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

Percentage Accurate: 85.7% → 98.2%

Time: 10.2s

Alternatives: 11

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: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. *-commutative 84.1%

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

   2. associate-*l/ 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120} \lor \neg \left(z \leq 1.6 \cdot 10^{-74}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) z)))))
   (if (<= z -2.2e+121)
     t_1
     (if (<= z -4.5e+33)
       (+ x (* t (/ y a)))
       (if (or (<= z -7e-120) (not (<= z 1.6e-74)))
         t_1
         (+ x (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.5e+33) {
		tmp = x + (t * (y / a));
	} else if ((z <= -7e-120) || !(z <= 1.6e-74)) {
		tmp = t_1;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((t - z) / z))
    if (z <= (-2.2d+121)) then
        tmp = t_1
    else if (z <= (-4.5d+33)) then
        tmp = x + (t * (y / a))
    else if ((z <= (-7d-120)) .or. (.not. (z <= 1.6d-74))) then
        tmp = t_1
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.5e+33) {
		tmp = x + (t * (y / a));
	} else if ((z <= -7e-120) || !(z <= 1.6e-74)) {
		tmp = t_1;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -2.2e+121:
		tmp = t_1
	elif z <= -4.5e+33:
		tmp = x + (t * (y / a))
	elif (z <= -7e-120) or not (z <= 1.6e-74):
		tmp = t_1
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.5e+33)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= -7e-120) || !(z <= 1.6e-74))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.5e+33)
		tmp = x + (t * (y / a));
	elseif ((z <= -7e-120) || ~((z <= 1.6e-74)))
		tmp = t_1;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+121], t$95$1, If[LessEqual[z, -4.5e+33], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7e-120], N[Not[LessEqual[z, 1.6e-74]], $MachinePrecision]], t$95$1, N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000001e121 or -4.5e33 < z < -7e-120 or 1.5999999999999999e-74 < z

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 85.2%

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

   if -2.20000000000000001e121 < z < -4.5e33

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 84.8%

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

      3. clear-num 84.9%

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

   7. Applied egg-rr 84.9%

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

   if -7e-120 < z < 1.5999999999999999e-74

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120} \lor \neg \left(z \leq 1.6 \cdot 10^{-74}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) z)))))
   (if (<= z -2.2e+121)
     t_1
     (if (<= z -4.8e+33)
       (+ x (* t (/ y a)))
       (if (<= z -7e-120)
         (+ x (/ (- z t) (/ z y)))
         (if (<= z 8.2e-75) (+ x (/ t (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.8e+33) {
		tmp = x + (t * (y / a));
	} else if (z <= -7e-120) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= 8.2e-75) {
		tmp = x + (t / (a / y));
	} 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 * ((t - z) / z))
    if (z <= (-2.2d+121)) then
        tmp = t_1
    else if (z <= (-4.8d+33)) then
        tmp = x + (t * (y / a))
    else if (z <= (-7d-120)) then
        tmp = x + ((z - t) / (z / y))
    else if (z <= 8.2d-75) then
        tmp = x + (t / (a / y))
    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 * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.8e+33) {
		tmp = x + (t * (y / a));
	} else if (z <= -7e-120) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= 8.2e-75) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -2.2e+121:
		tmp = t_1
	elif z <= -4.8e+33:
		tmp = x + (t * (y / a))
	elif z <= -7e-120:
		tmp = x + ((z - t) / (z / y))
	elif z <= 8.2e-75:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.8e+33)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= -7e-120)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (z <= 8.2e-75)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.8e+33)
		tmp = x + (t * (y / a));
	elseif (z <= -7e-120)
		tmp = x + ((z - t) / (z / y));
	elseif (z <= 8.2e-75)
		tmp = x + (t / (a / y));
	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[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+121], t$95$1, If[LessEqual[z, -4.8e+33], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-120], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-75], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.20000000000000001e121 or 8.20000000000000005e-75 < z

