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

Percentage Accurate: 86.3% → 98.2%

Time: 8.3s

Alternatives: 12

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: 86.3% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - (y * ((t - z) / (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 * ((t - z) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

   1. associate-*l/ 94.3%

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

3. Simplified 94.3%

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

4. Taylor expanded in y around 0 89.2%

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

   1. associate-*r/ 97.3%

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

6. Simplified 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+131)
   (+ x y)
   (if (<= z -7.5e+49)
     (- x (* t (/ y z)))
     (if (<= z -6.7e-32)
       (+ x y)
       (if (<= z 2.9e-217)
         (+ x (/ t (/ a y)))
         (if (<= z 6.8e-162)
           (- x (/ (* y t) z))
           (if (<= z 2.45e-27) (+ x (/ y (/ a t))) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+131) {
		tmp = x + y;
	} else if (z <= -7.5e+49) {
		tmp = x - (t * (y / z));
	} else if (z <= -6.7e-32) {
		tmp = x + y;
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 6.8e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 2.45e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+131)) then
        tmp = x + y
    else if (z <= (-7.5d+49)) then
        tmp = x - (t * (y / z))
    else if (z <= (-6.7d-32)) then
        tmp = x + y
    else if (z <= 2.9d-217) then
        tmp = x + (t / (a / y))
    else if (z <= 6.8d-162) then
        tmp = x - ((y * t) / z)
    else if (z <= 2.45d-27) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+131) {
		tmp = x + y;
	} else if (z <= -7.5e+49) {
		tmp = x - (t * (y / z));
	} else if (z <= -6.7e-32) {
		tmp = x + y;
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 6.8e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 2.45e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+131:
		tmp = x + y
	elif z <= -7.5e+49:
		tmp = x - (t * (y / z))
	elif z <= -6.7e-32:
		tmp = x + y
	elif z <= 2.9e-217:
		tmp = x + (t / (a / y))
	elif z <= 6.8e-162:
		tmp = x - ((y * t) / z)
	elif z <= 2.45e-27:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+131)
		tmp = Float64(x + y);
	elseif (z <= -7.5e+49)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -6.7e-32)
		tmp = Float64(x + y);
	elseif (z <= 2.9e-217)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 6.8e-162)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 2.45e-27)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+131)
		tmp = x + y;
	elseif (z <= -7.5e+49)
		tmp = x - (t * (y / z));
	elseif (z <= -6.7e-32)
		tmp = x + y;
	elseif (z <= 2.9e-217)
		tmp = x + (t / (a / y));
	elseif (z <= 6.8e-162)
		tmp = x - ((y * t) / z);
	elseif (z <= 2.45e-27)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+131], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.5e+49], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.7e-32], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.9e-217], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-162], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-27], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.4999999999999999e131 or -7.4999999999999995e49 < z < -6.7e-32 or 2.44999999999999988e-27 < z

   1. Initial program 82.8%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -3.4999999999999999e131 < z < -7.4999999999999995e49

   1. Initial program 93.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 87.4%

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

      1. associate-/l* 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. associate-*r* 87.9%

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

      3. neg-mul-1 87.9%

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

   9. Simplified 87.9%

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

       1. associate-/l* 94.1%

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

       2. associate-/r/ 94.1%

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

       3. add-sqr-sqrt 47.5%

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

       4. sqrt-unprod 66.9%

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

       5. sqr-neg 66.9%

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

       6. sqrt-unprod 20.0%

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

       7. add-sqr-sqrt 66.8%

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

   11. Applied egg-rr 66.8%

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

       1. frac-2neg 66.8%

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

       2. distribute-frac-neg 66.8%

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

       3. add-sqr-sqrt 20.0%

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

       4. sqrt-unprod 66.9%

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

       5. sqr-neg 66.9%

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

       6. sqrt-unprod 47.5%

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

       7. add-sqr-sqrt 94.1%

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

       8. frac-2neg 94.1%

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

       9. cancel-sign-sub-inv 94.1%

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

   13. Applied egg-rr 94.1%

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

   if -6.7e-32 < z < 2.89999999999999982e-217

   1. Initial program 94.7%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. associate-*r/ 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in z around 0 83.3%

