Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Percentage Accurate: 97.9% → 98.7%

Time: 9.5s

Alternatives: 16

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+277}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+277) (- x (* t (/ y (- z a)))) (+ x (* t_1 y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+277) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (t_1 * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-5d+277)) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (t_1 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+277) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (t_1 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+277:
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (t_1 * y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+277)
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(t_1 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+277)
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (t_1 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+277], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.99999999999999982e277

   1. Initial program 27.3%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 27.3%

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

      1. neg-mul-1 27.3%

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

      2. distribute-neg-frac 27.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 27.3%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z - a}} \]

      2. mul-1-neg 99.3%

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

      3. associate-*l/ 99.5%

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

      4. distribute-lft-neg-in 99.5%

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

      5. cancel-sign-sub-inv 99.5%

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

   7. Simplified 99.5%

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

   if -4.99999999999999982e277 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+277}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{z - a} \cdot y\\ \end{array} \]

Alternative 2: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= z -4.5e+93)
     (+ x y)
     (if (<= z -3.4e-27)
       t_1
       (if (<= z -1.62e-87)
         (+ x (/ y (/ a t)))
         (if (<= z -5.1e-115)
           t_1
           (if (<= z 1.1e-194)
             (+ x (* y (/ t a)))
             (if (<= z 1.8e+32) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -4.5e+93) {
		tmp = x + y;
	} else if (z <= -3.4e-27) {
		tmp = t_1;
	} else if (z <= -1.62e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = t_1;
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.8e+32) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (z <= (-4.5d+93)) then
        tmp = x + y
    else if (z <= (-3.4d-27)) then
        tmp = t_1
    else if (z <= (-1.62d-87)) then
        tmp = x + (y / (a / t))
    else if (z <= (-5.1d-115)) then
        tmp = t_1
    else if (z <= 1.1d-194) then
        tmp = x + (y * (t / a))
    else if (z <= 1.8d+32) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -4.5e+93) {
		tmp = x + y;
	} else if (z <= -3.4e-27) {
		tmp = t_1;
	} else if (z <= -1.62e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = t_1;
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.8e+32) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if z <= -4.5e+93:
		tmp = x + y
	elif z <= -3.4e-27:
		tmp = t_1
	elif z <= -1.62e-87:
		tmp = x + (y / (a / t))
	elif z <= -5.1e-115:
		tmp = t_1
	elif z <= 1.1e-194:
		tmp = x + (y * (t / a))
	elif z <= 1.8e+32:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -4.5e+93)
		tmp = Float64(x + y);
	elseif (z <= -3.4e-27)
		tmp = t_1;
	elseif (z <= -1.62e-87)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -5.1e-115)
		tmp = t_1;
	elseif (z <= 1.1e-194)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.8e+32)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -4.5e+93)
		tmp = x + y;
	elseif (z <= -3.4e-27)
		tmp = t_1;
	elseif (z <= -1.62e-87)
		tmp = x + (y / (a / t));
	elseif (z <= -5.1e-115)
		tmp = t_1;
	elseif (z <= 1.1e-194)
		tmp = x + (y * (t / a));
	elseif (z <= 1.8e+32)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+93], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.4e-27], t$95$1, If[LessEqual[z, -1.62e-87], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-115], t$95$1, If[LessEqual[z, 1.1e-194], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+32], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999991e93 or 1.7999999999999998e32 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 81.6%

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

   if -4.49999999999999991e93 < z < -3.3999999999999997e-27 or -1.6200000000000001e-87 < z < -5.0999999999999997e-115 or 1.1000000000000001e-194 < z < 1.7999999999999998e32

   1. Initial program 93.0%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 76.3%

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

      1. neg-mul-1 76.3%

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

      2. distribute-neg-frac 76.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 76.3%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in z around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. associate-/l* 69.8%

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

      5. associate-/r/ 72.2%

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

   7. Simplified 72.2%

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

   if -3.3999999999999997e-27 < z < -1.6200000000000001e-87

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   3. Step-by-step derivation

      1. associate-/l* 87.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} + x \]

