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

Percentage Accurate: 86.0% → 98.1%

Time: 9.8s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.0% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate-/l* 98.4%

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

   3. fma-define 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing

5. Final simplification 98.4%

   \[\leadsto \mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right) \]
6. Add Preprocessing

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+120}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z t)) z))))
   (if (<= z -4.8e+120)
     (+ y x)
     (if (<= z -1.55e-153)
       t_1
       (if (<= z 1.35e-191)
         (+ x (/ (* y t) a))
         (if (<= z 6.2e+200) t_1 (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / z);
	double tmp;
	if (z <= -4.8e+120) {
		tmp = y + x;
	} else if (z <= -1.55e-153) {
		tmp = t_1;
	} else if (z <= 1.35e-191) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.2e+200) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (z - t)) / z)
    if (z <= (-4.8d+120)) then
        tmp = y + x
    else if (z <= (-1.55d-153)) then
        tmp = t_1
    else if (z <= 1.35d-191) then
        tmp = x + ((y * t) / a)
    else if (z <= 6.2d+200) then
        tmp = t_1
    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 t_1 = x + ((y * (z - t)) / z);
	double tmp;
	if (z <= -4.8e+120) {
		tmp = y + x;
	} else if (z <= -1.55e-153) {
		tmp = t_1;
	} else if (z <= 1.35e-191) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.2e+200) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (z - t)) / z)
	tmp = 0
	if z <= -4.8e+120:
		tmp = y + x
	elif z <= -1.55e-153:
		tmp = t_1
	elif z <= 1.35e-191:
		tmp = x + ((y * t) / a)
	elif z <= 6.2e+200:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - t)) / z))
	tmp = 0.0
	if (z <= -4.8e+120)
		tmp = Float64(y + x);
	elseif (z <= -1.55e-153)
		tmp = t_1;
	elseif (z <= 1.35e-191)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 6.2e+200)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (z - t)) / z);
	tmp = 0.0;
	if (z <= -4.8e+120)
		tmp = y + x;
	elseif (z <= -1.55e-153)
		tmp = t_1;
	elseif (z <= 1.35e-191)
		tmp = x + ((y * t) / a);
	elseif (z <= 6.2e+200)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+120], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.55e-153], t$95$1, If[LessEqual[z, 1.35e-191], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+200], t$95$1, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000002e120 or 6.19999999999999988e200 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 93.6%

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

      1. +-commutative 93.6%

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

   5. Simplified 93.6%

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

   if -4.80000000000000002e120 < z < -1.54999999999999997e-153 or 1.34999999999999999e-191 < z < 6.19999999999999988e200

   1. Initial program 94.2%

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

   3. Taylor expanded in a around 0 77.6%

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

   if -1.54999999999999997e-153 < z < 1.34999999999999999e-191

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+120}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+200}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 50000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+204}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= t -2.9e+53)
     t_1
     (if (<= t 50000000000.0)
       (+ y x)
       (if (<= t 3.6e+204)
         (+ x (* y (/ t a)))
         (if (<= t 3.8e+285) t_1 (+ x (/ (* y t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (t <= -2.9e+53) {
		tmp = t_1;
	} else if (t <= 50000000000.0) {
		tmp = y + x;
	} else if (t <= 3.6e+204) {
		tmp = x + (y * (t / a));
	} else if (t <= 3.8e+285) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (t <= (-2.9d+53)) then
        tmp = t_1
    else if (t <= 50000000000.0d0) then
        tmp = y + x
    else if (t <= 3.6d+204) then
        tmp = x + (y * (t / a))
    else if (t <= 3.8d+285) then
        tmp = t_1
    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 t_1 = x - (y * (t / z));
	double tmp;
	if (t <= -2.9e+53) {
		tmp = t_1;
	} else if (t <= 50000000000.0) {
		tmp = y + x;
	} else if (t <= 3.6e+204) {
		tmp = x + (y * (t / a));
	} else if (t <= 3.8e+285) {
		tmp = t_1;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if t <= -2.9e+53:
		tmp = t_1
	elif t <= 50000000000.0:
		tmp = y + x
	elif t <= 3.6e+204:
		tmp = x + (y * (t / a))
	elif t <= 3.8e+285:
		tmp = t_1
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (t <= -2.9e+53)
		tmp = t_1;
	elseif (t <= 50000000000.0)
		tmp = Float64(y + x);
	elseif (t <= 3.6e+204)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 3.8e+285)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (t <= -2.9e+53)
		tmp = t_1;
	elseif (t <= 50000000000.0)
		tmp = y + x;
	elseif (t <= 3.6e+204)
		tmp = x + (y * (t / a));
	elseif (t <= 3.8e+285)
		tmp = t_1;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+53], t$95$1, If[LessEqual[t, 50000000000.0], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.6e+204], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+285], t$95$1, N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9000000000000002e53 or 3.6000000000000002e204 < t < 3.7999999999999999e285