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

      1. associate-*r/ 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/l* 83.5%

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

   9. Applied egg-rr 83.5%

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

   if 2.89999999999999982e-217 < z < 6.8e-162

   1. Initial program 99.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around 0 80.1%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in z around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   if 6.8e-162 < z < 2.44999999999999988e-27

   1. Initial program 96.1%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 72.4%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -6.4e-28)
     t_1
     (if (<= z 2.9e-217)
       (+ x (/ t (/ a y)))
       (if (<= z 3e-162)
         (- x (/ (* y t) z))
         (if (<= z 1.8e-45) (+ x (/ y (/ a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -6.4e-28) {
		tmp = t_1;
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 3e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.8e-45) {
		tmp = x + (y / (a / t));
	} 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 - t)))
    if (z <= (-6.4d-28)) then
        tmp = t_1
    else if (z <= 2.9d-217) then
        tmp = x + (t / (a / y))
    else if (z <= 3d-162) then
        tmp = x - ((y * t) / z)
    else if (z <= 1.8d-45) then
        tmp = x + (y / (a / t))
    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 - t)));
	double tmp;
	if (z <= -6.4e-28) {
		tmp = t_1;
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 3e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.8e-45) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -6.4e-28:
		tmp = t_1
	elif z <= 2.9e-217:
		tmp = x + (t / (a / y))
	elif z <= 3e-162:
		tmp = x - ((y * t) / z)
	elif z <= 1.8e-45:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -6.4e-28)
		tmp = t_1;
	elseif (z <= 2.9e-217)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3e-162)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 1.8e-45)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -6.4e-28)
		tmp = t_1;
	elseif (z <= 2.9e-217)
		tmp = x + (t / (a / y));
	elseif (z <= 3e-162)
		tmp = x - ((y * t) / z);
	elseif (z <= 1.8e-45)
		tmp = x + (y / (a / t));
	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 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e-28], t$95$1, If[LessEqual[z, 2.9e-217], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-162], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-45], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.39999999999999964e-28 or 1.8e-45 < z

   1. Initial program 84.7%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around 0 84.7%

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

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 88.0%

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

   9. Simplified 88.0%

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

   if -6.39999999999999964e-28 < z < 2.89999999999999982e-217

   1. Initial program 93.5%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around 0 93.5%

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

      1. associate-*r/ 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in z around 0 82.5%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-/l* 82.6%

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

   9. Applied egg-rr 82.6%

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

   if 2.89999999999999982e-217 < z < 2.99999999999999999e-162

   1. Initial program 99.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around 0 80.1%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in z around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   if 2.99999999999999999e-162 < z < 1.8e-45

   1. Initial program 95.8%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 74.3%

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

      1. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 4: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e-107)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z 2.9e-217)
     (+ x (/ t (/ a y)))
     (if (<= z 3e-162)
       (- x (/ (* y t) z))
       (if (<= z 4.3e-45) (+ x (/ y (/ a t))) (+ x (/ y (/ z (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e-107) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 3e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 4.3e-45) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d-107)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 2.9d-217) then
        tmp = x + (t / (a / y))
    else if (z <= 3d-162) then
        tmp = x - ((y * t) / z)
    else if (z <= 4.3d-45) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e-107) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 2.9e-217) {
		tmp = x + (t / (a / y));
	} else if (z <= 3e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 4.3e-45) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e-107:
		tmp = x + (y / ((z - a) / z))
	elif z <= 2.9e-217:
		tmp = x + (t / (a / y))
	elif z <= 3e-162:
		tmp = x - ((y * t) / z)
	elif z <= 4.3e-45:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e-107)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 2.9e-217)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3e-162)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 4.3e-45)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e-107)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 2.9e-217)
		tmp = x + (t / (a / y));
	elseif (z <= 3e-162)
		tmp = x - ((y * t) / z);
	elseif (z <= 4.3e-45)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e-107], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-217], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-162], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-45], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.79999999999999989e-107

   1. Initial program 85.1%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

   if -4.79999999999999989e-107 < z < 2.89999999999999982e-217

   1. Initial program 94.0%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 94.0%

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

      1. associate-*r/ 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in z around 0 84.5%

