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

Percentage Accurate: 98.0% → 98.1%

Time: 9.7s

Alternatives: 14

Speedup: 0.5×

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: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (<= t_1 5e+287) (+ t_1 x) (+ x (* t (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (t_1 <= 5e+287) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if (t_1 <= 5d+287) then
        tmp = t_1 + x
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (t_1 <= 5e+287) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if t_1 <= 5e+287:
		tmp = t_1 + x
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= 5e+287)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (t_1 <= 5e+287)
		tmp = t_1 + x;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+287], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 5e287

   1. Initial program 99.5%

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

   if 5e287 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. mul-1-neg 96.4%

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

      3. distribute-rgt-neg-in 96.4%

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

      4. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{z - a} \leq 5 \cdot 10^{+287}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+53} \lor \neg \left(z \leq 1.9 \cdot 10^{+157}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+17)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 1.8e-53)
     (+ x (/ 1.0 (/ (/ a y) t)))
     (if (or (<= z 1.35e+53) (not (<= z 1.9e+157)))
       (+ x (* y (- 1.0 (/ t z))))
       (+ x (/ y (/ (- z a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.8e-53) {
		tmp = x + (1.0 / ((a / y) / t));
	} else if ((z <= 1.35e+53) || !(z <= 1.9e+157)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / ((z - 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 <= (-6.5d+17)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 1.8d-53) then
        tmp = x + (1.0d0 / ((a / y) / t))
    else if ((z <= 1.35d+53) .or. (.not. (z <= 1.9d+157))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (y / ((z - 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 <= -6.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.8e-53) {
		tmp = x + (1.0 / ((a / y) / t));
	} else if ((z <= 1.35e+53) || !(z <= 1.9e+157)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+17:
		tmp = x + (y * ((z - t) / z))
	elif z <= 1.8e-53:
		tmp = x + (1.0 / ((a / y) / t))
	elif (z <= 1.35e+53) or not (z <= 1.9e+157):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 1.8e-53)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a / y) / t)));
	elseif ((z <= 1.35e+53) || !(z <= 1.9e+157))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 1.8e-53)
		tmp = x + (1.0 / ((a / y) / t));
	elseif ((z <= 1.35e+53) || ~((z <= 1.9e+157)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+17], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-53], N[(x + N[(1.0 / N[(N[(a / y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.35e+53], N[Not[LessEqual[z, 1.9e+157]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -6.5e17 < z < 1.7999999999999999e-53

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. clear-num 80.4%

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

      2. inv-pow 80.4%

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

      3. *-commutative 80.4%

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

   5. Applied egg-rr 80.4%

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

      1. unpow-1 80.4%

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

      2. associate-/r* 81.1%

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

   7. Simplified 81.1%

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

   if 1.7999999999999999e-53 < z < 1.3500000000000001e53 or 1.9e157 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.9%

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

      1. associate-/l* 92.3%

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

      2. div-sub 92.3%

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

      3. *-inverses 92.3%

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

   5. Simplified 92.3%

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

   if 1.3500000000000001e53 < z < 1.9e157

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      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 t around 0 96.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+53} \lor \neg \left(z \leq 1.9 \cdot 10^{+157}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+86}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+17)
   (+ y x)
   (if (<= z 1.15e-32)
     (+ x (* t (/ y a)))
     (if (<= z 5e+86) (- x (* t (/ y z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+17) {
		tmp = y + x;
	} else if (z <= 1.15e-32) {
		tmp = x + (t * (y / a));
	} else if (z <= 5e+86) {
		tmp = x - (t * (y / z));
	} else {
		tmp = y + 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 (z <= (-8d+17)) then
        tmp = y + x
    else if (z <= 1.15d-32) then
        tmp = x + (t * (y / a))
    else if (z <= 5d+86) then
        tmp = x - (t * (y / z))
    else
        tmp = y + 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 (z <= -8e+17) {
		tmp = y + x;
	} else if (z <= 1.15e-32) {
		tmp = x + (t * (y / a));
	} else if (z <= 5e+86) {
		tmp = x - (t * (y / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+17:
		tmp = y + x
	elif z <= 1.15e-32:
		tmp = x + (t * (y / a))
	elif z <= 5e+86:
		tmp = x - (t * (y / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+17)
		tmp = Float64(y + x);
	elseif (z <= 1.15e-32)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 5e+86)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+17)
		tmp = y + x;
	elseif (z <= 1.15e-32)
		tmp = x + (t * (y / a));
	elseif (z <= 5e+86)
		tmp = x - (t * (y / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+17], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.15e-32], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+86], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e17 or 4.9999999999999998e86 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