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 86.3%

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

   if -2.20000000000000001e121 < z < -4.8e33

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 84.8%

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

      3. clear-num 84.9%

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

   7. Applied egg-rr 84.9%

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

   if -4.8e33 < z < -7e-120

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.4%

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

   if -7e-120 < z < 8.20000000000000005e-75

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) z)))))
   (if (<= z -2.2e+121)
     t_1
     (if (<= z -4.8e+33)
       (+ x (* t (/ y a)))
       (if (<= z -7e-120)
         (+ x (/ y (/ z (- z t))))
         (if (<= z 1.5e-74) (+ x (/ t (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.8e+33) {
		tmp = x + (t * (y / a));
	} else if (z <= -7e-120) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.5e-74) {
		tmp = x + (t / (a / y));
	} 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 * ((t - z) / z))
    if (z <= (-2.2d+121)) then
        tmp = t_1
    else if (z <= (-4.8d+33)) then
        tmp = x + (t * (y / a))
    else if (z <= (-7d-120)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.5d-74) then
        tmp = x + (t / (a / y))
    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 * ((t - z) / z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_1;
	} else if (z <= -4.8e+33) {
		tmp = x + (t * (y / a));
	} else if (z <= -7e-120) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.5e-74) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -2.2e+121:
		tmp = t_1
	elif z <= -4.8e+33:
		tmp = x + (t * (y / a))
	elif z <= -7e-120:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.5e-74:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.8e+33)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= -7e-120)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.5e-74)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -2.2e+121)
		tmp = t_1;
	elseif (z <= -4.8e+33)
		tmp = x + (t * (y / a));
	elseif (z <= -7e-120)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.5e-74)
		tmp = x + (t / (a / y));
	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[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+121], t$95$1, If[LessEqual[z, -4.8e+33], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-120], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-74], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.20000000000000001e121 or 1.50000000000000003e-74 < z

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 86.3%

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

   if -2.20000000000000001e121 < z < -4.8e33

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 84.8%

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

      3. clear-num 84.9%

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

   7. Applied egg-rr 84.9%

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

   if -4.8e33 < z < -7e-120

   1. Initial program 93.8%

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

   3. Taylor expanded in a around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   if -7e-120 < z < 1.50000000000000003e-74

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+32}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) (- t z)))))
   (if (<= a -1.9e-26)
     t_1
     (if (<= a 6e-123)
       (+ x (/ y (/ z (- z t))))
       (if (<= a 8.2e-81)
         (+ x (/ (* t y) a))
         (if (<= a 6.6e+32) (+ x (* z (/ y (- z a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * (t - z));
	double tmp;
	if (a <= -1.9e-26) {
		tmp = t_1;
	} else if (a <= 6e-123) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 8.2e-81) {
		tmp = x + ((t * y) / a);
	} else if (a <= 6.6e+32) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / a) * (t - z))
    if (a <= (-1.9d-26)) then
        tmp = t_1
    else if (a <= 6d-123) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 8.2d-81) then
        tmp = x + ((t * y) / a)
    else if (a <= 6.6d+32) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * (t - z));
	double tmp;
	if (a <= -1.9e-26) {
		tmp = t_1;
	} else if (a <= 6e-123) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 8.2e-81) {
		tmp = x + ((t * y) / a);
	} else if (a <= 6.6e+32) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * (t - z))
	tmp = 0
	if a <= -1.9e-26:
		tmp = t_1
	elif a <= 6e-123:
		tmp = x + (y / (z / (z - t)))
	elif a <= 8.2e-81:
		tmp = x + ((t * y) / a)
	elif a <= 6.6e+32:
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * Float64(t - z)))
	tmp = 0.0
	if (a <= -1.9e-26)
		tmp = t_1;
	elseif (a <= 6e-123)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 8.2e-81)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (a <= 6.6e+32)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * (t - z));
	tmp = 0.0;
	if (a <= -1.9e-26)
		tmp = t_1;
	elseif (a <= 6e-123)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 8.2e-81)
		tmp = x + ((t * y) / a);
	elseif (a <= 6.6e+32)
		tmp = x + (z * (y / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-26], t$95$1, If[LessEqual[a, 6e-123], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-81], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+32], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.90000000000000007e-26 or 6.60000000000000039e32 < a