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

      1. associate-*r/ 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-/l* 84.6%

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

   9. Applied egg-rr 84.6%

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

   if 2.89999999999999982e-217 < z < 2.99999999999999999e-162

   1. Initial program 99.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around 0 80.1%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in z around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   if 2.99999999999999999e-162 < z < 4.2999999999999999e-45

   1. Initial program 95.8%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 74.3%

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

      1. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

   if 4.2999999999999999e-45 < z

   1. Initial program 84.9%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 84.9%

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

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -4.55 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) (- t z)))))
   (if (<= z -4.55e-107)
     (+ x (/ y (/ (- z a) z)))
     (if (<= z 2.9e-217)
       t_1
       (if (<= z 3.1e-162)
         (- x (/ (* y t) z))
         (if (<= z 1.42e-106) t_1 (+ x (/ y (/ z (- z t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * (t - z));
	double tmp;
	if (z <= -4.55e-107) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 2.9e-217) {
		tmp = t_1;
	} else if (z <= 3.1e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.42e-106) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / a) * (t - z))
    if (z <= (-4.55d-107)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 2.9d-217) then
        tmp = t_1
    else if (z <= 3.1d-162) then
        tmp = x - ((y * t) / z)
    else if (z <= 1.42d-106) then
        tmp = t_1
    else
        tmp = x + (y / (z / (z - t)))
    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 / a) * (t - z));
	double tmp;
	if (z <= -4.55e-107) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 2.9e-217) {
		tmp = t_1;
	} else if (z <= 3.1e-162) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.42e-106) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * (t - z))
	tmp = 0
	if z <= -4.55e-107:
		tmp = x + (y / ((z - a) / z))
	elif z <= 2.9e-217:
		tmp = t_1
	elif z <= 3.1e-162:
		tmp = x - ((y * t) / z)
	elif z <= 1.42e-106:
		tmp = t_1
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * Float64(t - z)))
	tmp = 0.0
	if (z <= -4.55e-107)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 2.9e-217)
		tmp = t_1;
	elseif (z <= 3.1e-162)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 1.42e-106)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * (t - z));
	tmp = 0.0;
	if (z <= -4.55e-107)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 2.9e-217)
		tmp = t_1;
	elseif (z <= 3.1e-162)
		tmp = x - ((y * t) / z);
	elseif (z <= 1.42e-106)
		tmp = t_1;
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.55e-107], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-217], t$95$1, If[LessEqual[z, 3.1e-162], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-106], t$95$1, N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5500000000000001e-107

   1. Initial program 85.1%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

   if -4.5500000000000001e-107 < z < 2.89999999999999982e-217 or 3.0999999999999999e-162 < z < 1.4199999999999999e-106

   1. Initial program 94.8%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

   6. Simplified 87.3%

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

   if 2.89999999999999982e-217 < z < 3.0999999999999999e-162

   1. Initial program 99.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around 0 80.1%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in z around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-*r* 80.1%

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

      3. neg-mul-1 80.1%

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

   9. Simplified 80.1%

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

   if 1.4199999999999999e-106 < z

   1. Initial program 86.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 86.0%

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

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/l* 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.55 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+131)
   (+ x y)
   (if (<= z -2.9e+47)
     (- x (* t (/ y z)))
     (if (<= z -5.1e-27)
       (+ x y)
       (if (<= z 1.06e-27) (+ x (/ y (/ a t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+131) {
		tmp = x + y;
	} else if (z <= -2.9e+47) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.1e-27) {
		tmp = x + y;
	} else if (z <= 1.06e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4d+131)) then
        tmp = x + y
    else if (z <= (-2.9d+47)) then
        tmp = x - (t * (y / z))
    else if (z <= (-5.1d-27)) then
        tmp = x + y
    else if (z <= 1.06d-27) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+131) {
		tmp = x + y;
	} else if (z <= -2.9e+47) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.1e-27) {
		tmp = x + y;
	} else if (z <= 1.06e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+131:
		tmp = x + y
	elif z <= -2.9e+47:
		tmp = x - (t * (y / z))
	elif z <= -5.1e-27:
		tmp = x + y
	elif z <= 1.06e-27:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+131)
		tmp = Float64(x + y);
	elseif (z <= -2.9e+47)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -5.1e-27)
		tmp = Float64(x + y);
	elseif (z <= 1.06e-27)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+131)
		tmp = x + y;
	elseif (z <= -2.9e+47)
		tmp = x - (t * (y / z));
	elseif (z <= -5.1e-27)
		tmp = x + y;
	elseif (z <= 1.06e-27)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+131], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.9e+47], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.06e-27], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999996e131 or -2.8999999999999998e47 < z < -5.0999999999999999e-27 or 1.05999999999999998e-27 < z