   5. Simplified 84.1%

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

   if -8e17 < z < 1.15e-32

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   if 1.15e-32 < z < 4.9999999999999998e86

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-neg-frac2 76.0%

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

   7. Simplified 76.0%

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

      1. frac-2neg 76.0%

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

      2. div-inv 75.9%

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

      3. distribute-neg-frac2 75.9%

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

      4. add-sqr-sqrt 20.2%

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

      5. sqrt-unprod 41.2%

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

      6. sqr-neg 41.2%

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

      7. sqrt-unprod 25.8%

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

      8. add-sqr-sqrt 35.9%

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

      9. clear-num 35.9%

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

      10. cancel-sign-sub-inv 35.9%

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

      11. clear-num 35.9%

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

      12. div-inv 35.9%

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

      13. div-inv 35.9%

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

      14. clear-num 35.9%

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

   9. Applied egg-rr 76.0%

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

   10. Taylor expanded in z around inf 71.1%

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

       1. associate-*r/ 75.6%

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

   12. Simplified 75.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+86}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+17)
   (+ y x)
   (if (<= z 1.4e-32)
     (+ x (* t (/ y a)))
     (if (<= z 3.5e+87) (- x (* y (/ t z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+17) {
		tmp = y + x;
	} else if (z <= 1.4e-32) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.5e+87) {
		tmp = x - (y * (t / z));
	} else {
		tmp = y + 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 (z <= (-9.8d+17)) then
        tmp = y + x
    else if (z <= 1.4d-32) then
        tmp = x + (t * (y / a))
    else if (z <= 3.5d+87) then
        tmp = x - (y * (t / z))
    else
        tmp = y + 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 (z <= -9.8e+17) {
		tmp = y + x;
	} else if (z <= 1.4e-32) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.5e+87) {
		tmp = x - (y * (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+17:
		tmp = y + x
	elif z <= 1.4e-32:
		tmp = x + (t * (y / a))
	elif z <= 3.5e+87:
		tmp = x - (y * (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+17)
		tmp = Float64(y + x);
	elseif (z <= 1.4e-32)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.5e+87)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+17)
		tmp = y + x;
	elseif (z <= 1.4e-32)
		tmp = x + (t * (y / a));
	elseif (z <= 3.5e+87)
		tmp = x - (y * (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+17], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.4e-32], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+87], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8e17 or 3.49999999999999986e87 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

   5. Simplified 84.1%

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

   if -9.8e17 < z < 1.3999999999999999e-32

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   if 1.3999999999999999e-32 < z < 3.49999999999999986e87

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-neg-frac2 76.0%

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

   7. Simplified 76.0%

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

      1. frac-2neg 76.0%

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

      2. div-inv 75.9%

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

      3. distribute-neg-frac2 75.9%

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

      4. add-sqr-sqrt 20.2%

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

      5. sqrt-unprod 41.2%

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

      6. sqr-neg 41.2%

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

      7. sqrt-unprod 25.8%

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

      8. add-sqr-sqrt 35.9%

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

      9. clear-num 35.9%

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

      10. cancel-sign-sub-inv 35.9%

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

      11. clear-num 35.9%

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

      12. div-inv 35.9%

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

      13. div-inv 35.9%

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

      14. clear-num 35.9%

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

   9. Applied egg-rr 76.0%

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

   10. Taylor expanded in z around inf 75.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17} \lor \neg \left(z \leq 1.42 \cdot 10^{-52}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+17) (not (<= z 1.42e-52)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+17) || !(z <= 1.42e-52)) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 <= (-6.5d+17)) .or. (.not. (z <= 1.42d-52))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 <= -6.5e+17) || !(z <= 1.42e-52)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+17) or not (z <= 1.42e-52):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+17) || !(z <= 1.42e-52))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 <= -6.5e+17) || ~((z <= 1.42e-52)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+17], N[Not[LessEqual[z, 1.42e-52]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e17 or 1.4200000000000001e-52 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 68.5%