   1. Initial program 82.9%

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

   3. Taylor expanded in a around 0 68.1%

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

      1. +-commutative 68.1%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. neg-mul-1 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in t around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-*r/ 73.4%

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

       3. sub-neg 73.4%

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

       4. *-commutative 73.4%

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

       5. associate-*l/ 68.1%

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

       6. associate-*r/ 70.7%

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

   11. Simplified 70.7%

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

   if -2.9000000000000002e53 < t < 5e10

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 5e10 < t < 3.6000000000000002e204

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   7. Applied egg-rr 78.6%

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

      1. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   if 3.7999999999999999e285 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 50000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+204}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+285}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+204}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+284}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+53)
   (- x (/ y (/ z t)))
   (if (<= t 3e+20)
     (+ y x)
     (if (<= t 7.8e+204)
       (+ x (* y (/ t a)))
       (if (<= t 1.4e+284) (- x (* y (/ t z))) (+ x (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+53) {
		tmp = x - (y / (z / t));
	} else if (t <= 3e+20) {
		tmp = y + x;
	} else if (t <= 7.8e+204) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.4e+284) {
		tmp = x - (y * (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 (t <= (-2.5d+53)) then
        tmp = x - (y / (z / t))
    else if (t <= 3d+20) then
        tmp = y + x
    else if (t <= 7.8d+204) then
        tmp = x + (y * (t / a))
    else if (t <= 1.4d+284) then
        tmp = x - (y * (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 (t <= -2.5e+53) {
		tmp = x - (y / (z / t));
	} else if (t <= 3e+20) {
		tmp = y + x;
	} else if (t <= 7.8e+204) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.4e+284) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+53:
		tmp = x - (y / (z / t))
	elif t <= 3e+20:
		tmp = y + x
	elif t <= 7.8e+204:
		tmp = x + (y * (t / a))
	elif t <= 1.4e+284:
		tmp = x - (y * (t / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+53)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (t <= 3e+20)
		tmp = Float64(y + x);
	elseif (t <= 7.8e+204)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 1.4e+284)
		tmp = Float64(x - Float64(y * 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 (t <= -2.5e+53)
		tmp = x - (y / (z / t));
	elseif (t <= 3e+20)
		tmp = y + x;
	elseif (t <= 7.8e+204)
		tmp = x + (y * (t / a));
	elseif (t <= 1.4e+284)
		tmp = x - (y * (t / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+53], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+20], N[(y + x), $MachinePrecision], If[LessEqual[t, 7.8e+204], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+284], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5000000000000002e53

   1. Initial program 82.2%

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

   3. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in z around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around 0 69.2%

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

       1. mul-1-neg 69.2%

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

       2. associate-*r/ 72.8%

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

       3. sub-neg 72.8%

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

       4. *-commutative 72.8%

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

       5. associate-*l/ 69.2%

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

       6. associate-*r/ 72.8%

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

   11. Simplified 72.8%

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

       1. clear-num 72.7%

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

       2. un-div-inv 72.8%

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

   13. Applied egg-rr 72.8%

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

   if -2.5000000000000002e53 < t < 3e20

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 3e20 < t < 7.80000000000000033e204

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   7. Applied egg-rr 78.6%

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

      1. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   if 7.80000000000000033e204 < t < 1.39999999999999998e284

   1. Initial program 84.7%

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

   3. Taylor expanded in a around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in z around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in t around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-*r/ 74.9%