   4. Simplified 87.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]

   if -5.0999999999999997e-115 < z < 1.1000000000000001e-194

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 88.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -2.7e+94)
     (+ x y)
     (if (<= z -9.5e-28)
       t_1
       (if (<= z -1.6e-87)
         (+ x (/ y (/ a t)))
         (if (<= z -5e-115)
           (- x (* t (/ y z)))
           (if (<= z 1.1e-194)
             (+ x (* y (/ t a)))
             (if (<= z 2.8e+32) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -2.7e+94) {
		tmp = x + y;
	} else if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= -1.6e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5e-115) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.8e+32) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-2.7d+94)) then
        tmp = x + y
    else if (z <= (-9.5d-28)) then
        tmp = t_1
    else if (z <= (-1.6d-87)) then
        tmp = x + (y / (a / t))
    else if (z <= (-5d-115)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.1d-194) then
        tmp = x + (y * (t / a))
    else if (z <= 2.8d+32) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -2.7e+94) {
		tmp = x + y;
	} else if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= -1.6e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5e-115) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.8e+32) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -2.7e+94:
		tmp = x + y
	elif z <= -9.5e-28:
		tmp = t_1
	elif z <= -1.6e-87:
		tmp = x + (y / (a / t))
	elif z <= -5e-115:
		tmp = x - (t * (y / z))
	elif z <= 1.1e-194:
		tmp = x + (y * (t / a))
	elif z <= 2.8e+32:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -2.7e+94)
		tmp = Float64(x + y);
	elseif (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= -1.6e-87)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -5e-115)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.1e-194)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.8e+32)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -2.7e+94)
		tmp = x + y;
	elseif (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= -1.6e-87)
		tmp = x + (y / (a / t));
	elseif (z <= -5e-115)
		tmp = x - (t * (y / z));
	elseif (z <= 1.1e-194)
		tmp = x + (y * (t / a));
	elseif (z <= 2.8e+32)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+94], N[(x + y), $MachinePrecision], If[LessEqual[z, -9.5e-28], t$95$1, If[LessEqual[z, -1.6e-87], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-115], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-194], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+32], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7000000000000001e94 or 2.8e32 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 81.6%

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

   if -2.7000000000000001e94 < z < -9.50000000000000001e-28 or 1.1000000000000001e-194 < z < 2.8e32

   1. Initial program 94.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-neg-frac 78.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 78.9%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in x around 0 82.6%

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

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z - a}} \]

      2. mul-1-neg 82.6%

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

      3. associate-*l/ 82.7%

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

      4. distribute-lft-neg-in 82.7%

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

      5. cancel-sign-sub-inv 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/l* 71.9%

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

   10. Simplified 71.9%

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

   if -9.50000000000000001e-28 < z < -1.59999999999999989e-87

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   3. Step-by-step derivation

      1. associate-/l* 87.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} + x \]

   4. Simplified 87.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]

   if -1.59999999999999989e-87 < z < -5.0000000000000003e-115

   1. Initial program 76.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 52.6%

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

      1. neg-mul-1 52.6%

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

      2. distribute-neg-frac 52.6%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 52.6%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in z around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. associate-/l* 52.8%

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

      5. associate-/r/ 75.5%

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

   7. Simplified 75.5%

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

   if -5.0000000000000003e-115 < z < 1.1000000000000001e-194

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 88.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -6.5e+93)
     (+ x y)
     (if (<= z -1.7e-27)
       t_1
       (if (<= z -1.62e-87)
         (+ x (/ y (/ a t)))
         (if (<= z -5.1e-115)
           (/ (* (- z t) y) z)
           (if (<= z 1.08e-194)
             (+ x (* y (/ t a)))
             (if (<= z 2.35e+34) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -6.5e+93) {
		tmp = x + y;
	} else if (z <= -1.7e-27) {
		tmp = t_1;
	} else if (z <= -1.62e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = ((z - t) * y) / z;
	} else if (z <= 1.08e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.35e+34) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-6.5d+93)) then
        tmp = x + y
    else if (z <= (-1.7d-27)) then
        tmp = t_1
    else if (z <= (-1.62d-87)) then
        tmp = x + (y / (a / t))
    else if (z <= (-5.1d-115)) then
        tmp = ((z - t) * y) / z
    else if (z <= 1.08d-194) then
        tmp = x + (y * (t / a))
    else if (z <= 2.35d+34) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -6.5e+93) {
		tmp = x + y;
	} else if (z <= -1.7e-27) {
		tmp = t_1;
	} else if (z <= -1.62e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = ((z - t) * y) / z;
	} else if (z <= 1.08e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.35e+34) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -6.5e+93:
		tmp = x + y
	elif z <= -1.7e-27:
		tmp = t_1
	elif z <= -1.62e-87:
		tmp = x + (y / (a / t))
	elif z <= -5.1e-115:
		tmp = ((z - t) * y) / z
	elif z <= 1.08e-194:
		tmp = x + (y * (t / a))
	elif z <= 2.35e+34:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -6.5e+93)
		tmp = Float64(x + y);
	elseif (z <= -1.7e-27)
		tmp = t_1;
	elseif (z <= -1.62e-87)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -5.1e-115)
		tmp = Float64(Float64(Float64(z - t) * y) / z);
	elseif (z <= 1.08e-194)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.35e+34)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -6.5e+93)
		tmp = x + y;
	elseif (z <= -1.7e-27)
		tmp = t_1;
	elseif (z <= -1.62e-87)
		tmp = x + (y / (a / t));
	elseif (z <= -5.1e-115)
		tmp = ((z - t) * y) / z;
	elseif (z <= 1.08e-194)
		tmp = x + (y * (t / a));
	elseif (z <= 2.35e+34)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+93], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.7e-27], t$95$1, If[LessEqual[z, -1.62e-87], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-115], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.08e-194], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+34], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4999999999999998e93 or 2.35000000000000007e34 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 81.6%

