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

Percentage Accurate: 85.3% → 98.2%

Time: 11.5s

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: 85.3% 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

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

FPCore

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

C

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

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 + (((z - t) / (z - a)) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. *-commutative 87.8%

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

   2. associate-*l/ 98.2%

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

3. Applied egg-rr 98.2%

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

4. Final simplification 98.2%

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

Alternative 2: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -3.4e+84)
     t_1
     (if (<= z -5.2e+33)
       (- x (/ t (/ z y)))
       (if (<= z -3.45e-37)
         t_1
         (if (<= z -8.6e-42)
           (* t (/ (- y) (- z a)))
           (if (<= z -1.46e-62)
             (+ x (/ y (/ (- z) t)))
             (if (<= z 1.65e-95) (+ 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 - a)));
	double tmp;
	if (z <= -3.4e+84) {
		tmp = t_1;
	} else if (z <= -5.2e+33) {
		tmp = x - (t / (z / y));
	} else if (z <= -3.45e-37) {
		tmp = t_1;
	} else if (z <= -8.6e-42) {
		tmp = t * (-y / (z - a));
	} else if (z <= -1.46e-62) {
		tmp = x + (y / (-z / t));
	} else if (z <= 1.65e-95) {
		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 - a)))
    if (z <= (-3.4d+84)) then
        tmp = t_1
    else if (z <= (-5.2d+33)) then
        tmp = x - (t / (z / y))
    else if (z <= (-3.45d-37)) then
        tmp = t_1
    else if (z <= (-8.6d-42)) then
        tmp = t * (-y / (z - a))
    else if (z <= (-1.46d-62)) then
        tmp = x + (y / (-z / t))
    else if (z <= 1.65d-95) 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 - a)));
	double tmp;
	if (z <= -3.4e+84) {
		tmp = t_1;
	} else if (z <= -5.2e+33) {
		tmp = x - (t / (z / y));
	} else if (z <= -3.45e-37) {
		tmp = t_1;
	} else if (z <= -8.6e-42) {
		tmp = t * (-y / (z - a));
	} else if (z <= -1.46e-62) {
		tmp = x + (y / (-z / t));
	} else if (z <= 1.65e-95) {
		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 - a)))
	tmp = 0
	if z <= -3.4e+84:
		tmp = t_1
	elif z <= -5.2e+33:
		tmp = x - (t / (z / y))
	elif z <= -3.45e-37:
		tmp = t_1
	elif z <= -8.6e-42:
		tmp = t * (-y / (z - a))
	elif z <= -1.46e-62:
		tmp = x + (y / (-z / t))
	elif z <= 1.65e-95:
		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 - a))))
	tmp = 0.0
	if (z <= -3.4e+84)
		tmp = t_1;
	elseif (z <= -5.2e+33)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= -3.45e-37)
		tmp = t_1;
	elseif (z <= -8.6e-42)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - a)));
	elseif (z <= -1.46e-62)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (z <= 1.65e-95)
		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 - a)));
	tmp = 0.0;
	if (z <= -3.4e+84)
		tmp = t_1;
	elseif (z <= -5.2e+33)
		tmp = x - (t / (z / y));
	elseif (z <= -3.45e-37)
		tmp = t_1;
	elseif (z <= -8.6e-42)
		tmp = t * (-y / (z - a));
	elseif (z <= -1.46e-62)
		tmp = x + (y / (-z / t));
	elseif (z <= 1.65e-95)
		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 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+84], t$95$1, If[LessEqual[z, -5.2e+33], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.45e-37], t$95$1, If[LessEqual[z, -8.6e-42], N[(t * N[((-y) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-62], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-95], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.3999999999999998e84 or -5.1999999999999995e33 < z < -3.4499999999999999e-37 or 1.65e-95 < z

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*l/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in t around 0 90.7%

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

   if -3.3999999999999998e84 < z < -5.1999999999999995e33

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 93.3%

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

      1. associate-*r/ 93.4%

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

      2. neg-mul-1 93.4%

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

      3. distribute-rgt-neg-in 93.4%

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

      4. distribute-neg-frac 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in z around inf 93.3%

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

      1. mul-1-neg 93.3%

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

      2. unsub-neg 93.3%

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

      3. associate-/l* 93.3%

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

   7. Simplified 93.3%

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

   if -3.4499999999999999e-37 < z < -8.6000000000000002e-42

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 99.5%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-*r/ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 99.5%

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

      5. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -8.6000000000000002e-42 < z < -1.46e-62

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. neg-mul-1 81.6%

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

   7. Simplified 81.6%

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

   if -1.46e-62 < z < 1.65e-95

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-*l/ 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. clear-num 80.9%

