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

Percentage Accurate: 85.6% → 96.0%

Time: 7.5s

Alternatives: 15

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: 85.6% 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: 96.0% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 83.1%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4800:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -6e+14)
     (+ x y)
     (if (<= z 1.8e-65)
       t_1
       (if (<= z 4800.0)
         (* y (- 1.0 (/ t z)))
         (if (<= z 9.8e+123) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = t_1;
	} else if (z <= 4800.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-6d+14)) then
        tmp = x + y
    else if (z <= 1.8d-65) then
        tmp = t_1
    else if (z <= 4800.0d0) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 9.8d+123) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = t_1;
	} else if (z <= 4800.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -6e+14:
		tmp = x + y
	elif z <= 1.8e-65:
		tmp = t_1
	elif z <= 4800.0:
		tmp = y * (1.0 - (t / z))
	elif z <= 9.8e+123:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -6e+14)
		tmp = Float64(x + y);
	elseif (z <= 1.8e-65)
		tmp = t_1;
	elseif (z <= 4800.0)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 9.8e+123)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -6e+14)
		tmp = x + y;
	elseif (z <= 1.8e-65)
		tmp = t_1;
	elseif (z <= 4800.0)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 9.8e+123)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+14], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.8e-65], t$95$1, If[LessEqual[z, 4800.0], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+123], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e14 or 9.79999999999999952e123 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 75.9%

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

   if -6e14 < z < 1.7999999999999999e-65 or 4800 < z < 9.79999999999999952e123

   1. Initial program 92.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around 0 78.2%

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

      1. associate-/l* 83.2%

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

      2. associate-/r/ 82.6%

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

   6. Applied egg-rr 82.6%

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

   if 1.7999999999999999e-65 < z < 4800

   1. Initial program 99.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.2%

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

   5. Taylor expanded in y around inf 86.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4800:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+14)
   (+ x y)
   (if (<= z 1.8e-65)
     (+ x (/ t (/ a y)))
     (if (<= z 4200.0)
       (* y (- 1.0 (/ t z)))
       (if (<= z 9.8e+123) (+ x (* t (/ y a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = x + (t / (a / y));
	} else if (z <= 4200.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.4d+14)) then
        tmp = x + y
    else if (z <= 1.8d-65) then
        tmp = x + (t / (a / y))
    else if (z <= 4200.0d0) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 9.8d+123) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = x + (t / (a / y));
	} else if (z <= 4200.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+14:
		tmp = x + y
	elif z <= 1.8e-65:
		tmp = x + (t / (a / y))
	elif z <= 4200.0:
		tmp = y * (1.0 - (t / z))
	elif z <= 9.8e+123:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+14)
		tmp = Float64(x + y);
	elseif (z <= 1.8e-65)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4200.0)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 9.8e+123)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+14)
		tmp = x + y;
	elseif (z <= 1.8e-65)
		tmp = x + (t / (a / y));
	elseif (z <= 4200.0)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 9.8e+123)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+14], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.8e-65], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4200.0], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+123], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4e14 or 9.79999999999999952e123 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 75.9%