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

   if -6.4999999999999998e93 < z < -1.69999999999999985e-27 or 1.08e-194 < z < 2.35000000000000007e34

   1. Initial program 94.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-neg-frac 78.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 78.9%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in x around 0 82.6%

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

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z - a}} \]

      2. mul-1-neg 82.6%

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

      3. associate-*l/ 82.7%

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

      4. distribute-lft-neg-in 82.7%

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

      5. cancel-sign-sub-inv 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/l* 71.9%

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

   10. Simplified 71.9%

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

   if -1.69999999999999985e-27 < z < -1.6200000000000001e-87

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   3. Step-by-step derivation

      1. associate-/l* 87.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} + x \]

   4. Simplified 87.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]

   if -1.6200000000000001e-87 < z < -5.0999999999999997e-115

   1. Initial program 76.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-/l* 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in x around 0 80.8%

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

   if -5.0999999999999997e-115 < z < 1.08e-194

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 88.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+92)
   (+ x y)
   (if (<= z -2.8e-27)
     (- x (/ t (/ z y)))
     (if (<= z -1.6e-87)
       (+ x (/ y (/ a t)))
       (if (<= z -5.1e-115)
         (/ (* (- z t) y) z)
         (if (<= z 1.1e-194)
           (+ x (* y (/ t a)))
           (if (<= z 2.3e+34) (- x (/ (* t y) z)) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+92) {
		tmp = x + y;
	} else if (z <= -2.8e-27) {
		tmp = x - (t / (z / y));
	} else if (z <= -1.6e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = ((z - t) * y) / z;
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.3e+34) {
		tmp = x - ((t * y) / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+92)) then
        tmp = x + y
    else if (z <= (-2.8d-27)) then
        tmp = x - (t / (z / y))
    else if (z <= (-1.6d-87)) then
        tmp = x + (y / (a / t))
    else if (z <= (-5.1d-115)) then
        tmp = ((z - t) * y) / z
    else if (z <= 1.1d-194) then
        tmp = x + (y * (t / a))
    else if (z <= 2.3d+34) then
        tmp = x - ((t * y) / z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+92) {
		tmp = x + y;
	} else if (z <= -2.8e-27) {
		tmp = x - (t / (z / y));
	} else if (z <= -1.6e-87) {
		tmp = x + (y / (a / t));
	} else if (z <= -5.1e-115) {
		tmp = ((z - t) * y) / z;
	} else if (z <= 1.1e-194) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.3e+34) {
		tmp = x - ((t * y) / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+92:
		tmp = x + y
	elif z <= -2.8e-27:
		tmp = x - (t / (z / y))
	elif z <= -1.6e-87:
		tmp = x + (y / (a / t))
	elif z <= -5.1e-115:
		tmp = ((z - t) * y) / z
	elif z <= 1.1e-194:
		tmp = x + (y * (t / a))
	elif z <= 2.3e+34:
		tmp = x - ((t * y) / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+92)
		tmp = Float64(x + y);
	elseif (z <= -2.8e-27)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= -1.6e-87)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -5.1e-115)
		tmp = Float64(Float64(Float64(z - t) * y) / z);
	elseif (z <= 1.1e-194)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.3e+34)
		tmp = Float64(x - Float64(Float64(t * y) / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+92)
		tmp = x + y;
	elseif (z <= -2.8e-27)
		tmp = x - (t / (z / y));
	elseif (z <= -1.6e-87)
		tmp = x + (y / (a / t));
	elseif (z <= -5.1e-115)
		tmp = ((z - t) * y) / z;
	elseif (z <= 1.1e-194)
		tmp = x + (y * (t / a));
	elseif (z <= 2.3e+34)
		tmp = x - ((t * y) / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+92], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.8e-27], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-87], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-115], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.1e-194], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+34], N[(x - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.20000000000000047e92 or 2.2999999999999998e34 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 81.6%