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

       3. sub-neg 74.9%

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

       4. *-commutative 74.9%

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

       5. associate-*l/ 64.9%

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

       6. associate-*r/ 65.0%

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

   11. Simplified 65.0%

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

   if 1.39999999999999998e284 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+204}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+284}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+206}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+263}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+52)
   (- x (/ y (/ z t)))
   (if (<= t 3.6e+19)
     (+ y x)
     (if (<= t 1.52e+206)
       (+ x (* y (/ t a)))
       (if (<= t 1.62e+263) (- x (/ (* y t) z)) (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+52) {
		tmp = x - (y / (z / t));
	} else if (t <= 3.6e+19) {
		tmp = y + x;
	} else if (t <= 1.52e+206) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.62e+263) {
		tmp = x - ((y * 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 (t <= (-4.4d+52)) then
        tmp = x - (y / (z / t))
    else if (t <= 3.6d+19) then
        tmp = y + x
    else if (t <= 1.52d+206) then
        tmp = x + (y * (t / a))
    else if (t <= 1.62d+263) then
        tmp = x - ((y * 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 (t <= -4.4e+52) {
		tmp = x - (y / (z / t));
	} else if (t <= 3.6e+19) {
		tmp = y + x;
	} else if (t <= 1.52e+206) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.62e+263) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+52:
		tmp = x - (y / (z / t))
	elif t <= 3.6e+19:
		tmp = y + x
	elif t <= 1.52e+206:
		tmp = x + (y * (t / a))
	elif t <= 1.62e+263:
		tmp = x - ((y * t) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+52)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (t <= 3.6e+19)
		tmp = Float64(y + x);
	elseif (t <= 1.52e+206)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 1.62e+263)
		tmp = Float64(x - Float64(Float64(y * 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 (t <= -4.4e+52)
		tmp = x - (y / (z / t));
	elseif (t <= 3.6e+19)
		tmp = y + x;
	elseif (t <= 1.52e+206)
		tmp = x + (y * (t / a));
	elseif (t <= 1.62e+263)
		tmp = x - ((y * t) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+52], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+19], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.52e+206], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.62e+263], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.4e52

   1. Initial program 82.2%

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

   3. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in z around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around 0 69.2%

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

       1. mul-1-neg 69.2%

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

       2. associate-*r/ 72.8%

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

       3. sub-neg 72.8%

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

       4. *-commutative 72.8%

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

       5. associate-*l/ 69.2%

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

       6. associate-*r/ 72.8%

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

   11. Simplified 72.8%

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

       1. clear-num 72.7%

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

       2. un-div-inv 72.8%

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

   13. Applied egg-rr 72.8%

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

   if -4.4e52 < t < 3.6e19

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 3.6e19 < t < 1.52e206

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   7. Applied egg-rr 78.6%

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

      1. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   if 1.52e206 < t < 1.61999999999999993e263

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

      3. distribute-rgt-neg-in 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in t around 0 70.6%

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

       1. mul-1-neg 70.6%

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

       2. associate-*r/ 76.5%

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

       3. sub-neg 76.5%

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

       4. *-commutative 76.5%

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

       5. associate-*l/ 70.6%

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

       6. associate-*r/ 64.7%

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

   11. Simplified 64.7%

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

       1. associate-*r/ 70.6%

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

   13. Applied egg-rr 70.6%

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

   if 1.61999999999999993e263 < t

   1. Initial program 72.9%

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

   3. Taylor expanded in z around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+206}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+263}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -3.6e-40)
     t_1
     (if (<= z -1.8e-151)
       (+ x (/ (* y (- z t)) z))
       (if (<= z 2.5e-168) (+ x (/ (* y t) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -3.6e-40) {
		tmp = t_1;
	} else if (z <= -1.8e-151) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2.5e-168) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-3.6d-40)) then
        tmp = t_1
    else if (z <= (-1.8d-151)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 2.5d-168) then
        tmp = x + ((y * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -3.6e-40) {
		tmp = t_1;
	} else if (z <= -1.8e-151) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2.5e-168) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -3.6e-40:
		tmp = t_1
	elif z <= -1.8e-151:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 2.5e-168:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -3.6e-40)
		tmp = t_1;
	elseif (z <= -1.8e-151)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 2.5e-168)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -3.6e-40)
		tmp = t_1;
	elseif (z <= -1.8e-151)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 2.5e-168)
		tmp = x + ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-40], t$95$1, If[LessEqual[z, -1.8e-151], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-168], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-40 or 2.50000000000000001e-168 < z