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

   if -3.4e14 < z < 1.7999999999999999e-65

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 80.7%

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

      1. associate-/l* 85.2%

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

      2. associate-/r/ 84.3%

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

   6. Applied egg-rr 84.3%

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

      1. *-commutative 84.3%

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

      2. clear-num 84.3%

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

      3. div-inv 84.3%

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

   8. Applied egg-rr 84.3%

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

   if 1.7999999999999999e-65 < z < 4200

   1. Initial program 99.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.2%

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

   5. Taylor expanded in y around inf 86.5%

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

   if 4200 < z < 9.79999999999999952e123

   1. Initial program 87.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 73.1%

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

      2. associate-/r/ 73.2%

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

   6. Applied egg-rr 73.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+14)
   (+ x y)
   (if (<= z 1.8e-65)
     (+ x (/ y (/ a t)))
     (if (<= z 4200.0)
       (* y (- 1.0 (/ t z)))
       (if (<= z 9.8e+123) (+ x (* t (/ y a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d+14)) then
        tmp = x + y
    else if (z <= 1.8d-65) then
        tmp = x + (y / (a / t))
    else if (z <= 4200.0d0) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 9.8d+123) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = x + y;
	} else if (z <= 1.8e-65) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+14:
		tmp = x + y
	elif z <= 1.8e-65:
		tmp = x + (y / (a / t))
	elif z <= 4200.0:
		tmp = y * (1.0 - (t / z))
	elif z <= 9.8e+123:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+14)
		tmp = Float64(x + y);
	elseif (z <= 1.8e-65)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4200.0)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 9.8e+123)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+14)
		tmp = x + y;
	elseif (z <= 1.8e-65)
		tmp = x + (y / (a / t));
	elseif (z <= 4200.0)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 9.8e+123)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+14], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.8e-65], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4200.0], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+123], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e14 or 9.79999999999999952e123 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 75.9%

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

   if -2.8e14 < z < 1.7999999999999999e-65

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 80.7%

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

      1. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   if 1.7999999999999999e-65 < z < 4200

   1. Initial program 99.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.2%

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

   5. Taylor expanded in y around inf 86.5%

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

   if 4200 < z < 9.79999999999999952e123

   1. Initial program 87.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 73.1%

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

      2. associate-/r/ 73.2%

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

   6. Applied egg-rr 73.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y z)))))
   (if (<= z -5.8e+110)
     t_1
     (if (<= z -1.55e-15)
       (+ x (/ y (/ (- z a) z)))
       (if (<= z 6.2e-68) (+ x (/ y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / z));
	double tmp;
	if (z <= -5.8e+110) {
		tmp = t_1;
	} else if (z <= -1.55e-15) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.2e-68) {
		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 + ((z - t) * (y / z))
    if (z <= (-5.8d+110)) then
        tmp = t_1
    else if (z <= (-1.55d-15)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 6.2d-68) 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 + ((z - t) * (y / z));
	double tmp;
	if (z <= -5.8e+110) {
		tmp = t_1;
	} else if (z <= -1.55e-15) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.2e-68) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / z))
	tmp = 0
	if z <= -5.8e+110:
		tmp = t_1
	elif z <= -1.55e-15:
		tmp = x + (y / ((z - a) / z))
	elif z <= 6.2e-68:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / z)))
	tmp = 0.0
	if (z <= -5.8e+110)
		tmp = t_1;
	elseif (z <= -1.55e-15)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 6.2e-68)
		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 + ((z - t) * (y / z));
	tmp = 0.0;
	if (z <= -5.8e+110)
		tmp = t_1;
	elseif (z <= -1.55e-15)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 6.2e-68)
		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[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+110], t$95$1, If[LessEqual[z, -1.55e-15], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-68], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e110 or 6.1999999999999999e-68 < z

   1. Initial program 74.0%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 88.5%

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

   if -5.7999999999999999e110 < z < -1.5499999999999999e-15

   1. Initial program 79.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 72.9%

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

      1. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   if -1.5499999999999999e-15 < z < 6.1999999999999999e-68

   1. Initial program 92.7%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+110}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 6: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -26000000000.0)
   (+ x y)
   (if (<= z 8e-66) x (if (<= z 3.6e+29) (* y (- 1.0 (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -26000000000.0) {
		tmp = x + y;
	} else if (z <= 8e-66) {
		tmp = x;
	} else if (z <= 3.6e+29) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-26000000000.0d0)) then
        tmp = x + y
    else if (z <= 8d-66) then
        tmp = x
    else if (z <= 3.6d+29) then
        tmp = y * (1.0d0 - (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -26000000000.0) {
		tmp = x + y;
	} else if (z <= 8e-66) {
		tmp = x;
	} else if (z <= 3.6e+29) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -26000000000.0:
		tmp = x + y
	elif z <= 8e-66:
		tmp = x
	elif z <= 3.6e+29:
		tmp = y * (1.0 - (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -26000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 8e-66)
		tmp = x;
	elseif (z <= 3.6e+29)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -26000000000.0)
		tmp = x + y;
	elseif (z <= 8e-66)
		tmp = x;
	elseif (z <= 3.6e+29)
		tmp = y * (1.0 - (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -26000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 8e-66], x, If[LessEqual[z, 3.6e+29], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e10 or 3.59999999999999976e29 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 72.6%