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

   if -8.20000000000000047e92 < z < -2.8e-27

   1. Initial program 96.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 86.2%

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

      1. neg-mul-1 86.2%

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

      2. distribute-neg-frac 86.2%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 86.2%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in x around 0 89.6%

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

      1. +-commutative 89.6%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z - a}} \]

      2. mul-1-neg 89.6%

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

      3. associate-*l/ 89.6%

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

      4. distribute-lft-neg-in 89.6%

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

      5. cancel-sign-sub-inv 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in z around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-/l* 82.5%

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

   10. Simplified 82.5%

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

   if -2.8e-27 < z < -1.59999999999999989e-87

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   3. Step-by-step derivation

      1. associate-/l* 87.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} + x \]

   4. Simplified 87.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]

   if -1.59999999999999989e-87 < z < -5.0999999999999997e-115

   1. Initial program 76.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-/l* 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in x around 0 80.8%

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

   if -5.0999999999999997e-115 < z < 1.1000000000000001e-194

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 88.8%

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

   if 1.1000000000000001e-194 < z < 2.2999999999999998e34

   1. Initial program 93.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-/l* 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. associate-*r* 67.6%

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

      3. neg-mul-1 67.6%

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

      4. *-commutative 67.6%

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

   7. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(-y\right)}{z}} + x \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5200000000000:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-27} \lor \neg \left(z \leq 2.9 \cdot 10^{-155}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -6.8e+90)
     t_1
     (if (<= z -5200000000000.0)
       (- x (/ y (/ z t)))
       (if (or (<= z -1.06e-27) (not (<= z 2.9e-155)))
         t_1
         (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -6.8e+90) {
		tmp = t_1;
	} else if (z <= -5200000000000.0) {
		tmp = x - (y / (z / t));
	} else if ((z <= -1.06e-27) || !(z <= 2.9e-155)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-6.8d+90)) then
        tmp = t_1
    else if (z <= (-5200000000000.0d0)) then
        tmp = x - (y / (z / t))
    else if ((z <= (-1.06d-27)) .or. (.not. (z <= 2.9d-155))) then
        tmp = t_1
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -6.8e+90) {
		tmp = t_1;
	} else if (z <= -5200000000000.0) {
		tmp = x - (y / (z / t));
	} else if ((z <= -1.06e-27) || !(z <= 2.9e-155)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -6.8e+90:
		tmp = t_1
	elif z <= -5200000000000.0:
		tmp = x - (y / (z / t))
	elif (z <= -1.06e-27) or not (z <= 2.9e-155):
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -6.8e+90)
		tmp = t_1;
	elseif (z <= -5200000000000.0)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif ((z <= -1.06e-27) || !(z <= 2.9e-155))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -6.8e+90)
		tmp = t_1;
	elseif (z <= -5200000000000.0)
		tmp = x - (y / (z / t));
	elseif ((z <= -1.06e-27) || ~((z <= 2.9e-155)))
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+90], t$95$1, If[LessEqual[z, -5200000000000.0], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.06e-27], N[Not[LessEqual[z, 2.9e-155]], $MachinePrecision]], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.80000000000000036e90 or -5.2e12 < z < -1.05999999999999998e-27 or 2.9000000000000001e-155 < z

   1. Initial program 97.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 83.4%

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

   if -6.80000000000000036e90 < z < -5.2e12

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-/l* 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in z around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. associate-/l* 94.0%

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

      3. distribute-neg-frac 94.0%

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

   7. Simplified 94.0%

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

   if -1.05999999999999998e-27 < z < 2.9000000000000001e-155

   1. Initial program 96.0%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 88.0%

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

      1. neg-mul-1 88.0%

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

      2. distribute-neg-frac 88.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 88.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in z around 0 73.8%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   6. Step-by-step derivation