   1. Initial program 81.7%

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

   3. Taylor expanded in t around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

   if -3.6e-40 < z < -1.80000000000000016e-151

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 90.1%

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

   if -1.80000000000000016e-151 < z < 2.50000000000000001e-168

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 86.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-40)
   (+ x (* y (/ z (- z a))))
   (if (<= z -2.25e-153)
     (+ x (/ (* y (- z t)) z))
     (if (<= z 1.3e-191) (+ x (/ (* y t) a)) (- x (* y (/ (- t z) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-40) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= -2.25e-153) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1.3e-191) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * ((t - z) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d-40)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= (-2.25d-153)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 1.3d-191) then
        tmp = x + ((y * t) / a)
    else
        tmp = x - (y * ((t - z) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-40) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= -2.25e-153) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1.3e-191) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * ((t - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e-40:
		tmp = x + (y * (z / (z - a)))
	elif z <= -2.25e-153:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 1.3e-191:
		tmp = x + ((y * t) / a)
	else:
		tmp = x - (y * ((t - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-40)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= -2.25e-153)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 1.3e-191)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e-40)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= -2.25e-153)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 1.3e-191)
		tmp = x + ((y * t) / a);
	else
		tmp = x - (y * ((t - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-40], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-153], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-191], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.49999999999999982e-40

   1. Initial program 78.1%

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

   3. Taylor expanded in t around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

   if -2.49999999999999982e-40 < z < -2.25e-153

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 90.1%

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

   if -2.25e-153 < z < 1.29999999999999993e-191

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.2%

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

   if 1.29999999999999993e-191 < z

   1. Initial program 84.6%

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

   3. Taylor expanded in a around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+28} \lor \neg \left(t \leq 2.8 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+28) (not (<= t 2.8e+75)))
   (+ x (/ y (/ (- a z) t)))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+28) || !(t <= 2.8e+75)) {
		tmp = x + (y / ((a - z) / t));
	} 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 <= (-2.1d+28)) .or. (.not. (t <= 2.8d+75))) then
        tmp = x + (y / ((a - z) / t))
    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 <= -2.1e+28) || !(t <= 2.8e+75)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+28) or not (t <= 2.8e+75):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+28) || !(t <= 2.8e+75))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	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 <= -2.1e+28) || ~((t <= 2.8e+75)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+28], N[Not[LessEqual[t, 2.8e+75]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $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 < -2.09999999999999989e28 or 2.80000000000000012e75 < t

   1. Initial program 85.3%

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

      1. associate-/l* 97.4%

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

      2. *-commutative 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in t around inf 90.0%

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

      1. neg-mul-1 90.0%

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

      2. distribute-neg-frac 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 90.8%

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

      3. distribute-lft-neg-in 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

      5. associate-/l* 85.2%

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

      6. *-rgt-identity 85.2%

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

      7. *-commutative 85.2%

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

      8. times-frac 90.8%

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

      9. /-rgt-identity 90.8%

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

      10. associate-/r/ 90.0%

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

   10. Simplified 90.0%

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

   if -2.09999999999999989e28 < t < 2.80000000000000012e75

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+28} \lor \neg \left(t \leq 2.8 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.06e+22)
   (+ x (/ y (/ (- a z) t)))
   (if (<= t 2.8e+75) (+ x (* y (/ z (- z a)))) (+ x (* t (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.06e+22) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 2.8e+75) {
		tmp = x + (y * (z / (z - a)));
	} 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) :: tmp
    if (t <= (-1.06d+22)) then
        tmp = x + (y / ((a - z) / t))
    else if (t <= 2.8d+75) then
        tmp = x + (y * (z / (z - a)))
    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 tmp;
	if (t <= -1.06e+22) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 2.8e+75) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.06e+22:
		tmp = x + (y / ((a - z) / t))
	elif t <= 2.8e+75:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.06e+22)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (t <= 2.8e+75)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	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)
	tmp = 0.0;
	if (t <= -1.06e+22)
		tmp = x + (y / ((a - z) / t));
	elseif (t <= 2.8e+75)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.06e+22], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+75], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.06e22

   1. Initial program 82.5%

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

      1. associate-/l* 98.3%

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

      2. *-commutative 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around inf 90.2%

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

      1. neg-mul-1 90.2%

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

      2. distribute-neg-frac 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in x around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/l* 90.2%