   1. Initial program 83.3%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around inf 77.7%

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

   if -3.9999999999999996e131 < z < -2.8999999999999998e47

   1. Initial program 93.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 87.4%

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

      1. associate-/l* 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. associate-*r* 87.9%

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

      3. neg-mul-1 87.9%

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

   9. Simplified 87.9%

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

       1. associate-/l* 94.1%

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

       2. associate-/r/ 94.1%

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

       3. add-sqr-sqrt 47.5%

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

       4. sqrt-unprod 66.9%

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

       5. sqr-neg 66.9%

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

       6. sqrt-unprod 20.0%

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

       7. add-sqr-sqrt 66.8%

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

   11. Applied egg-rr 66.8%

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

       1. frac-2neg 66.8%

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

       2. distribute-frac-neg 66.8%

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

       3. add-sqr-sqrt 20.0%

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

       4. sqrt-unprod 66.9%

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

       5. sqr-neg 66.9%

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

       6. sqrt-unprod 47.5%

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

       7. add-sqr-sqrt 94.1%

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

       8. frac-2neg 94.1%

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

       9. cancel-sign-sub-inv 94.1%

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

   13. Applied egg-rr 94.1%

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

   if -5.0999999999999999e-27 < z < 1.05999999999999998e-27

   1. Initial program 94.9%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+50}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+185}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+72)
   (- x (* t (/ y z)))
   (if (<= t 6.9e+50)
     (+ x (* z (/ y (- z a))))
     (if (<= t 5.2e+124)
       (+ x (* y (/ t a)))
       (if (<= t 1.7e+185) (- x (/ t (/ z y))) (+ x (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+72) {
		tmp = x - (t * (y / z));
	} else if (t <= 6.9e+50) {
		tmp = x + (z * (y / (z - a)));
	} else if (t <= 5.2e+124) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.7e+185) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + (t / (a / 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 (t <= (-4.6d+72)) then
        tmp = x - (t * (y / z))
    else if (t <= 6.9d+50) then
        tmp = x + (z * (y / (z - a)))
    else if (t <= 5.2d+124) then
        tmp = x + (y * (t / a))
    else if (t <= 1.7d+185) then
        tmp = x - (t / (z / y))
    else
        tmp = x + (t / (a / 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 (t <= -4.6e+72) {
		tmp = x - (t * (y / z));
	} else if (t <= 6.9e+50) {
		tmp = x + (z * (y / (z - a)));
	} else if (t <= 5.2e+124) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.7e+185) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+72:
		tmp = x - (t * (y / z))
	elif t <= 6.9e+50:
		tmp = x + (z * (y / (z - a)))
	elif t <= 5.2e+124:
		tmp = x + (y * (t / a))
	elif t <= 1.7e+185:
		tmp = x - (t / (z / y))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+72)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t <= 6.9e+50)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (t <= 5.2e+124)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 1.7e+185)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.6e+72)
		tmp = x - (t * (y / z));
	elseif (t <= 6.9e+50)
		tmp = x + (z * (y / (z - a)));
	elseif (t <= 5.2e+124)
		tmp = x + (y * (t / a));
	elseif (t <= 1.7e+185)
		tmp = x - (t / (z / y));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+72], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.9e+50], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+124], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+185], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.6e72

   1. Initial program 85.2%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 68.1%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in z around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. associate-*r* 68.1%

