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

Percentage Accurate: 98.1% → 98.1%

Time: 9.6s

Alternatives: 12

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: 98.1% 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, 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]

Derivation

1. Initial program 96.6%

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

Alternative 2: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+152}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+51)
   (+ x y)
   (if (<= z 3.5e-141)
     (+ x (/ (* y t) a))
     (if (<= z 1.1e+152) (- x (* t (/ y z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+51) {
		tmp = x + y;
	} else if (z <= 3.5e-141) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.1e+152) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+51)) then
        tmp = x + y
    else if (z <= 3.5d-141) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.1d+152) then
        tmp = x - (t * (y / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+51) {
		tmp = x + y;
	} else if (z <= 3.5e-141) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.1e+152) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+51:
		tmp = x + y
	elif z <= 3.5e-141:
		tmp = x + ((y * t) / a)
	elif z <= 1.1e+152:
		tmp = x - (t * (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+51)
		tmp = Float64(x + y);
	elseif (z <= 3.5e-141)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.1e+152)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+51)
		tmp = x + y;
	elseif (z <= 3.5e-141)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.1e+152)
		tmp = x - (t * (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+51], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.5e-141], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+152], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999997e51 or 1.0999999999999999e152 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.7%

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

      1. +-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -3.2999999999999997e51 < z < 3.5000000000000003e-141

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 82.8%

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

   if 3.5000000000000003e-141 < z < 1.0999999999999999e152

   1. Initial program 95.0%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. neg-mul-1 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in z around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. unsub-neg 61.3%

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

      3. associate-/l* 63.6%

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

   10. Simplified 63.6%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+152}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -246000 \lor \neg \left(t \leq 8.8 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -246000.0) (not (<= t 8.8e-58)))
   (+ 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 <= -246000.0) || !(t <= 8.8e-58)) {
		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 <= (-246000.0d0)) .or. (.not. (t <= 8.8d-58))) 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 <= -246000.0) || !(t <= 8.8e-58)) {
		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 <= -246000.0) or not (t <= 8.8e-58):
		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 <= -246000.0) || !(t <= 8.8e-58))
		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 <= -246000.0) || ~((t <= 8.8e-58)))
		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, -246000.0], N[Not[LessEqual[t, 8.8e-58]], $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 < -246000 or 8.80000000000000023e-58 < t

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. associate-*r/ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. distribute-lft-neg-out 82.8%

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

      4. *-commutative 82.8%

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

      5. *-lft-identity 82.8%

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

      6. times-frac 84.6%

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

      7. /-rgt-identity 84.6%

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

      8. distribute-neg-frac 84.6%

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

      9. distribute-neg-frac2 84.6%

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

      10. neg-sub0 84.6%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 84.6%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 84.6%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 84.6%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 84.6%

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

      15. remove-double-neg 84.6%

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

   5. Simplified 84.6%

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

   if -246000 < t < 8.80000000000000023e-58

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -246000 \lor \neg \left(t \leq 8.8 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+64} \lor \neg \left(z \leq 8.2 \cdot 10^{+80}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.1e+64) (not (<= z 8.2e+80)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.1e+64) || !(z <= 8.2e+80)) {
		tmp = x + (y * (1.0 - (t / 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 <= (-4.1d+64)) .or. (.not. (z <= 8.2d+80))) then
        tmp = x + (y * (1.0d0 - (t / 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 <= -4.1e+64) || !(z <= 8.2e+80)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.1e+64) or not (z <= 8.2e+80):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.1e+64) || !(z <= 8.2e+80))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.1e+64) || ~((z <= 8.2e+80)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.1e+64], N[Not[LessEqual[z, 8.2e+80]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999978e64 or 8.20000000000000003e80 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 73.4%

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

      1. associate-/l* 92.4%

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

      2. div-sub 92.4%

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

      3. *-inverses 92.4%

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

   5. Simplified 92.4%

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

   if -4.09999999999999978e64 < z < 8.20000000000000003e80

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. distribute-lft-neg-out 84.7%