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

      1. associate-/l* 88.8%

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

      2. div-sub 88.8%

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

      3. *-inverses 88.8%

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

   5. Simplified 88.8%

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

   if -6.5e17 < z < 1.4200000000000001e-52

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17} \lor \neg \left(z \leq 1.42 \cdot 10^{-52}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+17)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 5.1e-54) (+ x (* t (/ y a))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 5.1e-54) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (1.0 - (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 <= (-6.5d+17)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 5.1d-54) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y * (1.0d0 - (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 <= -6.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 5.1e-54) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+17:
		tmp = x + (y * ((z - t) / z))
	elif z <= 5.1e-54:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 5.1e-54)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 5.1e-54)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+17], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-54], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -6.5e17 < z < 5.1000000000000001e-54

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   if 5.1000000000000001e-54 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 85.9%

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

      2. div-sub 86.0%

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

      3. *-inverses 86.0%

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

   5. Simplified 86.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+17)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 4e-53) (+ x (/ 1.0 (/ (/ a y) t))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 4e-53) {
		tmp = x + (1.0 / ((a / y) / t));
	} else {
		tmp = x + (y * (1.0 - (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 <= (-7.5d+17)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 4d-53) then
        tmp = x + (1.0d0 / ((a / y) / t))
    else
        tmp = x + (y * (1.0d0 - (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 <= -7.5e+17) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 4e-53) {
		tmp = x + (1.0 / ((a / y) / t));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+17:
		tmp = x + (y * ((z - t) / z))
	elif z <= 4e-53:
		tmp = x + (1.0 / ((a / y) / t))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+17)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 4e-53)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a / y) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+17)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 4e-53)
		tmp = x + (1.0 / ((a / y) / t));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+17], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-53], N[(x + N[(1.0 / N[(N[(a / y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -7.5e17 < z < 4.00000000000000012e-53

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. clear-num 80.4%

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

      2. inv-pow 80.4%

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

      3. *-commutative 80.4%

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

   5. Applied egg-rr 80.4%

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

      1. unpow-1 80.4%

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

      2. associate-/r* 81.1%

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

   7. Simplified 81.1%

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

   if 4.00000000000000012e-53 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 85.9%

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

      2. div-sub 86.0%

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

      3. *-inverses 86.0%

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

   5. Simplified 86.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.54 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+18)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 1.54e+41) (+ x (* y (/ t (- a z)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+18) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.54e+41) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y / ((z - 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 <= (-1.8d+18)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 1.54d+41) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (y / ((z - 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 <= -1.8e+18) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.54e+41) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+18:
		tmp = x + (y * ((z - t) / z))
	elif z <= 1.54e+41:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+18)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 1.54e+41)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+18)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 1.54e+41)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+18], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.54e+41], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e18

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -1.8e18 < z < 1.53999999999999993e41

   1. Initial program 96.0%

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

      1. clear-num 95.8%

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

      2. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in t around inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   7. Simplified 90.3%

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

      1. frac-2neg 90.3%

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

      2. div-inv 89.8%

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

      3. distribute-neg-frac2 89.8%

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

      4. add-sqr-sqrt 40.0%

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

      5. sqrt-unprod 49.6%

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

      6. sqr-neg 49.6%

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

      7. sqrt-unprod 22.6%

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

      8. add-sqr-sqrt 41.3%

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

      9. clear-num 41.3%

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

      10. cancel-sign-sub-inv 41.3%

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

      11. clear-num 41.3%

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

      12. div-inv 41.3%

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

      13. div-inv 41.3%

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

      14. clear-num 41.3%

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

   9. Applied egg-rr 89.9%

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

   if 1.53999999999999993e41 < z

   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 t around 0 90.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.54 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+18)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 2.1e+41) (+ x (* t (/ y (- a z)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+18) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 2.1e+41) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y / ((z - 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 <= (-1.2d+18)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 2.1d+41) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y / ((z - 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 <= -1.2e+18) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 2.1e+41) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+18:
		tmp = x + (y * ((z - t) / z))
	elif z <= 2.1e+41:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+18)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 2.1e+41)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+18)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 2.1e+41)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+18], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+41], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e18

