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

Percentage Accurate: 98.0% → 98.8%

Time: 8.4s

Alternatives: 14

Speedup: 1.0×

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: 98.0% 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: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{+192}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- z t) (- z a)) 4e+192)
   (- x (* y (/ (- z t) (- a z))))
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (z - a)) <= 4e+192) {
		tmp = x - (y * ((z - t) / (a - z)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	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 - t) / (z - a)) <= 4d+192) then
        tmp = x - (y * ((z - t) / (a - z)))
    else
        tmp = x + ((y * t) / (a - z))
    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 - t) / (z - a)) <= 4e+192) {
		tmp = x - (y * ((z - t) / (a - z)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) / (z - a)) <= 4e+192:
		tmp = x - (y * ((z - t) / (a - z)))
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - t) / Float64(z - a)) <= 4e+192)
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) / (z - a)) <= 4e+192)
		tmp = x - (y * ((z - t) / (a - z)));
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], 4e+192], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 4.00000000000000016e192

   1. Initial program 99.1%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   if 4.00000000000000016e192 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 76.8%

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

      1. clear-num 76.6%

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

      2. un-div-inv 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 76.8%

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

      4. sub-neg 76.8%

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

      5. *-commutative 76.8%

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

      6. associate-/r/ 99.6%

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

   10. Simplified 99.6%

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

   11. Taylor expanded in t around 0 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{+192}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.95e+36)
     t_1
     (if (<= z -5.2e-140)
       (- x (/ (* y t) z))
       (if (<= z 1.6e-52) (+ x (* t (/ y a))) t_1)))))

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 <= -1.95e+36) {
		tmp = t_1;
	} else if (z <= -5.2e-140) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.6e-52) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	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 <= (-1.95d+36)) then
        tmp = t_1
    else if (z <= (-5.2d-140)) then
        tmp = x - ((y * t) / z)
    else if (z <= 1.6d-52) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    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 <= -1.95e+36) {
		tmp = t_1;
	} else if (z <= -5.2e-140) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.6e-52) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -1.95e+36:
		tmp = t_1
	elif z <= -5.2e-140:
		tmp = x - ((y * t) / z)
	elif z <= 1.6e-52:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	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 <= -1.95e+36)
		tmp = t_1;
	elseif (z <= -5.2e-140)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 1.6e-52)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	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 <= -1.95e+36)
		tmp = t_1;
	elseif (z <= -5.2e-140)
		tmp = x - ((y * t) / z);
	elseif (z <= 1.6e-52)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	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, -1.95e+36], t$95$1, If[LessEqual[z, -5.2e-140], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-52], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9500000000000001e36 or 1.60000000000000005e-52 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 74.9%

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

      1. associate-/l* 88.2%

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

   5. Simplified 88.2%

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

   if -1.9500000000000001e36 < z < -5.1999999999999996e-140

   1. Initial program 97.2%

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

      1. clear-num 97.3%

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

      2. un-div-inv 97.3%

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

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in t around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. associate-/l* 85.9%

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

      3. distribute-lft-neg-out 85.9%

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

      4. *-commutative 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in x around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r/ 83.2%

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

      4. sub-neg 83.2%

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

      5. *-commutative 83.2%

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

      6. associate-/r/ 86.1%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in z around inf 78.3%

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

   if -5.1999999999999996e-140 < z < 1.60000000000000005e-52

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 82.2%

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

      1. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+140)
   (+ x y)
   (if (<= z -3.4e-140)
     (- x (* t (/ y z)))
     (if (<= z 1.42e+62) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+140) {
		tmp = x + y;
	} else if (z <= -3.4e-140) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.42e+62) {
		tmp = x + (t * (y / 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 <= (-2.5d+140)) then
        tmp = x + y
    else if (z <= (-3.4d-140)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.42d+62) then
        tmp = x + (t * (y / 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 <= -2.5e+140) {
		tmp = x + y;
	} else if (z <= -3.4e-140) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.42e+62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+140:
		tmp = x + y
	elif z <= -3.4e-140:
		tmp = x - (t * (y / z))
	elif z <= 1.42e+62:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+140)
		tmp = Float64(x + y);
	elseif (z <= -3.4e-140)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.42e+62)
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -2.5e+140)
		tmp = x + y;
	elseif (z <= -3.4e-140)
		tmp = x - (t * (y / z));
	elseif (z <= 1.42e+62)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+140], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.4e-140], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000004e140 or 1.42e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.8%

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

   if -2.50000000000000004e140 < z < -3.40000000000000008e-140

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 83.4%

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

      3. distribute-lft-neg-out 83.4%

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

      4. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in z around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. associate-/l* 77.1%