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

      3. neg-mul-1 68.1%

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

   9. Simplified 68.1%

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

       1. associate-/l* 71.9%

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

       2. associate-/r/ 73.9%

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

       3. add-sqr-sqrt 31.5%

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

       4. sqrt-unprod 49.7%

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

       5. sqr-neg 49.7%

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

       6. sqrt-unprod 20.4%

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

       7. add-sqr-sqrt 34.1%

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

   11. Applied egg-rr 34.1%

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

       1. frac-2neg 34.1%

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

       2. distribute-frac-neg 34.1%

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

       3. add-sqr-sqrt 20.4%

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

       4. sqrt-unprod 49.7%

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

       5. sqr-neg 49.7%

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

       6. sqrt-unprod 31.5%

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

       7. add-sqr-sqrt 73.9%

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

       8. frac-2neg 73.9%

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

       9. cancel-sign-sub-inv 73.9%

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

   13. Applied egg-rr 73.9%

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

   if -4.6e72 < t < 6.90000000000000032e50

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 89.3%

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

   6. Simplified 89.3%

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

      1. associate-/r/ 85.7%

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

   8. Applied egg-rr 85.7%

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

   if 6.90000000000000032e50 < t < 5.2000000000000001e124

   1. Initial program 90.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 90.1%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 84.5%

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

   if 5.2000000000000001e124 < t < 1.70000000000000009e185

   1. Initial program 89.0%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 77.9%

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

      1. associate-/l* 88.7%

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

   6. Simplified 88.7%

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

   7. Taylor expanded in z around 0 77.6%

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

      1. associate-*r/ 77.6%

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

      2. associate-*r* 77.6%

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

      3. neg-mul-1 77.6%

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

   9. Simplified 77.6%

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

       1. associate-/l* 56.9%

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

       2. associate-/r/ 77.6%

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

       3. add-sqr-sqrt 22.2%

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

       4. sqrt-unprod 23.6%

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

       5. sqr-neg 23.6%

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

       6. sqrt-unprod 12.0%

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

       7. add-sqr-sqrt 12.3%

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

   11. Applied egg-rr 12.3%

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

       1. frac-2neg 12.3%

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

       2. distribute-frac-neg 12.3%

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

       3. add-sqr-sqrt 12.0%

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

       4. sqrt-unprod 23.6%

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

       5. sqr-neg 23.6%

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

       6. sqrt-unprod 22.2%

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

       7. add-sqr-sqrt 77.6%

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

       8. frac-2neg 77.6%

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

       9. cancel-sign-sub-inv 77.6%

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

   13. Applied egg-rr 77.6%

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

       1. associate-*l/ 77.6%

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

       2. *-commutative 77.6%

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

       3. associate-/l* 77.8%

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

   15. Simplified 77.8%

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

   if 1.70000000000000009e185 < t

   1. Initial program 89.8%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 89.8%

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

      1. associate-*r/ 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in z around 0 59.9%

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

      1. associate-*r/ 56.6%

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

      2. *-commutative 56.6%

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

      3. associate-/l* 65.6%

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

   9. Applied egg-rr 65.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+50}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+185}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-64} \lor \neg \left(t \leq 4.2 \cdot 10^{+33}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e-64) (not (<= t 4.2e+33)))
   (+ x (/ y (/ (- z a) (- t))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-64) || !(t <= 4.2e+33)) {
		tmp = x + (y / ((z - a) / -t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d-64)) .or. (.not. (t <= 4.2d+33))) then
        tmp = x + (y / ((z - a) / -t))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-64) || !(t <= 4.2e+33)) {
		tmp = x + (y / ((z - a) / -t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e-64) or not (t <= 4.2e+33):
		tmp = x + (y / ((z - a) / -t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e-64) || !(t <= 4.2e+33))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(-t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e-64) || ~((t <= 4.2e+33)))
		tmp = x + (y / ((z - a) / -t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e-64], N[Not[LessEqual[t, 4.2e+33]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999986e-64 or 4.2000000000000001e33 < t