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

      3. un-div-inv 81.0%

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

   6. Applied egg-rr 81.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 3: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.7e+104)
     t_1
     (if (<= z -7.8e-64)
       (+ x (/ (* (- z t) y) z))
       (if (<= z 5.8e-98) (+ 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 - a)));
	double tmp;
	if (z <= -1.7e+104) {
		tmp = t_1;
	} else if (z <= -7.8e-64) {
		tmp = x + (((z - t) * y) / z);
	} else if (z <= 5.8e-98) {
		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 - a)))
    if (z <= (-1.7d+104)) then
        tmp = t_1
    else if (z <= (-7.8d-64)) then
        tmp = x + (((z - t) * y) / z)
    else if (z <= 5.8d-98) 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 - a)));
	double tmp;
	if (z <= -1.7e+104) {
		tmp = t_1;
	} else if (z <= -7.8e-64) {
		tmp = x + (((z - t) * y) / z);
	} else if (z <= 5.8e-98) {
		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 - a)))
	tmp = 0
	if z <= -1.7e+104:
		tmp = t_1
	elif z <= -7.8e-64:
		tmp = x + (((z - t) * y) / z)
	elif z <= 5.8e-98:
		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 - a))))
	tmp = 0.0
	if (z <= -1.7e+104)
		tmp = t_1;
	elseif (z <= -7.8e-64)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / z));
	elseif (z <= 5.8e-98)
		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 - a)));
	tmp = 0.0;
	if (z <= -1.7e+104)
		tmp = t_1;
	elseif (z <= -7.8e-64)
		tmp = x + (((z - t) * y) / z);
	elseif (z <= 5.8e-98)
		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 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+104], t$95$1, If[LessEqual[z, -7.8e-64], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-98], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6999999999999998e104 or 5.8e-98 < z

   1. Initial program 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*l/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in t around 0 90.9%

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

   if -1.6999999999999998e104 < z < -7.7999999999999994e-64

   1. Initial program 99.7%

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

   2. Taylor expanded in a around 0 84.5%

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

   if -7.7999999999999994e-64 < z < 5.8e-98

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-*l/ 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. clear-num 80.9%

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

      3. un-div-inv 81.0%

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

   6. Applied egg-rr 81.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 4: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+81)
   (+ x y)
   (if (<= z -2.4e+42)
     (* y (- 1.0 (/ t z)))
     (if (<= z 4.8e-52) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -2.4e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 4.8e-52) {
		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 <= (-1.8d+81)) then
        tmp = x + y
    else if (z <= (-2.4d+42)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 4.8d-52) 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 <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -2.4e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 4.8e-52) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+81:
		tmp = x + y
	elif z <= -2.4e+42:
		tmp = y * (1.0 - (t / z))
	elif z <= 4.8e-52:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+81)
		tmp = Float64(x + y);
	elseif (z <= -2.4e+42)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 4.8e-52)
		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 <= -1.8e+81)
		tmp = x + y;
	elseif (z <= -2.4e+42)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 4.8e-52)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+81], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.4e+42], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-52], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000003e81 or 4.8000000000000003e-52 < z

   1. Initial program 77.6%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -1.80000000000000003e81 < z < -2.3999999999999999e42

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 88.7%

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

   if -2.3999999999999999e42 < z < 4.8000000000000003e-52

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 90.0%

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

      1. associate-*r/ 88.6%

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

      2. neg-mul-1 88.6%

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

      3. distribute-rgt-neg-in 88.6%

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

      4. distribute-neg-frac 88.6%

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

   4. Simplified 88.6%

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

   5. Taylor expanded in z around 0 75.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+81)
   (+ x y)
   (if (<= z -2e+40)
     (* y (- 1.0 (/ t z)))
     (if (<= z 3.8e-48) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -2e+40) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.8e-48) {
		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 <= (-1.8d+81)) then
        tmp = x + y
    else if (z <= (-2d+40)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 3.8d-48) 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 <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -2e+40) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.8e-48) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+81:
		tmp = x + y
	elif z <= -2e+40:
		tmp = y * (1.0 - (t / z))
	elif z <= 3.8e-48:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+81)
		tmp = Float64(x + y);
	elseif (z <= -2e+40)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.8e-48)
		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 <= -1.8e+81)
		tmp = x + y;
	elseif (z <= -2e+40)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 3.8e-48)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+81], N[(x + y), $MachinePrecision], If[LessEqual[z, -2e+40], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-48], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000003e81 or 3.80000000000000002e-48 < z

   1. Initial program 77.6%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -1.80000000000000003e81 < z < -2.00000000000000006e40