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

   10. Simplified 77.1%

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

   if -3.40000000000000008e-140 < z < 1.42e62

   1. Initial program 95.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 79.2%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+140)
   (+ x y)
   (if (<= z -3.8e-140)
     (- x (/ t (/ z y)))
     (if (<= z 2.4e+62) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+140) {
		tmp = x + y;
	} else if (z <= -3.8e-140) {
		tmp = x - (t / (z / y));
	} else if (z <= 2.4e+62) {
		tmp = x + (t * (y / 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 <= (-2.5d+140)) then
        tmp = x + y
    else if (z <= (-3.8d-140)) then
        tmp = x - (t / (z / y))
    else if (z <= 2.4d+62) then
        tmp = x + (t * (y / 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 <= -2.5e+140) {
		tmp = x + y;
	} else if (z <= -3.8e-140) {
		tmp = x - (t / (z / y));
	} else if (z <= 2.4e+62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+140:
		tmp = x + y
	elif z <= -3.8e-140:
		tmp = x - (t / (z / y))
	elif z <= 2.4e+62:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+140)
		tmp = Float64(x + y);
	elseif (z <= -3.8e-140)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 2.4e+62)
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -2.5e+140)
		tmp = x + y;
	elseif (z <= -3.8e-140)
		tmp = x - (t / (z / y));
	elseif (z <= 2.4e+62)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+140], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.8e-140], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000004e140 or 2.4e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.8%

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

   if -2.50000000000000004e140 < z < -3.79999999999999998e-140

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 83.4%

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

      3. distribute-lft-neg-out 83.4%

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

      4. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in x around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r/ 83.3%

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

      4. sub-neg 83.3%

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

      5. *-commutative 83.3%

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

      6. associate-/r/ 83.4%

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

   10. Simplified 83.4%

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

   11. Taylor expanded in z around inf 77.1%

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

   if -3.79999999999999998e-140 < z < 2.4e62

   1. Initial program 95.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 79.2%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.45e+140)
   (+ x y)
   (if (<= z -4.1e-140)
     (- x (/ (* y t) z))
     (if (<= z 1.86e+62) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.45e+140) {
		tmp = x + y;
	} else if (z <= -4.1e-140) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.86e+62) {
		tmp = x + (t * (y / 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 <= (-3.45d+140)) then
        tmp = x + y
    else if (z <= (-4.1d-140)) then
        tmp = x - ((y * t) / z)
    else if (z <= 1.86d+62) then
        tmp = x + (t * (y / 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 <= -3.45e+140) {
		tmp = x + y;
	} else if (z <= -4.1e-140) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.86e+62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.45e+140:
		tmp = x + y
	elif z <= -4.1e-140:
		tmp = x - ((y * t) / z)
	elif z <= 1.86e+62:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.45e+140)
		tmp = Float64(x + y);
	elseif (z <= -4.1e-140)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 1.86e+62)
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -3.45e+140)
		tmp = x + y;
	elseif (z <= -4.1e-140)
		tmp = x - ((y * t) / z);
	elseif (z <= 1.86e+62)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.45e+140], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.1e-140], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.86e+62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4500000000000001e140 or 1.85999999999999995e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.8%

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

   if -3.4500000000000001e140 < z < -4.1000000000000001e-140

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 83.4%

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

      3. distribute-lft-neg-out 83.4%

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

      4. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in x around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r/ 83.3%

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

      4. sub-neg 83.3%

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

      5. *-commutative 83.3%

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

      6. associate-/r/ 83.4%

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

   10. Simplified 83.4%

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

   11. Taylor expanded in z around inf 80.3%

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

   if -4.1000000000000001e-140 < z < 1.85999999999999995e62

   1. Initial program 95.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 79.2%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-42} \lor \neg \left(t \leq 3.65 \cdot 10^{+93}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e-42) (not (<= t 3.65e+93)))
   (+ x (* y (/ t (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e-42) || !(t <= 3.65e+93)) {
		tmp = x + (y * (t / (a - z)));
	} 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 <= (-4.1d-42)) .or. (.not. (t <= 3.65d+93))) then
        tmp = x + (y * (t / (a - z)))
    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 <= -4.1e-42) || !(t <= 3.65e+93)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.1e-42) or not (t <= 3.65e+93):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.1e-42) || !(t <= 3.65e+93))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	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 <= -4.1e-42) || ~((t <= 3.65e+93)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.1e-42], N[Not[LessEqual[t, 3.65e+93]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $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 < -4.1000000000000001e-42 or 3.65000000000000013e93 < t

   1. Initial program 95.0%

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

      1. clear-num 95.0%

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

      2. un-div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in t around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. associate-/l* 91.6%

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

      3. distribute-lft-neg-out 91.6%

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

      4. *-commutative 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in x around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r/ 88.3%

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

      4. sub-neg 88.3%

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

   10. Simplified 88.3%

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

   if -4.1000000000000001e-42 < t < 3.65000000000000013e93

   1. Initial program 99.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 82.9%

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

      1. associate-/l* 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-42} \lor \neg \left(t \leq 3.65 \cdot 10^{+93}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-146}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e-146)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 5.8e-52) (+ x (* t (/ y a))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-146) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 5.8e-52) {
		tmp = x + (t * (y / 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 (z <= (-3.3d-146)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 5.8d-52) then
        tmp = x + (t * (y / 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 (z <= -3.3e-146) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 5.8e-52) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e-146:
		tmp = x + (y * ((z - t) / z))
	elif z <= 5.8e-52:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e-146)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 5.8e-52)
		tmp = Float64(x + Float64(t * Float64(y / 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 (z <= -3.3e-146)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 5.8e-52)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e-146], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-52], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e-146