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -5200000000000:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-27} \lor \neg \left(z \leq 2.9 \cdot 10^{-155}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-77} \lor \neg \left(t \leq 5 \cdot 10^{-63}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.6e-77) (not (<= t 5e-63)))
   (- x (* t (/ y (- z a))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.6e-77) || !(t <= 5e-63)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.6d-77)) .or. (.not. (t <= 5d-63))) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.6e-77) || !(t <= 5e-63)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.6e-77) or not (t <= 5e-63):
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.6e-77) || !(t <= 5e-63))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.6e-77) || ~((t <= 5e-63)))
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.6e-77], N[Not[LessEqual[t, 5e-63]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.59999999999999961e-77 or 5.0000000000000002e-63 < t

   1. Initial program 95.5%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 84.4%

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

      1. neg-mul-1 84.4%

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

      2. distribute-neg-frac 84.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   4. Simplified 84.4%

      \[\leadsto x + y \cdot \color{blue}{\frac{-t}{z - a}} \]

   5. Taylor expanded in x around 0 82.5%

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

      1. +-commutative 82.5%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z - a}} \]

      2. mul-1-neg 82.5%

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

      3. associate-*l/ 88.6%

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

      4. distribute-lft-neg-in 88.6%

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

      5. cancel-sign-sub-inv 88.6%

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

   7. Simplified 88.6%

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

   if -9.59999999999999961e-77 < t < 5.0000000000000002e-63

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 91.2%

      \[\leadsto x + y \cdot \color{blue}{\frac{z}{z - a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-77} \lor \neg \left(t \leq 5 \cdot 10^{-63}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 8: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.62e-12)
   (+ x (* y (/ z (- z a))))
   (if (<= a 4.3e-52) (+ x (* y (/ (- z t) z))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.62e-12) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 4.3e-52) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.62d-12)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= 4.3d-52) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.62e-12) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 4.3e-52) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.62e-12:
		tmp = x + (y * (z / (z - a)))
	elif a <= 4.3e-52:
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.62e-12)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= 4.3e-52)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.62e-12)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= 4.3e-52)
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.62e-12], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-52], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.62e-12

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 77.4%

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

   if -1.62e-12 < a < 4.3000000000000003e-52

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 83.2%

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

   if 4.3000000000000003e-52 < a

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 83.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-12)
   (+ x (* y (/ z (- z a))))
   (if (<= a 1.22e-51) (+ x (/ (- z t) (/ z y))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-12) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 1.22e-51) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-12)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= 1.22d-51) then
        tmp = x + ((z - t) / (z / y))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-12) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 1.22e-51) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-12:
		tmp = x + (y * (z / (z - a)))
	elif a <= 1.22e-51:
		tmp = x + ((z - t) / (z / y))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-12)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= 1.22e-51)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-12)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= 1.22e-51)
		tmp = x + ((z - t) / (z / y));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-12], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-51], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e-12

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 77.4%

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

   if -1.6e-12 < a < 1.21999999999999998e-51

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Step-by-step derivation

      1. *-commutative 94.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{z - a} \cdot y} \]

      2. associate-*l/ 89.5%

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

      3. associate-/l* 95.1%

         \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

   3. Applied egg-rr 95.1%

      \[\leadsto x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

   4. Taylor expanded in z around inf 84.1%

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

   if 1.21999999999999998e-51 < a

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 83.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e-11)
   (+ x (* y (/ z (- z a))))
   (if (<= a 1.38e-52) (+ x (/ y (/ z (- z t)))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-11) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 1.38e-52) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.6d-11)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= 1.38d-52) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-11) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 1.38e-52) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e-11:
		tmp = x + (y * (z / (z - a)))
	elif a <= 1.38e-52:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e-11)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= 1.38e-52)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e-11)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= 1.38e-52)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e-11], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.38e-52], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6000000000000001e-11

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 77.4%

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

   if -2.6000000000000001e-11 < a < 1.38000000000000008e-52

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-/l* 84.5%

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

   4. Simplified 84.5%

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

   if 1.38000000000000008e-52 < a

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 83.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 11: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+78} \lor \neg \left(y \leq 1.35 \cdot 10^{+161}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.7e+78) (not (<= y 1.35e+161)))
   (* y (- 1.0 (/ t z)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.7e+78) || !(y <= 1.35e+161)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.7d+78)) .or. (.not. (y <= 1.35d+161))) then
        tmp = y * (1.0d0 - (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.7e+78) || !(y <= 1.35e+161)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.7e+78) or not (y <= 1.35e+161):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.7e+78) || !(y <= 1.35e+161))
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.7e+78) || ~((y <= 1.35e+161)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.7e+78], N[Not[LessEqual[y, 1.35e+161]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.69999999999999986e78 or 1.3499999999999999e161 < y