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

   if -2.6e10 < z < 7.9999999999999998e-66

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 80.7%

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

   5. Taylor expanded in x around inf 54.2%

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

   if 7.9999999999999998e-66 < z < 3.59999999999999976e29

   1. Initial program 94.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 77.7%

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

   5. Taylor expanded in y around inf 70.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+14)
   (+ x y)
   (if (<= z 2.1e-86)
     (+ x (/ y (/ a t)))
     (if (<= z 3e+213) (- x (* t (/ y z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+14) {
		tmp = x + y;
	} else if (z <= 2.1e-86) {
		tmp = x + (y / (a / t));
	} else if (z <= 3e+213) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+14)) then
        tmp = x + y
    else if (z <= 2.1d-86) then
        tmp = x + (y / (a / t))
    else if (z <= 3d+213) then
        tmp = x - (t * (y / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+14) {
		tmp = x + y;
	} else if (z <= 2.1e-86) {
		tmp = x + (y / (a / t));
	} else if (z <= 3e+213) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+14:
		tmp = x + y
	elif z <= 2.1e-86:
		tmp = x + (y / (a / t))
	elif z <= 3e+213:
		tmp = x - (t * (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+14)
		tmp = Float64(x + y);
	elseif (z <= 2.1e-86)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3e+213)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+14)
		tmp = x + y;
	elseif (z <= 2.1e-86)
		tmp = x + (y / (a / t));
	elseif (z <= 3e+213)
		tmp = x - (t * (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+14], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.1e-86], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+213], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e14 or 3.0000000000000001e213 < z

   1. Initial program 65.4%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -1.45e14 < z < 2.1e-86

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 z around 0 80.8%

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

      1. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   if 2.1e-86 < z < 3.0000000000000001e213

   1. Initial program 90.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. distribute-rgt-neg-out 82.9%

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

      4. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in x around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. associate-/l* 88.4%

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

      4. sub-neg 88.4%

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

      5. associate-/r/ 88.3%

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

      6. *-commutative 88.3%

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

   9. Simplified 88.3%

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

   10. Taylor expanded in z around inf 78.5%

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

       1. associate-*l/ 80.3%

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

       2. *-commutative 80.3%

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

   12. Simplified 80.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+213}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -52000000000000.0)
   (+ x y)
   (if (<= z 1.7e-86)
     (+ x (/ y (/ a t)))
     (if (<= z 3e+213) (- x (/ y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -52000000000000.0) {
		tmp = x + y;
	} else if (z <= 1.7e-86) {
		tmp = x + (y / (a / t));
	} else if (z <= 3e+213) {
		tmp = x - (y / (z / 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 <= (-52000000000000.0d0)) then
        tmp = x + y
    else if (z <= 1.7d-86) then
        tmp = x + (y / (a / t))
    else if (z <= 3d+213) then
        tmp = x - (y / (z / 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 <= -52000000000000.0) {
		tmp = x + y;
	} else if (z <= 1.7e-86) {
		tmp = x + (y / (a / t));
	} else if (z <= 3e+213) {
		tmp = x - (y / (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -52000000000000.0:
		tmp = x + y
	elif z <= 1.7e-86:
		tmp = x + (y / (a / t))
	elif z <= 3e+213:
		tmp = x - (y / (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -52000000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.7e-86)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3e+213)
		tmp = Float64(x - Float64(y / Float64(z / 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 <= -52000000000000.0)
		tmp = x + y;
	elseif (z <= 1.7e-86)
		tmp = x + (y / (a / t));
	elseif (z <= 3e+213)
		tmp = x - (y / (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -52000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.7e-86], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+213], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e13 or 3.0000000000000001e213 < z

   1. Initial program 65.4%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -5.2e13 < z < 1.7e-86

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 z around 0 80.8%

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

      1. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   if 1.7e-86 < z < 3.0000000000000001e213