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

      3. distribute-lft-neg-in 90.2%

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

      4. cancel-sign-sub-inv 90.2%

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

      5. associate-/l* 83.9%

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

      6. *-rgt-identity 83.9%

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

      7. *-commutative 83.9%

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

      8. times-frac 90.2%

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

      9. /-rgt-identity 90.2%

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

      10. associate-/r/ 90.2%

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

   10. Simplified 90.2%

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

   if -1.06e22 < t < 2.80000000000000012e75

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

   if 2.80000000000000012e75 < t

   1. Initial program 88.2%

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

   3. Taylor expanded in t around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. associate-/l* 91.4%

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

      3. distribute-rgt-neg-in 91.4%

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

      4. distribute-neg-frac2 91.4%

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

      5. sub-neg 91.4%

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

      6. distribute-neg-in 91.4%

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

      7. remove-double-neg 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+23} \lor \neg \left(z \leq 3.2 \cdot 10^{-168}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+23) (not (<= z 3.2e-168))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+23) || !(z <= 3.2e-168)) {
		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 <= (-7d+23)) .or. (.not. (z <= 3.2d-168))) 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 <= -7e+23) || !(z <= 3.2e-168)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+23) or not (z <= 3.2e-168):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+23) || !(z <= 3.2e-168))
		tmp = Float64(y + x);
	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 <= -7e+23) || ~((z <= 3.2e-168)))
		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, -7e+23], N[Not[LessEqual[z, 3.2e-168]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000004e23 or 3.20000000000000006e-168 < z

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -7.0000000000000004e23 < z < 3.20000000000000006e-168

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 74.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+23} \lor \neg \left(z \leq 3.2 \cdot 10^{-168}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.7e-122) x (if (<= x 2.6e-161) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.7e-122) {
		tmp = x;
	} else if (x <= 2.6e-161) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.7d-122)) then
        tmp = x
    else if (x <= 2.6d-161) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.7e-122) {
		tmp = x;
	} else if (x <= 2.6e-161) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.7e-122:
		tmp = x
	elif x <= 2.6e-161:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.7e-122)
		tmp = x;
	elseif (x <= 2.6e-161)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.7e-122)
		tmp = x;
	elseif (x <= 2.6e-161)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.7e-122], x, If[LessEqual[x, 2.6e-161], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e-122 or 2.59999999999999995e-161 < x

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf 61.9%

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

   if -1.6999999999999999e-122 < x < 2.59999999999999995e-161

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 74.5%

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

   4. Taylor expanded in z around inf 43.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+221) (* y (/ t (- z))) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+221) {
		tmp = 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 (t <= (-2.6d+221)) then
        tmp = 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 (t <= -2.6e+221) {
		tmp = y * (t / -z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+221:
		tmp = y * (t / -z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+221)
		tmp = Float64(y * Float64(t / Float64(-z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+221)
		tmp = y * (t / -z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+221], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000004e221

   1. Initial program 84.3%

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

   3. Taylor expanded in a around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. neg-mul-1 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in t around 0 72.0%

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

       1. mul-1-neg 72.0%

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

       2. associate-*r/ 72.4%

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

       3. sub-neg 72.4%

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

       4. *-commutative 72.4%

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

       5. associate-*l/ 72.0%

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

       6. associate-*r/ 72.5%

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

   11. Simplified 72.5%

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

   12. Taylor expanded in x around 0 62.6%

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

       1. associate-*r/ 62.6%

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

       2. *-commutative 62.6%

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

       3. neg-mul-1 62.6%

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

       4. distribute-rgt-neg-in 62.6%

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

       5. associate-/l* 60.5%

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

   14. Simplified 60.5%

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

   if -2.60000000000000004e221 < t

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. +-commutative 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 87.1%

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

   1. associate-/l* 98.4%

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

   2. *-commutative 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

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

Alternative 14: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+223) (* t (/ y a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+223) {
		tmp = t * (y / a);
	} 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 (t <= (-4d+223)) then
        tmp = t * (y / a)
    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 (t <= -4e+223) {
		tmp = t * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+223:
		tmp = t * (y / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+223)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+223)
		tmp = t * (y / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+223], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000019e223

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 69.7%

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

   4. Taylor expanded in z around 0 41.0%

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

      1. associate-/l* 47.2%

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

   6. Simplified 47.2%

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

   if -4.00000000000000019e223 < t

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 70.0%

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

      1. +-commutative 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.42e+163) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+163) {
		tmp = x;
	} 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 (a <= (-1.42d+163)) then
        tmp = x
    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 (a <= -1.42e+163) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.42e+163:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.42e+163)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.42e+163)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.42e+163], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4199999999999999e163

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 71.1%

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

   if -1.4199999999999999e163 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.7% 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 87.1%

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

3. Taylor expanded in x around inf 49.5%

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

4. Final simplification 49.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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