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 88.7%

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

   if -2.00000000000000006e40 < z < 3.80000000000000002e-48

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l/ 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in z around 0 77.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+81)
   (+ x y)
   (if (<= z -7.2e+41)
     (* y (- 1.0 (/ t z)))
     (if (<= z 1.5e-52) (+ x (/ y (/ a t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -7.2e+41) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 1.5e-52) {
		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 <= (-1.8d+81)) then
        tmp = x + y
    else if (z <= (-7.2d+41)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 1.5d-52) 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 <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -7.2e+41) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 1.5e-52) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+81:
		tmp = x + y
	elif z <= -7.2e+41:
		tmp = y * (1.0 - (t / z))
	elif z <= 1.5e-52:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+81)
		tmp = Float64(x + y);
	elseif (z <= -7.2e+41)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 1.5e-52)
		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 <= -1.8e+81)
		tmp = x + y;
	elseif (z <= -7.2e+41)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 1.5e-52)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+81], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.2e+41], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-52], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000003e81 or 1.5e-52 < z

   1. Initial program 77.6%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -1.80000000000000003e81 < z < -7.20000000000000051e41

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 88.7%

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

   if -7.20000000000000051e41 < z < 1.5e-52

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l/ 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. clear-num 77.1%

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

      3. un-div-inv 77.1%

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

   6. Applied egg-rr 77.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+85)
   (+ x y)
   (if (<= z -8.8e-60)
     (- x (/ t (/ z y)))
     (if (<= z 3.2e-54) (+ x (/ y (/ a t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+85) {
		tmp = x + y;
	} else if (z <= -8.8e-60) {
		tmp = x - (t / (z / y));
	} else if (z <= 3.2e-54) {
		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 <= (-2.5d+85)) then
        tmp = x + y
    else if (z <= (-8.8d-60)) then
        tmp = x - (t / (z / y))
    else if (z <= 3.2d-54) 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 <= -2.5e+85) {
		tmp = x + y;
	} else if (z <= -8.8e-60) {
		tmp = x - (t / (z / y));
	} else if (z <= 3.2e-54) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+85:
		tmp = x + y
	elif z <= -8.8e-60:
		tmp = x - (t / (z / y))
	elif z <= 3.2e-54:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+85)
		tmp = Float64(x + y);
	elseif (z <= -8.8e-60)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 3.2e-54)
		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 <= -2.5e+85)
		tmp = x + y;
	elseif (z <= -8.8e-60)
		tmp = x - (t / (z / y));
	elseif (z <= 3.2e-54)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+85], N[(x + y), $MachinePrecision], If[LessEqual[z, -8.8e-60], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-54], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e85 or 3.19999999999999998e-54 < z

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 80.6%

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

      1. +-commutative 80.6%

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

   4. Simplified 80.6%

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

   if -2.5e85 < z < -8.7999999999999995e-60

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 85.9%

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

      1. associate-*r/ 86.2%

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

      2. neg-mul-1 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-neg-frac 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if -8.7999999999999995e-60 < z < 3.19999999999999998e-54

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*l/ 95.4%

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

   3. Applied egg-rr 95.4%

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

   4. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. clear-num 80.3%

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

      3. un-div-inv 80.3%

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

   6. Applied egg-rr 80.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.95e-62)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 4.4e-93) (+ x (/ y (/ a t))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e-62) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.4e-93) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.95d-62)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 4.4d-93) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e-62) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.4e-93) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.95e-62:
		tmp = x + (y / (z / (z - t)))
	elif z <= 4.4e-93:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.95e-62)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 4.4e-93)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.95e-62)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 4.4e-93)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.95e-62], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-93], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9500000000000002e-62

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 79.0%

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

      1. +-commutative 79.0%

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

      2. associate-/l* 89.1%

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

   4. Simplified 89.1%

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

   if -2.9500000000000002e-62 < z < 4.39999999999999991e-93

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-*l/ 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. clear-num 80.9%

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

      3. un-div-inv 81.0%

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

   6. Applied egg-rr 81.0%

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

   if 4.39999999999999991e-93 < z

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l/ 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in t around 0 88.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 9: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e-5)
   (+ x (* z (/ y (- z a))))
   (if (<= a 9.5e+33) (+ x (/ y (/ z (- z t)))) (+ x (* (/ y a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-5) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 9.5e+33) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d-5)) then
        tmp = x + (z * (y / (z - a)))
    else if (a <= 9.5d+33) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-5) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 9.5e+33) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e-5:
		tmp = x + (z * (y / (z - a)))
	elif a <= 9.5e+33:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e-5)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (a <= 9.5e+33)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e-5)
		tmp = x + (z * (y / (z - a)));
	elseif (a <= 9.5e+33)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e-5], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+33], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e-5