   1. Initial program 90.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. distribute-rgt-neg-out 82.9%

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

      4. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. associate-*r/ 80.3%

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

      4. sub-neg 80.3%

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

   9. Simplified 80.3%

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

       1. clear-num 80.1%

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

       2. un-div-inv 80.3%

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

   11. Applied egg-rr 80.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+213}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115000000000 \lor \neg \left(z \leq 2.8 \cdot 10^{-67}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -115000000000.0) (not (<= z 2.8e-67)))
   (+ x (* (- z t) (/ y z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -115000000000.0) || !(z <= 2.8e-67)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-115000000000.0d0)) .or. (.not. (z <= 2.8d-67))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -115000000000.0) || !(z <= 2.8e-67)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -115000000000.0) or not (z <= 2.8e-67):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -115000000000.0) || !(z <= 2.8e-67))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -115000000000.0) || ~((z <= 2.8e-67)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -115000000000.0], N[Not[LessEqual[z, 2.8e-67]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e11 or 2.8000000000000001e-67 < z

   1. Initial program 74.2%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around inf 84.0%

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

   if -1.15e11 < z < 2.8000000000000001e-67

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 80.6%

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

      1. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000000000 \lor \neg \left(z \leq 2.8 \cdot 10^{-67}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+62} \lor \neg \left(t \leq 2.55 \cdot 10^{-36}\right):\\ \;\;\;\;x - \frac{y}{z - a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e+62) (not (<= t 2.55e-36)))
   (- 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 <= -4.1e+62) || !(t <= 2.55e-36)) {
		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 <= (-4.1d+62)) .or. (.not. (t <= 2.55d-36))) 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 <= -4.1e+62) || !(t <= 2.55e-36)) {
		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 <= -4.1e+62) or not (t <= 2.55e-36):
		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 <= -4.1e+62) || !(t <= 2.55e-36))
		tmp = Float64(x - Float64(Float64(y / Float64(z - a)) * 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 <= -4.1e+62) || ~((t <= 2.55e-36)))
		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, -4.1e+62], N[Not[LessEqual[t, 2.55e-36]], $MachinePrecision]], N[(x - N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $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 < -4.09999999999999984e62 or 2.54999999999999987e-36 < t

   1. Initial program 81.5%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 78.1%

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

      1. associate-*r/ 78.1%

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

      2. mul-1-neg 78.1%

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

      3. distribute-rgt-neg-out 78.1%

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

      4. associate-/l* 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in x around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. associate-/l* 89.4%

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

      4. sub-neg 89.4%

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

      5. associate-/r/ 91.6%

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

      6. *-commutative 91.6%

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

   9. Simplified 91.6%

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

   if -4.09999999999999984e62 < t < 2.54999999999999987e-36

   1. Initial program 84.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 t around 0 77.0%

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

      1. associate-/l* 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+62} \lor \neg \left(t \leq 2.55 \cdot 10^{-36}\right):\\ \;\;\;\;x - \frac{y}{z - a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 11: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z - a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+60)
   (- x (/ t (/ (- z a) y)))
   (if (<= t 3.1e-44) (+ x (/ y (/ (- z a) z))) (- x (* (/ y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+60) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 3.1e-44) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - ((y / (z - a)) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1d+60)) then
        tmp = x - (t / ((z - a) / y))
    else if (t <= 3.1d-44) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - ((y / (z - a)) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+60) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 3.1e-44) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - ((y / (z - a)) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+60:
		tmp = x - (t / ((z - a) / y))
	elif t <= 3.1e-44:
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - ((y / (z - a)) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+60)
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	elseif (t <= 3.1e-44)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(Float64(y / Float64(z - a)) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+60)
		tmp = x - (t / ((z - a) / y));
	elseif (t <= 3.1e-44)
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - ((y / (z - a)) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+60], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-44], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999995e59

   1. Initial program 77.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. mul-1-neg 69.9%

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

      3. distribute-rgt-neg-out 69.9%

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

      4. associate-/l* 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. associate-/l* 86.9%