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -1.2e18 < z < 2.1e41

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. mul-1-neg 88.7%

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

      3. distribute-rgt-neg-in 88.7%

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

      4. associate-*r/ 91.1%

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

   5. Simplified 91.1%

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

   if 2.1e41 < z

   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 t around 0 90.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+18} \lor \neg \left(z \leq 4.3 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+18) (not (<= z 4.3e-45))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+18) || !(z <= 4.3e-45)) {
		tmp = y + x;
	} 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 ((z <= (-1.5d+18)) .or. (.not. (z <= 4.3d-45))) then
        tmp = y + x
    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 ((z <= -1.5e+18) || !(z <= 4.3e-45)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+18) or not (z <= 4.3e-45):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+18) || !(z <= 4.3e-45))
		tmp = Float64(y + x);
	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 ((z <= -1.5e+18) || ~((z <= 4.3e-45)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+18], N[Not[LessEqual[z, 4.3e-45]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e18 or 4.2999999999999999e-45 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.0%

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

      1. +-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.5e18 < z < 4.2999999999999999e-45

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+18} \lor \neg \left(z \leq 4.3 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18} \lor \neg \left(z \leq 4.3 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+18) (not (<= z 4.3e-45))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+18) || !(z <= 4.3e-45)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	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+18)) .or. (.not. (z <= 4.3d-45))) then
        tmp = y + x
    else
        tmp = x + (y / (a / t))
    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+18) || !(z <= 4.3e-45)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+18) or not (z <= 4.3e-45):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+18) || !(z <= 4.3e-45))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+18) || ~((z <= 4.3e-45)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+18], N[Not[LessEqual[z, 4.3e-45]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e18 or 4.2999999999999999e-45 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.0%

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

      1. +-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.2e18 < z < 4.2999999999999999e-45

   1. Initial program 95.4%

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

      1. clear-num 95.3%

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

      2. un-div-inv 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around 0 80.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18} \lor \neg \left(z \leq 4.3 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+18} \lor \neg \left(z \leq 2.1 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+18) (not (<= z 2.1e-45))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+18) || !(z <= 2.1e-45)) {
		tmp = y + x;
	} 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 <= (-1.45d+18)) .or. (.not. (z <= 2.1d-45))) then
        tmp = y + x
    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 <= -1.45e+18) || !(z <= 2.1e-45)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+18) or not (z <= 2.1e-45):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+18) || !(z <= 2.1e-45))
		tmp = Float64(y + x);
	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 <= -1.45e+18) || ~((z <= 2.1e-45)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+18], N[Not[LessEqual[z, 2.1e-45]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e18 or 2.09999999999999995e-45 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.0%

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

      1. +-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.45e18 < z < 2.09999999999999995e-45

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+18} \lor \neg \left(z \leq 2.1 \cdot 10^{-45}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17} \lor \neg \left(z \leq 8.5 \cdot 10^{-54}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+17) (not (<= z 8.5e-54))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+17) || !(z <= 8.5e-54)) {
		tmp = y + x;
	} 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 ((z <= (-6.5d+17)) .or. (.not. (z <= 8.5d-54))) then
        tmp = y + x
    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 ((z <= -6.5e+17) || !(z <= 8.5e-54)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+17) or not (z <= 8.5e-54):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+17) || !(z <= 8.5e-54))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+17) || ~((z <= 8.5e-54)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+17], N[Not[LessEqual[z, 8.5e-54]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e17 or 8.5e-54 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. +-commutative 75.7%

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

   5. Simplified 75.7%

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

   if -6.5e17 < z < 8.5e-54

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 42.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17} \lor \neg \left(z \leq 8.5 \cdot 10^{-54}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% 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 97.7%

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

3. Taylor expanded in x around inf 47.2%

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

4. Final simplification 47.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.0% 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 2024071 
(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)))))