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-*l/ 83.5%

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

      3. *-commutative 83.5%

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

   4. Simplified 83.5%

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

   if -1.9000000000000001e-5 < a < 9.5000000000000003e33

   1. Initial program 88.6%

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

   2. Taylor expanded in a around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 86.3%

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

   4. Simplified 86.3%

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

   if 9.5000000000000003e33 < a

   1. Initial program 84.1%

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

   2. Taylor expanded in a around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. associate-/l* 86.7%

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

   4. Simplified 86.7%

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

      1. associate-/r/ 93.2%

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

   6. Applied egg-rr 93.2%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 10: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.16e-36)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 2.15e+92) (- x (/ t (/ (- z a) y))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-36) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 2.15e+92) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.16d-36)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 2.15d+92) then
        tmp = x - (t / ((z - a) / y))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-36) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 2.15e+92) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.16e-36:
		tmp = x + (y / (z / (z - t)))
	elif z <= 2.15e+92:
		tmp = x - (t / ((z - a) / y))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.16e-36)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 2.15e+92)
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.16e-36)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 2.15e+92)
		tmp = x - (t / ((z - a) / y));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.16e-36], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+92], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16000000000000002e-36

   1. Initial program 86.2%

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

   2. Taylor expanded in a around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 92.3%

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

   4. Simplified 92.3%

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

   if -1.16000000000000002e-36 < z < 2.1499999999999999e92

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 90.0%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

      3. distribute-rgt-neg-in 89.4%

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

      4. distribute-neg-frac 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in x around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. associate-*r/ 89.4%

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

      3. sub-neg 89.4%

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

      4. associate-*r/ 90.0%

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

      5. associate-/l* 90.1%

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

   7. Simplified 90.1%

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

   if 2.1499999999999999e92 < z

   1. Initial program 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*l/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 91.1%

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

      2. div-sub 91.1%

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

      3. *-inverses 91.1%

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

   6. Simplified 91.1%

      \[\leadsto x + \color{blue}{\frac{y}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 11: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+171} \lor \neg \left(y \leq 4 \cdot 10^{+148}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.8e+171) (not (<= y 4e+148))) (* y (- 1.0 (/ t z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e+171) || !(y <= 4e+148)) {
		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 ((y <= (-2.8d+171)) .or. (.not. (y <= 4d+148))) 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 ((y <= -2.8e+171) || !(y <= 4e+148)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.8e+171) or not (y <= 4e+148):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.8e+171) || !(y <= 4e+148))
		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 ((y <= -2.8e+171) || ~((y <= 4e+148)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.8e+171], N[Not[LessEqual[y, 4e+148]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000004e171 or 4.0000000000000002e148 < y

   1. Initial program 61.5%

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

   2. Taylor expanded in a around 0 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-/l* 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in y around inf 63.4%

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

   if -2.80000000000000004e171 < y < 4.0000000000000002e148

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

   4. Simplified 69.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+171} \lor \neg \left(y \leq 4 \cdot 10^{+148}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. associate-*l/ 95.0%

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

3. Applied egg-rr 95.0%

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

4. Final simplification 95.0%

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

Alternative 13: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+223) x (if (<= a 2.95e+119) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+223) {
		tmp = x;
	} else if (a <= 2.95e+119) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.8d+223)) then
        tmp = x
    else if (a <= 2.95d+119) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+223) {
		tmp = x;
	} else if (a <= 2.95e+119) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+223:
		tmp = x
	elif a <= 2.95e+119:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+223)
		tmp = x;
	elseif (a <= 2.95e+119)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e+223)
		tmp = x;
	elseif (a <= 2.95e+119)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+223], x, If[LessEqual[a, 2.95e+119], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.7999999999999995e223 or 2.95e119 < a

   1. Initial program 83.1%

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

   2. Taylor expanded in x around inf 75.4%

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

   if -6.7999999999999995e223 < a < 2.95e119

   1. Initial program 89.0%

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

   2. Taylor expanded in z around inf 66.2%

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

      1. +-commutative 66.2%

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

   4. Simplified 66.2%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 53.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.5e+186) y (if (<= y 1.9e+111) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.5e+186) {
		tmp = y;
	} else if (y <= 1.9e+111) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.5d+186)) then
        tmp = y
    else if (y <= 1.9d+111) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.5e+186) {
		tmp = y;
	} else if (y <= 1.9e+111) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.5e+186:
		tmp = y
	elif y <= 1.9e+111:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.5e+186)
		tmp = y;
	elseif (y <= 1.9e+111)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.5e+186)
		tmp = y;
	elseif (y <= 1.9e+111)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.5e+186], y, If[LessEqual[y, 1.9e+111], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999998e186 or 1.89999999999999988e111 < y

   1. Initial program 63.1%

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

   2. Taylor expanded in a around 0 40.0%

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

      1. +-commutative 40.0%

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

      2. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in y around inf 62.1%

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

   6. Taylor expanded in t around 0 38.9%

      \[\leadsto y \cdot \color{blue}{1} \]

   if -7.4999999999999998e186 < y < 1.89999999999999988e111

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 68.0%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 50.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in x around inf 53.1%

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

3. Final simplification 53.1%

   \[\leadsto x \]

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 2023321 
(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))))