <= 5.1e+17) {
		tmp = t_2;
	} else if (x <= 1.75e+59) {
		tmp = Math.log(t) + t_1;
	} else if (x <= 1.2e+119) {
		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) - z
	tmp = 0
	if x <= -1.32e+79:
		tmp = t_1
	elif x <= 5.1e+17:
		tmp = t_2
	elif x <= 1.75e+59:
		tmp = math.log(t) + t_1
	elif x <= 1.2e+119:
		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(Float64(log(t) - y) - z)
	tmp = 0.0
	if (x <= -1.32e+79)
		tmp = t_1;
	elseif (x <= 5.1e+17)
		tmp = t_2;
	elseif (x <= 1.75e+59)
		tmp = Float64(log(t) + t_1);
	elseif (x <= 1.2e+119)
		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) - z;
	tmp = 0.0;
	if (x <= -1.32e+79)
		tmp = t_1;
	elseif (x <= 5.1e+17)
		tmp = t_2;
	elseif (x <= 1.75e+59)
		tmp = log(t) + t_1;
	elseif (x <= 1.2e+119)
		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[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -1.32e+79], t$95$1, If[LessEqual[x, 5.1e+17], t$95$2, If[LessEqual[x, 1.75e+59], N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.2e+119], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.32e79 or 1.2e119 < 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%

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

      2. associate-+l- 99.7%

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

      3. add-cube-cbrt 98.4%

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

      4. associate-*r* 98.4%

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

      5. fma-neg 98.4%

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

      6. pow2 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in x around inf 73.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 73.4%

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

      2. *-lft-identity 73.4%

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

   6. Simplified 73.4%

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

   if -1.32e79 < x < 5.1e17 or 1.75e59 < x < 1.2e119

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.5%

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

      1. associate--r+ 94.5%

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

   4. Simplified 94.5%

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

   if 5.1e17 < x < 1.75e59

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 89.5%

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

   3. Taylor expanded in z around 0 70.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+17}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+59}:\\ \;\;\;\;\log t + x \cdot \log y\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-16} \lor \neg \left(x \leq 5 \cdot 10^{+17}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.8e-16) (not (<= x 5e+17)))
   (- (+ (log t) (* x (log y))) y)
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e-16) || !(x <= 5e+17)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = (log(t) - y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.8d-16)) .or. (.not. (x <= 5d+17))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = (log(t) - y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e-16) || !(x <= 5e+17)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = (Math.log(t) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.8e-16) or not (x <= 5e+17):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = (math.log(t) - y) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.8e-16) || !(x <= 5e+17))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.8e-16) || ~((x <= 5e+17)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = (log(t) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.8e-16], N[Not[LessEqual[x, 5e+17]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e-16 or 5e17 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 83.8%

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

   if -2.8000000000000001e-16 < x < 5e17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. associate--r+ 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-16} \lor \neg \left(x \leq 5 \cdot 10^{+17}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]

Alternative 4: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;y \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= y 6.5e+19) (- t_1 z) (- t_1 y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (y <= 6.5e+19) {
		tmp = t_1 - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) + (x * log(y))
    if (y <= 6.5d+19) then
        tmp = t_1 - z
    else
        tmp = t_1 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) + (x * Math.log(y));
	double tmp;
	if (y <= 6.5e+19) {
		tmp = t_1 - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if y <= 6.5e+19:
		tmp = t_1 - z
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (y <= 6.5e+19)
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (y <= 6.5e+19)
		tmp = t_1 - z;
	else
		tmp = t_1 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 6.5e+19], N[(t$95$1 - z), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5e19

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.1%

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

   if 6.5e19 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]

Alternative 5: 82.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+79} \lor \neg \left(x \leq 3 \cdot 10^{+17} \lor \neg \left(x \leq 2 \cdot 10^{+59}\right) \land x \leq 1.55 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.8e+79)
         (not (or (<= x 3e+17) (and (not (<= x 2e+59)) (<= x 1.55e+119)))))
   (* x (log y))
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e+79) || !((x <= 3e+17) || (!(x <= 2e+59) && (x <= 1.55e+119)))) {
		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 <= (-4.8d+79)) .or. (.not. (x <= 3d+17) .or. (.not. (x <= 2d+59)) .and. (x <= 1.55d+119))) 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 <= -4.8e+79) || !((x <= 3e+17) || (!(x <= 2e+59) && (x <= 1.55e+119)))) {
		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 <= -4.8e+79) or not ((x <= 3e+17) or (not (x <= 2e+59) and (x <= 1.55e+119))):
		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 <= -4.8e+79) || !((x <= 3e+17) || (!(x <= 2e+59) && (x <= 1.55e+119))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.8e+79) || ~(((x <= 3e+17) || (~((x <= 2e+59)) && (x <= 1.55e+119)))))
		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, -4.8e+79], N[Not[Or[LessEqual[x, 3e+17], And[N[Not[LessEqual[x, 2e+59]], $MachinePrecision], LessEqual[x, 1.55e+119]]]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999971e79 or 3e17 < x < 1.99999999999999994e59 or 1.54999999999999998e119 < x

