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

Percentage Accurate: 98.2% → 98.2%

Time: 9.5s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -32000000.0) (not (<= z 2.35e+111)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-32000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -32000000.0) or not (z <= 2.35e+111):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -32000000.0) || !(z <= 2.35e+111))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 <= -32000000.0) || ~((z <= 2.35e+111)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -32000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e7 or 2.35000000000000004e111 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 92.1%

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

   if -3.2e7 < z < 2.35000000000000004e111

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 81.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+50} \lor \neg \left(z \leq 1.9 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.6e+50) (not (<= z 1.9e+113)))
   (+ x (/ y (/ (- z a) z)))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e+50) || !(z <= 1.9e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y * (t / (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 <= (-5.6d+50)) .or. (.not. (z <= 1.9d+113))) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x + (y * (t / (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 <= -5.6e+50) || !(z <= 1.9e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.6e+50) or not (z <= 1.9e+113):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.6e+50) || !(z <= 1.9e+113))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.6e+50) || ~((z <= 1.9e+113)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.6e+50], N[Not[LessEqual[z, 1.9e+113]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999996e50 or 1.9000000000000002e113 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 65.6%

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

      1. associate-/l* 96.3%

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

   5. Simplified 96.3%

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

   if -5.5999999999999996e50 < z < 1.9000000000000002e113

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 88.7%

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

      1. neg-mul-1 88.7%

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

      2. distribute-neg-frac 88.7%

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

   5. Simplified 88.7%

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

      1. frac-2neg 88.7%

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

      2. remove-double-neg 88.7%

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

      3. associate-*r/ 86.6%

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

   7. Applied egg-rr 86.6%

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

      1. associate-/l* 88.7%

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

   9. Simplified 88.7%

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

   10. Taylor expanded in y around 0 86.6%

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

       1. associate-/l* 87.1%

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

       2. associate-/r/ 88.7%

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

   12. Simplified 88.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+50} \lor \neg \left(z \leq 1.9 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+19)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 1.75e+122) (+ x (* y (/ t (- a z)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.75e+122) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+19)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 1.75d+122) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.75e+122) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+19:
		tmp = x + (y * ((z - t) / z))
	elif z <= 1.75e+122:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+19)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 1.75e+122)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+19)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 1.75e+122)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+19], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+122], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e19

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 88.5%

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

   if -4.2e19 < z < 1.75000000000000007e122

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 89.2%

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

      1. neg-mul-1 89.2%

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

      2. distribute-neg-frac 89.2%

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

   5. Simplified 89.2%

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

      1. frac-2neg 89.2%

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

      2. remove-double-neg 89.2%

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

      3. associate-*r/ 86.5%

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

   7. Applied egg-rr 86.5%

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

      1. associate-/l* 89.2%

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

   9. Simplified 89.2%

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

   10. Taylor expanded in y around 0 86.5%

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

       1. associate-/l* 87.6%

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

       2. associate-/r/ 89.2%

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

   12. Simplified 89.2%

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

   if 1.75000000000000007e122 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+118}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+48)
   (+ x (* z (/ y (- z a))))
   (if (<= z 4.3e+118) (+ x (* y (/ t (- a z)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+48) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.3e+118) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+48)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 4.3d+118) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+48) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.3e+118) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+48:
		tmp = x + (z * (y / (z - a)))
	elif z <= 4.3e+118:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+48)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 4.3e+118)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+48)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 4.3e+118)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+48], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+118], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999999e48

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 64.2%

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

      1. associate-/l* 92.7%

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

      2. associate-/r/ 92.5%

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

   5. Applied egg-rr 92.5%

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

   if -5.1999999999999999e48 < z < 4.3000000000000003e118

   1. Initial program 97.6%

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

   3. Taylor expanded in t around inf 88.8%

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

      1. neg-mul-1 88.8%

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

      2. distribute-neg-frac 88.8%

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

   5. Simplified 88.8%

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

      1. frac-2neg 88.8%

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

      2. remove-double-neg 88.8%

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

      3. associate-*r/ 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-/l* 88.8%

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

   9. Simplified 88.8%

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

   10. Taylor expanded in y around 0 86.2%

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

       1. associate-/l* 87.3%

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

       2. associate-/r/ 88.8%

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

   12. Simplified 88.8%

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

   if 4.3000000000000003e118 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+118}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35000000 \lor \neg \left(z \leq 1.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -35000000.0) (not (<= z 1.5e+112)))
   (+ x y)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -35000000.0) || !(z <= 1.5e+112)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-35000000.0d0)) .or. (.not. (z <= 1.5d+112))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -35000000.0) || !(z <= 1.5e+112)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -35000000.0) or not (z <= 1.5e+112):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -35000000.0) || !(z <= 1.5e+112))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -35000000.0) || ~((z <= 1.5e+112)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -35000000.0], N[Not[LessEqual[z, 1.5e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e7 or 1.4999999999999999e112 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 85.9%

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

   if -3.5e7 < z < 1.4999999999999999e112

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 88.9%

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

      1. neg-mul-1 88.9%

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

      2. distribute-neg-frac 88.9%

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

   5. Simplified 88.9%

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

      1. frac-2neg 88.9%

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

      2. remove-double-neg 88.9%

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

      3. associate-*r/ 87.3%

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

   7. Applied egg-rr 87.3%

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

      1. associate-/l* 88.9%

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

   9. Simplified 88.9%

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

   10. Taylor expanded in z around 0 79.1%

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

       1. *-commutative 79.1%

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

       2. associate-*l/ 79.2%

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

       3. *-commutative 79.2%

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

   12. Simplified 79.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35000000 \lor \neg \left(z \leq 1.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -175000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -175000000.0) (not (<= z 2.35e+111)))
   (+ x y)
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -175000000.0) || !(z <= 2.35e+111)) {
		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 <= (-175000000.0d0)) .or. (.not. (z <= 2.35d+111))) 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 <= -175000000.0) || !(z <= 2.35e+111)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -175000000.0) or not (z <= 2.35e+111):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -175000000.0) || !(z <= 2.35e+111))
		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 <= -175000000.0) || ~((z <= 2.35e+111)))
		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, -175000000.0], N[Not[LessEqual[z, 2.35e+111]], $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 < -1.75e8 or 2.35000000000000004e111 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 85.9%

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

   if -1.75e8 < z < 2.35000000000000004e111

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 81.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -175000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -8.2e+91) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e+91) {
		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 <= (-8.2d+91)) 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 <= -8.2e+91) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.2e+91:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.2e+91)
		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 <= -8.2e+91)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.2e+91], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2000000000000005e91

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.8%

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

   4. Taylor expanded in z around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-/l* 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in x around inf 73.2%

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

   if -8.2000000000000005e91 < a

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 60.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in t around 0 61.3%

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

4. Taylor expanded in z around 0 44.8%

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

   1. mul-1-neg 44.8%

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

   2. associate-/l* 45.3%

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

6. Simplified 45.3%

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

7. Taylor expanded in x around inf 51.9%

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

8. Final simplification 51.9%

   \[\leadsto x \]
9. Add Preprocessing

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 2024036 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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