   1. Initial program 98.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 87.9%

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

   if -3.3e-146 < z < 5.8000000000000003e-52

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.0%

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

      1. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if 5.8000000000000003e-52 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.1%

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

      1. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-146}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-56}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-143)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 7.6e-56) (+ x (* t (/ y a))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-143) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 7.6e-56) {
		tmp = x + (t * (y / 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 (z <= (-8.5d-143)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 7.6d-56) then
        tmp = x + (t * (y / 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 (z <= -8.5e-143) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 7.6e-56) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-143:
		tmp = x + (y / (z / (z - t)))
	elif z <= 7.6e-56:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-143)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 7.6e-56)
		tmp = Float64(x + Float64(t * Float64(y / 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 (z <= -8.5e-143)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 7.6e-56)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-143], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-56], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000072e-143

   1. Initial program 98.8%

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

      1. clear-num 98.8%

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

      2. un-div-inv 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in a around 0 87.9%

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

   if -8.50000000000000072e-143 < z < 7.6000000000000004e-56

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.0%

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

      1. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if 7.6000000000000004e-56 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.1%

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

      1. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-56}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-19)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 1.8e+62) (+ x (/ t (/ (- a z) y))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-19) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.8e+62) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	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 <= (-2.9d-19)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.8d+62) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (y * ((z - t) / z))
    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 <= -2.9e-19) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.8e+62) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-19:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.8e+62:
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-19)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.8e+62)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e-19)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.8e+62)
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-19], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+62], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-19

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 95.3%

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

   if -2.9e-19 < z < 1.8e62

   1. Initial program 95.5%

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

      1. clear-num 95.5%

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

      2. un-div-inv 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 90.2%

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

      3. distribute-lft-neg-out 90.2%

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

      4. *-commutative 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in x around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r/ 86.4%

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

      4. sub-neg 86.4%

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

      5. *-commutative 86.4%

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

      6. associate-/r/ 90.2%

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

   10. Simplified 90.2%

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

   if 1.8e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 95.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.16e-20)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 1.3e+62) (+ x (* t (/ y (- a z)))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.3e+62) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	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 <= (-1.16d-20)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.3d+62) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * ((z - t) / z))
    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 <= -1.16e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.3e+62) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.16e-20:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.3e+62:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.16e-20)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.3e+62)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.16e-20)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.3e+62)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.16e-20], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+62], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e-20

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 95.3%

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

   if -1.16e-20 < z < 1.29999999999999992e62

   1. Initial program 95.5%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if 1.29999999999999992e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 95.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-22} \lor \neg \left(z \leq 1.56 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.4e-22) (not (<= z 1.56e+62))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.4e-22) || !(z <= 1.56e+62)) {
		tmp = x + y;
	} 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) :: tmp
    if ((z <= (-8.4d-22)) .or. (.not. (z <= 1.56d+62))) then
        tmp = x + y
    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 tmp;
	if ((z <= -8.4e-22) || !(z <= 1.56e+62)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.4e-22) or not (z <= 1.56e+62):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.4e-22) || !(z <= 1.56e+62))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.4e-22) || ~((z <= 1.56e+62)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.4e-22], N[Not[LessEqual[z, 1.56e+62]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.40000000000000031e-22 or 1.55999999999999995e62 < z

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.1%

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

   if -8.40000000000000031e-22 < z < 1.55999999999999995e62

   1. Initial program 95.5%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-22} \lor \neg \left(z \leq 1.56 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 65000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+81) x (if (<= a 65000000000000.0) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+81) {
		tmp = x;
	} else if (a <= 65000000000000.0) {
		tmp = x + 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 (a <= (-3.2d+81)) then
        tmp = x
    else if (a <= 65000000000000.0d0) then
        tmp = x + 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 (a <= -3.2e+81) {
		tmp = x;
	} else if (a <= 65000000000000.0) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+81:
		tmp = x
	elif a <= 65000000000000.0:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+81)
		tmp = x;
	elseif (a <= 65000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+81)
		tmp = x;
	elseif (a <= 65000000000000.0)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+81], x, If[LessEqual[a, 65000000000000.0], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2e81 or 6.5e13 < a

   1. Initial program 98.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 76.2%

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

      1. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x around inf 70.2%

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

   if -3.2e81 < a < 6.5e13

   1. Initial program 96.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 65000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.2% 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]

Derivation

1. Initial program 97.3%

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

   1. clear-num 97.3%

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

   2. un-div-inv 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

   \[\leadsto x + \frac{y}{\frac{z - a}{z - t}} \]
6. Add Preprocessing

Alternative 14: 50.4% 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. Add Preprocessing

3. Taylor expanded in t around 0 64.8%

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

   1. associate-/l* 71.0%

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

5. Simplified 71.0%

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

6. Taylor expanded in x around inf 52.9%

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

7. Final simplification 52.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 98.2% 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 2024084 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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