   1. Initial program 89.8%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. mul-1-neg 86.1%

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

      3. distribute-rgt-neg-out 86.1%

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

      4. associate-/l* 88.9%

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

   6. Simplified 88.9%

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

   if -3.99999999999999986e-64 < t < 4.2000000000000001e33

   1. Initial program 88.6%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. associate-/l* 91.7%

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

   6. Simplified 91.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-64} \lor \neg \left(t \leq 4.2 \cdot 10^{+33}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 9: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e-28) (+ x y) (if (<= z 6.6e-29) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-28) {
		tmp = x + y;
	} else if (z <= 6.6e-29) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d-28)) then
        tmp = x + y
    else if (z <= 6.6d-29) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-28) {
		tmp = x + y;
	} else if (z <= 6.6e-29) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e-28:
		tmp = x + y
	elif z <= 6.6e-29:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e-28)
		tmp = Float64(x + y);
	elseif (z <= 6.6e-29)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e-28)
		tmp = x + y;
	elseif (z <= 6.6e-29)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e-28], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.6e-29], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999982e-28 or 6.60000000000000055e-29 < z

   1. Initial program 84.5%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around inf 76.6%

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

   if -3.19999999999999982e-28 < z < 6.60000000000000055e-29

   1. Initial program 94.9%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 94.9%

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

      1. associate-*r/ 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in z around 0 76.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e-26) (+ x y) (if (<= z 3.8e-27) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-26) {
		tmp = x + y;
	} else if (z <= 3.8e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d-26)) then
        tmp = x + y
    else if (z <= 3.8d-27) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-26) {
		tmp = x + y;
	} else if (z <= 3.8e-27) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e-26:
		tmp = x + y
	elif z <= 3.8e-27:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e-26)
		tmp = Float64(x + y);
	elseif (z <= 3.8e-27)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e-26)
		tmp = x + y;
	elseif (z <= 3.8e-27)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e-26], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.8e-27], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000002e-26 or 3.8e-27 < z

   1. Initial program 84.5%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around inf 76.6%

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

   if -5.2000000000000002e-26 < z < 3.8e-27

   1. Initial program 94.9%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 64.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-32) (+ x y) (if (<= z 1.1e-28) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-32) {
		tmp = x + y;
	} else if (z <= 1.1e-28) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d-32)) then
        tmp = x + y
    else if (z <= 1.1d-28) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-32) {
		tmp = x + y;
	} else if (z <= 1.1e-28) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-32:
		tmp = x + y
	elif z <= 1.1e-28:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-32)
		tmp = Float64(x + y);
	elseif (z <= 1.1e-28)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-32)
		tmp = x + y;
	elseif (z <= 1.1e-28)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-32], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.1e-28], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000011e-32 or 1.09999999999999998e-28 < z

   1. Initial program 84.0%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around inf 76.2%

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

   if -2.00000000000000011e-32 < z < 1.09999999999999998e-28

   1. Initial program 95.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 53.1%

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

      1. associate-/l* 48.1%

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

   6. Simplified 48.1%

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

   7. Taylor expanded in z around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. associate-*r* 51.0%

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

      3. neg-mul-1 51.0%

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

   9. Simplified 51.0%

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

       1. associate-/l* 47.5%

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

       2. associate-/r/ 46.2%

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

       3. add-sqr-sqrt 24.6%

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

       4. sqrt-unprod 40.9%

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

       5. sqr-neg 40.9%

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

       6. sqrt-unprod 14.7%

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

       7. add-sqr-sqrt 30.4%

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

   11. Applied egg-rr 30.4%

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

   12. Taylor expanded in x around inf 48.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 51.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

   1. associate-*l/ 94.3%

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

3. Simplified 94.3%

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

4. Taylor expanded in a around 0 65.0%

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

   1. associate-/l* 66.7%

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

6. Simplified 66.7%

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

7. Taylor expanded in z around 0 53.8%

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

   1. associate-*r/ 53.8%

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

   2. associate-*r* 53.8%

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

   3. neg-mul-1 53.8%

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

9. Simplified 53.8%

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

    1. associate-/l* 53.3%

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

    2. associate-/r/ 52.5%

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

    3. add-sqr-sqrt 25.8%

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

    4. sqrt-unprod 44.8%

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

    5. sqr-neg 44.8%

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

    6. sqrt-unprod 20.1%

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

    7. add-sqr-sqrt 38.8%

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

11. Applied egg-rr 38.8%

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

12. Taylor expanded in x around inf 47.9%

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

13. Final simplification 47.9%

    \[\leadsto x \]

Developer target: 98.3% 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 2023266 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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