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 44.1%

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

      1. +-commutative 44.1%

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

      2. *-commutative 44.1%

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

      3. associate-/l* 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 51.1%

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

   if -5.69999999999999986e78 < y < 1.3499999999999999e161

   1. Initial program 96.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 67.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+78} \lor \neg \left(y \leq 1.35 \cdot 10^{+161}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2700000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+102)
   (+ x y)
   (if (<= z 2700000.0) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+102) {
		tmp = x + y;
	} else if (z <= 2700000.0) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d+102)) then
        tmp = x + y
    else if (z <= 2700000.0d0) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+102) {
		tmp = x + y;
	} else if (z <= 2700000.0) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+102:
		tmp = x + y
	elif z <= 2700000.0:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+102)
		tmp = Float64(x + y);
	elseif (z <= 2700000.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+102)
		tmp = x + y;
	elseif (z <= 2700000.0)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+102], N[(x + y), $MachinePrecision], If[LessEqual[z, 2700000.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000001e102 or 2.7e6 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 80.2%

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

   if -4.3000000000000001e102 < z < 2.7e6

   1. Initial program 95.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 72.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2700000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 44000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+102)
   (+ x y)
   (if (<= z 44000000.0) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+102) {
		tmp = x + y;
	} else if (z <= 44000000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+102)) then
        tmp = x + y
    else if (z <= 44000000.0d0) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+102) {
		tmp = x + y;
	} else if (z <= 44000000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+102:
		tmp = x + y
	elif z <= 44000000.0:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+102)
		tmp = Float64(x + y);
	elseif (z <= 44000000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+102)
		tmp = x + y;
	elseif (z <= 44000000.0)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+102], N[(x + y), $MachinePrecision], If[LessEqual[z, 44000000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000006e102 or 4.4e7 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 80.2%

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

   if -2.60000000000000006e102 < z < 4.4e7

   1. Initial program 95.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 68.3%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   3. Step-by-step derivation

      1. associate-/l* 72.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} + x \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 44000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 63.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e-27) (+ x y) (if (<= z 9e-27) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-27) {
		tmp = x + y;
	} else if (z <= 9e-27) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d-27)) then
        tmp = x + y
    else if (z <= 9d-27) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-27) {
		tmp = x + y;
	} else if (z <= 9e-27) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e-27:
		tmp = x + y
	elif z <= 9e-27:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e-27)
		tmp = Float64(x + y);
	elseif (z <= 9e-27)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e-27)
		tmp = x + y;
	elseif (z <= 9e-27)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, 9e-27], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e-27 or 9.0000000000000003e-27 < z

   1. Initial program 99.2%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around inf 74.4%

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

   if -1.20000000000000001e-27 < z < 9.0000000000000003e-27

   1. Initial program 95.3%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in x around inf 47.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15: 52.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e-246) x (if (<= x 8.8e-114) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e-246) {
		tmp = x;
	} else if (x <= 8.8e-114) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.75d-246)) then
        tmp = x
    else if (x <= 8.8d-114) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e-246) {
		tmp = x;
	} else if (x <= 8.8e-114) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.75e-246:
		tmp = x
	elif x <= 8.8e-114:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e-246)
		tmp = x;
	elseif (x <= 8.8e-114)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.75e-246)
		tmp = x;
	elseif (x <= 8.8e-114)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e-246], x, If[LessEqual[x, 8.8e-114], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-246 or 8.80000000000000045e-114 < x

   1. Initial program 97.0%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in x around inf 62.2%

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

   if -1.7500000000000001e-246 < x < 8.80000000000000045e-114

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-/l* 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in y around inf 53.3%

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

   6. Taylor expanded in t around 0 33.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 50.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 97.3%

   \[x + y \cdot \frac{z - t}{z - a} \]

2. Taylor expanded in x around inf 51.1%

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

3. Final simplification 51.1%

   \[\leadsto x \]

Developer target: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- z a) (- z t)))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))