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

      1. associate-/r/ 84.3%

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

   7. Applied egg-rr 84.3%

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

   if -1.90000000000000007e-26 < a < 5.99999999999999968e-123

   1. Initial program 89.3%

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

   3. Taylor expanded in a around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

   if 5.99999999999999968e-123 < a < 8.19999999999999968e-81

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 87.3%

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

   if 8.19999999999999968e-81 < a < 6.60000000000000039e32

   1. Initial program 77.1%

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

   3. Taylor expanded in t around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-*l/ 83.9%

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

      3. *-commutative 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+32}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121} \lor \neg \left(z \leq 3.3 \cdot 10^{+71}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+121) (not (<= z 3.3e+71)))
   (- x (* y (/ (- t z) z)))
   (- x (* t (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+121) || !(z <= 3.3e+71)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x - (t * (y / (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 <= (-2.2d+121)) .or. (.not. (z <= 3.3d+71))) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = x - (t * (y / (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 <= -2.2e+121) || !(z <= 3.3e+71)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+121) or not (z <= 3.3e+71):
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+121) || !(z <= 3.3e+71))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e+121) || ~((z <= 3.3e+71)))
		tmp = x - (y * ((t - z) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+121], N[Not[LessEqual[z, 3.3e+71]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000001e121 or 3.2999999999999998e71 < z

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 91.2%

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

   if -2.20000000000000001e121 < z < 3.2999999999999998e71

   1. Initial program 90.8%

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

   3. Taylor expanded in t around inf 84.1%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

      4. distribute-neg-frac 88.9%

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

   5. Simplified 88.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121} \lor \neg \left(z \leq 3.3 \cdot 10^{+71}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+123} \lor \neg \left(z \leq 4.8 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+123) (not (<= z 4.8e+71))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+123) || !(z <= 4.8e+71)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.3d+123)) .or. (.not. (z <= 4.8d+71))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+123) || !(z <= 4.8e+71)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e+123) or not (z <= 4.8e+71):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e+123) || !(z <= 4.8e+71))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e+123) || ~((z <= 4.8e+71)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e+123], N[Not[LessEqual[z, 4.8e+71]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999986e123 or 4.79999999999999961e71 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -4.29999999999999986e123 < z < 4.79999999999999961e71

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in z around 0 76.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+123} \lor \neg \left(z \leq 4.8 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-157} \lor \neg \left(z \leq 1.75 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.9e-157) (not (<= z 1.75e-75))) (+ x y) (/ t (/ a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e-157) || !(z <= 1.75e-75)) {
		tmp = x + y;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.9d-157)) .or. (.not. (z <= 1.75d-75))) then
        tmp = x + y
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e-157) || !(z <= 1.75e-75)) {
		tmp = x + y;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.9e-157) or not (z <= 1.75e-75):
		tmp = x + y
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.9e-157) || !(z <= 1.75e-75))
		tmp = Float64(x + y);
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.9e-157) || ~((z <= 1.75e-75)))
		tmp = x + y;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.9e-157], N[Not[LessEqual[z, 1.75e-75]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999988e-157 or 1.74999999999999993e-75 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. +-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -2.89999999999999988e-157 < z < 1.74999999999999993e-75

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 59.4%

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

   4. Taylor expanded in z around 0 49.7%

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

      1. associate-/l* 57.7%

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

   6. Simplified 57.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-157} \lor \neg \left(z \leq 1.75 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-150}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.4e-194) x (if (<= x 2.3e-150) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e-194) {
		tmp = x;
	} else if (x <= 2.3e-150) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.4d-194)) then
        tmp = x
    else if (x <= 2.3d-150) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e-194) {
		tmp = x;
	} else if (x <= 2.3e-150) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.4e-194:
		tmp = x
	elif x <= 2.3e-150:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.4e-194)
		tmp = x;
	elseif (x <= 2.3e-150)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.4e-194)
		tmp = x;
	elseif (x <= 2.3e-150)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.4e-194], x, If[LessEqual[x, 2.3e-150], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000006e-194 or 2.30000000000000003e-150 < x

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 56.7%

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

   if -1.40000000000000006e-194 < x < 2.30000000000000003e-150

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 69.6%

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

   4. Taylor expanded in z around inf 34.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-150}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.06e+157) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e+157) {
		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 (a <= (-1.06d+157)) 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 (a <= -1.06e+157) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.06e+157:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e+157)
		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 (a <= -1.06e+157)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e+157], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.06e157

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf 43.7%

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

   if -1.06e157 < a

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

   5. Simplified 61.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.0% 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 84.1%

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

3. Taylor expanded in x around inf 46.5%

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

4. Final simplification 46.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.4% 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 2024011 
(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))))