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

      4. sub-neg 86.9%

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

      5. associate-/r/ 88.7%

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

      6. *-commutative 88.7%

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

   9. Simplified 88.7%

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

       1. clear-num 88.7%

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

       2. un-div-inv 88.8%

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

   11. Applied egg-rr 88.8%

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

   if -9.9999999999999995e59 < t < 3.09999999999999984e-44

   1. Initial program 84.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 t around 0 77.0%

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

      1. associate-/l* 91.5%

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

   6. Simplified 91.5%

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

   if 3.09999999999999984e-44 < t

   1. Initial program 84.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

      3. distribute-rgt-neg-out 83.9%

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

      4. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. associate-/l* 91.1%

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

      4. sub-neg 91.1%

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

      5. associate-/r/ 93.6%

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

      6. *-commutative 93.6%

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

   9. Simplified 93.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z - a} \cdot t\\ \end{array} \]

Alternative 12: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -112000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -112000000000.0)
   (+ x y)
   (if (<= z 1.75e-65) x (if (<= z 1.28e+26) (* y (/ (- t) z)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -112000000000.0) {
		tmp = x + y;
	} else if (z <= 1.75e-65) {
		tmp = x;
	} else if (z <= 1.28e+26) {
		tmp = y * (-t / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-112000000000.0d0)) then
        tmp = x + y
    else if (z <= 1.75d-65) then
        tmp = x
    else if (z <= 1.28d+26) then
        tmp = y * (-t / z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -112000000000.0) {
		tmp = x + y;
	} else if (z <= 1.75e-65) {
		tmp = x;
	} else if (z <= 1.28e+26) {
		tmp = y * (-t / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -112000000000.0:
		tmp = x + y
	elif z <= 1.75e-65:
		tmp = x
	elif z <= 1.28e+26:
		tmp = y * (-t / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -112000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.75e-65)
		tmp = x;
	elseif (z <= 1.28e+26)
		tmp = Float64(y * Float64(Float64(-t) / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -112000000000.0)
		tmp = x + y;
	elseif (z <= 1.75e-65)
		tmp = x;
	elseif (z <= 1.28e+26)
		tmp = y * (-t / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -112000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.75e-65], x, If[LessEqual[z, 1.28e+26], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e11 or 1.28e26 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 72.6%

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

   if -1.12e11 < z < 1.75000000000000002e-65

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 80.7%

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

   5. Taylor expanded in x around inf 54.2%

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

   if 1.75000000000000002e-65 < z < 1.28e26

   1. Initial program 94.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. distribute-rgt-neg-out 84.7%

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

      4. associate-/l* 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in z around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. associate-*r/ 77.8%

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

      4. sub-neg 77.8%

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

   9. Simplified 77.8%

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

   10. Taylor expanded in x around 0 67.6%

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

       1. associate-*r/ 67.6%

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

       2. neg-mul-1 67.6%

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

       3. distribute-rgt-neg-in 67.6%

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

       4. associate-*r/ 67.7%

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

   12. Simplified 67.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -112000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 64.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -28000000000000.0) (+ x y) (if (<= z 1.75e+23) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -28000000000000.0) {
		tmp = x + y;
	} else if (z <= 1.75e+23) {
		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 <= (-28000000000000.0d0)) then
        tmp = x + y
    else if (z <= 1.75d+23) 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 <= -28000000000000.0) {
		tmp = x + y;
	} else if (z <= 1.75e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -28000000000000.0:
		tmp = x + y
	elif z <= 1.75e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -28000000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.75e+23)
		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 <= -28000000000000.0)
		tmp = x + y;
	elseif (z <= 1.75e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -28000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.75e+23], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e13 or 1.7500000000000001e23 < z

   1. Initial program 71.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 71.7%

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

   if -2.8e13 < z < 1.7500000000000001e23

   1. Initial program 93.2%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 74.6%

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

   5. Taylor expanded in x around inf 49.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -28000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 49.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z -6e+132) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+132) {
		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 (z <= (-6d+132)) 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 (z <= -6e+132) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+132:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+132)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+132)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+132], y, x]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999996e132

   1. Initial program 60.5%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around 0 60.5%

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

   5. Taylor expanded in y around inf 69.6%

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

   6. Taylor expanded in t around 0 54.9%

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

   if -5.9999999999999996e132 < z

   1. Initial program 87.0%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 64.3%

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

   5. Taylor expanded in x around inf 48.6%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 51.6% 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 83.1%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in z around 0 59.8%

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

5. Taylor expanded in x around inf 45.6%

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

6. Final simplification 45.6%

   \[\leadsto x \]

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 2023268 
(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))))