   1. Initial program 99.6%

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

      1. associate--l- 99.6%

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

      2. associate-+l- 99.6%

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

      3. add-cube-cbrt 98.4%

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

      4. associate-*r* 98.4%

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

      5. fma-neg 98.4%

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

      6. pow2 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in x around inf 73.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 73.1%

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

      2. *-lft-identity 73.1%

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

   6. Simplified 73.1%

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

   if -4.79999999999999971e79 < x < 3e17 or 1.99999999999999994e59 < x < 1.54999999999999998e119

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.5%

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

      1. associate--r+ 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+79} \lor \neg \left(x \leq 3 \cdot 10^{+17} \lor \neg \left(x \leq 2 \cdot 10^{+59}\right) \land x \leq 1.55 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]

Alternative 6: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.18 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-163}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 1.18e-287)
     t_1
     (if (<= y 5.3e-163) (- z) (if (<= y 4.7e+67) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 1.18e-287) {
		tmp = t_1;
	} else if (y <= 5.3e-163) {
		tmp = -z;
	} else if (y <= 4.7e+67) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 1.18d-287) then
        tmp = t_1
    else if (y <= 5.3d-163) then
        tmp = -z
    else if (y <= 4.7d+67) then
        tmp = t_1
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (y <= 1.18e-287) {
		tmp = t_1;
	} else if (y <= 5.3e-163) {
		tmp = -z;
	} else if (y <= 4.7e+67) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 1.18e-287:
		tmp = t_1
	elif y <= 5.3e-163:
		tmp = -z
	elif y <= 4.7e+67:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.18e-287)
		tmp = t_1;
	elseif (y <= 5.3e-163)
		tmp = Float64(-z);
	elseif (y <= 4.7e+67)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 1.18e-287)
		tmp = t_1;
	elseif (y <= 5.3e-163)
		tmp = -z;
	elseif (y <= 4.7e+67)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.18e-287], t$95$1, If[LessEqual[y, 5.3e-163], (-z), If[LessEqual[y, 4.7e+67], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.18000000000000003e-287 or 5.30000000000000016e-163 < y < 4.70000000000000017e67

   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%

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

      2. associate-+l- 99.7%

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

      3. add-cube-cbrt 98.9%

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

      4. associate-*r* 98.9%

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

      5. fma-neg 98.9%

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

      6. pow2 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in x around inf 46.6%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 46.6%

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

      2. *-lft-identity 46.6%

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

   6. Simplified 46.6%

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

   if 1.18000000000000003e-287 < y < 5.30000000000000016e-163

   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%

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

      2. associate-+l- 99.9%

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

      3. add-cube-cbrt 99.5%

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

      4. associate-*r* 99.6%

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

      5. fma-neg 99.6%

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

      6. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around inf 50.2%

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

      1. neg-mul-1 50.2%

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

   6. Simplified 50.2%

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

   if 4.70000000000000017e67 < y

   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%

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

      2. associate-+l- 100.0%

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

      3. add-cube-cbrt 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-neg 99.7%

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

      6. pow2 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. neg-mul-1 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-163}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7: 58.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 3 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= y 3e-106)
     t_1
     (if (<= y 5.8e-53) (* x (log y)) (if (<= y 3.5e+19) t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (y <= 3e-106) {
		tmp = t_1;
	} else if (y <= 5.8e-53) {
		tmp = x * log(y);
	} else if (y <= 3.5e+19) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (y <= 3d-106) then
        tmp = t_1
    else if (y <= 5.8d-53) then
        tmp = x * log(y)
    else if (y <= 3.5d+19) then
        tmp = t_1
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double tmp;
	if (y <= 3e-106) {
		tmp = t_1;
	} else if (y <= 5.8e-53) {
		tmp = x * Math.log(y);
	} else if (y <= 3.5e+19) {
		tmp = t_1;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if y <= 3e-106:
		tmp = t_1
	elif y <= 5.8e-53:
		tmp = x * math.log(y)
	elif y <= 3.5e+19:
		tmp = t_1
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (y <= 3e-106)
		tmp = t_1;
	elseif (y <= 5.8e-53)
		tmp = Float64(x * log(y));
	elseif (y <= 3.5e+19)
		tmp = t_1;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (y <= 3e-106)
		tmp = t_1;
	elseif (y <= 5.8e-53)
		tmp = x * log(y);
	elseif (y <= 3.5e+19)
		tmp = t_1;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 3e-106], t$95$1, If[LessEqual[y, 5.8e-53], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+19], t$95$1, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.00000000000000019e-106 or 5.7999999999999996e-53 < y < 3.5e19