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

      4. *-commutative 84.7%

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

      5. *-lft-identity 84.7%

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

      6. times-frac 83.3%

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

      7. /-rgt-identity 83.3%

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

      8. distribute-neg-frac 83.3%

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

      9. distribute-neg-frac2 83.3%

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

      10. neg-sub0 83.3%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 83.3%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 83.3%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 83.3%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 83.3%

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

      15. remove-double-neg 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+64} \lor \neg \left(z \leq 8.2 \cdot 10^{+80}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+53} \lor \neg \left(z \leq 1.4 \cdot 10^{-62}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+53) (not (<= z 1.4e-62)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+53) || !(z <= 1.4e-62)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+53)) .or. (.not. (z <= 1.4d-62))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+53) || !(z <= 1.4e-62)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+53) or not (z <= 1.4e-62):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+53) || !(z <= 1.4e-62))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+53) || ~((z <= 1.4e-62)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+53], N[Not[LessEqual[z, 1.4e-62]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e53 or 1.40000000000000001e-62 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.7%

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

      1. associate-/l* 86.5%

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

      2. div-sub 86.5%

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

      3. *-inverses 86.5%

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

   5. Simplified 86.5%

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

   if -1.4e53 < z < 1.40000000000000001e-62

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 78.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+53} \lor \neg \left(z \leq 1.4 \cdot 10^{-62}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9)
   (+ x (/ y (/ (- a z) t)))
   (if (<= t 6.5e-58) (+ x (* y (/ z (- z a)))) (+ x (* y (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 6.5e-58) {
		tmp = x + (y * (z / (z - a)));
	} 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 (t <= (-2.9d0)) then
        tmp = x + (y / ((a - z) / t))
    else if (t <= 6.5d-58) then
        tmp = x + (y * (z / (z - a)))
    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 (t <= -2.9) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 6.5e-58) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9:
		tmp = x + (y / ((a - z) / t))
	elif t <= 6.5e-58:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (t <= 6.5e-58)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9)
		tmp = x + (y / ((a - z) / t));
	elseif (t <= 6.5e-58)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-58], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.89999999999999991

   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 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. neg-mul-1 83.7%

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

   7. Simplified 83.7%

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

   if -2.89999999999999991 < t < 6.49999999999999964e-58

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

   if 6.49999999999999964e-58 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf 84.3%

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

      1. associate-*r/ 84.3%

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

      2. mul-1-neg 84.3%

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

      3. distribute-lft-neg-out 84.3%

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

      4. *-commutative 84.3%

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

      5. *-lft-identity 84.3%

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

      6. times-frac 85.4%

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

      7. /-rgt-identity 85.4%

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

      8. distribute-neg-frac 85.4%

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

      9. distribute-neg-frac2 85.4%

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

      10. neg-sub0 85.4%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 85.4%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 85.4%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 85.4%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 85.4%

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

      15. remove-double-neg 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e+51)
   (- x (/ y (/ z (- t z))))
   (if (<= z 1.25e+81) (+ x (* y (/ t (- a z)))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+51) {
		tmp = x - (y / (z / (t - z)));
	} else if (z <= 1.25e+81) {
		tmp = x + (y * (t / (a - z)));
	} 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 <= (-3.7d+51)) then
        tmp = x - (y / (z / (t - z)))
    else if (z <= 1.25d+81) then
        tmp = x + (y * (t / (a - z)))
    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 <= -3.7e+51) {
		tmp = x - (y / (z / (t - z)));
	} else if (z <= 1.25e+81) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e+51:
		tmp = x - (y / (z / (t - z)))
	elif z <= 1.25e+81:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e+51)
		tmp = Float64(x - Float64(y / Float64(z / Float64(t - z))));
	elseif (z <= 1.25e+81)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	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 <= -3.7e+51)
		tmp = x - (y / (z / (t - z)));
	elseif (z <= 1.25e+81)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e+51], N[(x - N[(y / N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+81], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $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 < -3.7000000000000002e51