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.7%

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

      1. neg-mul-1 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. +-commutative 66.7%

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

      3. sub-neg 66.7%

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

   7. Simplified 66.7%

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

   if 3.00000000000000019e-106 < y < 5.7999999999999996e-53

   1. Initial program 99.6%

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

      1. associate--l- 99.6%

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

      2. associate-+l- 99.6%

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

      3. add-cube-cbrt 98.1%

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

      4. associate-*r* 98.1%

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

      5. fma-neg 98.1%

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

      6. pow2 98.1%

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

   3. Applied egg-rr 98.1%

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

   4. Taylor expanded in x around inf 66.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 66.3%

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

      2. *-lft-identity 66.3%

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

   6. Simplified 66.3%

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

   if 3.5e19 < 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%

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

      2. associate-+l- 99.9%

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

      3. add-cube-cbrt 99.6%

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

      4. associate-*r* 99.6%

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

      5. fma-neg 99.6%

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

      6. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 61.6%

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

      1. neg-mul-1 61.6%

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

   6. Simplified 61.6%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-106}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 8: 47.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-41}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1e-74)
   (- z)
   (if (<= y 9e-41) (log t) (if (<= y 7.8e+18) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e-74) {
		tmp = -z;
	} else if (y <= 9e-41) {
		tmp = log(t);
	} else if (y <= 7.8e+18) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1d-74) then
        tmp = -z
    else if (y <= 9d-41) then
        tmp = log(t)
    else if (y <= 7.8d+18) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e-74) {
		tmp = -z;
	} else if (y <= 9e-41) {
		tmp = Math.log(t);
	} else if (y <= 7.8e+18) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1e-74:
		tmp = -z
	elif y <= 9e-41:
		tmp = math.log(t)
	elif y <= 7.8e+18:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1e-74)
		tmp = Float64(-z);
	elseif (y <= 9e-41)
		tmp = log(t);
	elseif (y <= 7.8e+18)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1e-74)
		tmp = -z;
	elseif (y <= 9e-41)
		tmp = log(t);
	elseif (y <= 7.8e+18)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1e-74], (-z), If[LessEqual[y, 9e-41], N[Log[t], $MachinePrecision], If[LessEqual[y, 7.8e+18], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 9.99999999999999958e-75 or 9e-41 < y < 7.8e18

   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%

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

      2. associate-+l- 99.8%

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

      3. add-cube-cbrt 99.2%

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

      4. associate-*r* 99.2%

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

      5. fma-neg 99.2%

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

      6. pow2 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in z around inf 42.1%

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

      1. neg-mul-1 42.1%

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

   6. Simplified 42.1%

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

   if 9.99999999999999958e-75 < y < 9e-41

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 50.2%

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

      1. neg-mul-1 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in z around 0 40.4%

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

   if 7.8e18 < 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%

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

      2. associate-+l- 99.9%

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

      3. add-cube-cbrt 99.6%

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

      4. associate-*r* 99.6%

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

      5. fma-neg 99.6%

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

      6. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. neg-mul-1 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{-74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-41}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9: 48.5% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4.3e+18) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.3e+18) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 4.3d+18) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.3e+18) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.3e+18:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.3e+18)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.3e+18)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.3e+18], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4.3e18

   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%

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

      2. associate-+l- 99.8%

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

      3. add-cube-cbrt 99.1%

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

      4. associate-*r* 99.1%

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

      5. fma-neg 99.1%

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

      6. pow2 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in z around inf 38.2%

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

      1. neg-mul-1 38.2%

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

   6. Simplified 38.2%

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

   if 4.3e18 < 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%

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

      2. associate-+l- 99.9%

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

      3. add-cube-cbrt 99.6%

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

      4. associate-*r* 99.6%

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

      5. fma-neg 99.6%

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

      6. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. neg-mul-1 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 30.0% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate--l- 99.9%

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

   2. associate-+l- 99.9%

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

   3. add-cube-cbrt 99.3%

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

   4. associate-*r* 99.3%

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

   5. fma-neg 99.3%

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

   6. pow2 99.3%

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

3. Applied egg-rr 99.3%

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

4. Taylor expanded in y around inf 29.7%

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

   1. neg-mul-1 29.7%

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

6. Simplified 29.7%

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

7. Final simplification 29.7%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023240 
(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)))