   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 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 96.3%

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

   if -3.7000000000000002e51 < z < 1.25e81

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. distribute-lft-neg-out 84.7%

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

      4. *-commutative 84.7%

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

      5. *-lft-identity 84.7%

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

      6. times-frac 83.3%

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

      7. /-rgt-identity 83.3%

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

      8. distribute-neg-frac 83.3%

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

      9. distribute-neg-frac2 83.3%

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

      10. neg-sub0 83.3%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 83.3%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 83.3%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 83.3%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 83.3%

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

      15. remove-double-neg 83.3%

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

   5. Simplified 83.3%

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

   if 1.25e81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 70.2%

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

      1. associate-/l* 88.4%

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

      2. div-sub 88.4%

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

      3. *-inverses 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+51} \lor \neg \left(z \leq 1.2 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+51) (not (<= z 1.2e+66))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+51) || !(z <= 1.2e+66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+51)) .or. (.not. (z <= 1.2d+66))) then
        tmp = x + y
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+51) || !(z <= 1.2e+66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+51) or not (z <= 1.2e+66):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+51) || !(z <= 1.2e+66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+51) || ~((z <= 1.2e+66)))
		tmp = x + y;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+51], N[Not[LessEqual[z, 1.2e+66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e51 or 1.2000000000000001e66 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -2.6000000000000001e51 < z < 1.2000000000000001e66

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 72.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+51} \lor \neg \left(z \leq 1.2 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+72} \lor \neg \left(z \leq 1.22 \cdot 10^{+69}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+72) (not (<= z 1.22e+69))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+72) || !(z <= 1.22e+69)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.9d+72)) .or. (.not. (z <= 1.22d+69))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+72) || !(z <= 1.22e+69)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+72) or not (z <= 1.22e+69):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+72) || !(z <= 1.22e+69))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+72) || ~((z <= 1.22e+69)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+72], N[Not[LessEqual[z, 1.22e+69]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000003e72 or 1.22e69 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -1.90000000000000003e72 < z < 1.22e69

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 72.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+72} \lor \neg \left(z \leq 1.22 \cdot 10^{+69}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+52} \lor \neg \left(z \leq 3.8 \cdot 10^{-69}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+52) (not (<= z 3.8e-69))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+52) || !(z <= 3.8e-69)) {
		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 ((z <= (-1.55d+52)) .or. (.not. (z <= 3.8d-69))) 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 ((z <= -1.55e+52) || !(z <= 3.8e-69)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+52) or not (z <= 3.8e-69):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+52) || !(z <= 3.8e-69))
		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 ((z <= -1.55e+52) || ~((z <= 3.8e-69)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+52], N[Not[LessEqual[z, 3.8e-69]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e52 or 3.7999999999999998e-69 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 70.1%

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

      1. +-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -1.55e52 < z < 3.7999999999999998e-69

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 49.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+52} \lor \neg \left(z \leq 3.8 \cdot 10^{-69}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+212}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.55e+212) y (if (<= y 1.55e+131) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+212) {
		tmp = y;
	} else if (y <= 1.55e+131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.55d+212)) then
        tmp = y
    else if (y <= 1.55d+131) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+212) {
		tmp = y;
	} else if (y <= 1.55e+131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e+212:
		tmp = y
	elif y <= 1.55e+131:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e+212)
		tmp = y;
	elseif (y <= 1.55e+131)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e+212)
		tmp = y;
	elseif (y <= 1.55e+131)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e+212], y, If[LessEqual[y, 1.55e+131], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999999e212 or 1.55000000000000008e131 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 34.8%

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

      1. +-commutative 34.8%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in y around inf 34.8%

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

   7. Taylor expanded in y around inf 30.5%

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

   if -1.54999999999999999e212 < y < 1.55000000000000008e131

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 61.0%

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

Alternative 12: 52.2% 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 96.6%

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

3. Taylor expanded in x around inf 49.2%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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