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

Percentage Accurate: 98.1% → 98.3%

Time: 8.5s

Alternatives: 15

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: 98.1% 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: 98.3% 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]

Derivation

1. Initial program 97.8%

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

   1. clear-num 97.7%

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

   2. un-div-inv 98.1%

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

4. Applied egg-rr 98.1%

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

Alternative 2: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+128)
   (+ x y)
   (if (<= z -2.2e-68)
     (- x (/ (* y t) z))
     (if (<= z 9.8e-11) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+128) {
		tmp = x + y;
	} else if (z <= -2.2e-68) {
		tmp = x - ((y * t) / z);
	} else if (z <= 9.8e-11) {
		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 <= (-4d+128)) then
        tmp = x + y
    else if (z <= (-2.2d-68)) then
        tmp = x - ((y * t) / z)
    else if (z <= 9.8d-11) 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 <= -4e+128) {
		tmp = x + y;
	} else if (z <= -2.2e-68) {
		tmp = x - ((y * t) / z);
	} else if (z <= 9.8e-11) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+128:
		tmp = x + y
	elif z <= -2.2e-68:
		tmp = x - ((y * t) / z)
	elif z <= 9.8e-11:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+128)
		tmp = Float64(x + y);
	elseif (z <= -2.2e-68)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 9.8e-11)
		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 <= -4e+128)
		tmp = x + y;
	elseif (z <= -2.2e-68)
		tmp = x - ((y * t) / z);
	elseif (z <= 9.8e-11)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+128], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.2e-68], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-11], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000003e128 or 9.7999999999999998e-11 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.8%

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

      1. +-commutative 80.8%

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

   5. Simplified 80.8%

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

   if -4.0000000000000003e128 < z < -2.20000000000000002e-68

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in a around 0 71.4%

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

   if -2.20000000000000002e-68 < z < 9.7999999999999998e-11

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+128)
   (+ x y)
   (if (<= z -1.12e-66)
     (- x (* t (/ y z)))
     (if (<= z 1.5e-9) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+128) {
		tmp = x + y;
	} else if (z <= -1.12e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.5e-9) {
		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 <= (-4.6d+128)) then
        tmp = x + y
    else if (z <= (-1.12d-66)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.5d-9) 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 <= -4.6e+128) {
		tmp = x + y;
	} else if (z <= -1.12e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.5e-9) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+128:
		tmp = x + y
	elif z <= -1.12e-66:
		tmp = x - (t * (y / z))
	elif z <= 1.5e-9:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+128)
		tmp = Float64(x + y);
	elseif (z <= -1.12e-66)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.5e-9)
		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 <= -4.6e+128)
		tmp = x + y;
	elseif (z <= -1.12e-66)
		tmp = x - (t * (y / z));
	elseif (z <= 1.5e-9)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+128], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.12e-66], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-9], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999996e128 or 1.49999999999999999e-9 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.8%

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

      1. +-commutative 80.8%

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

   5. Simplified 80.8%

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

   if -4.59999999999999996e128 < z < -1.12000000000000004e-66

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in z around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. sub-neg 71.4%

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

      3. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -1.12000000000000004e-66 < z < 1.49999999999999999e-9

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+58} \lor \neg \left(z \leq 1.05 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+58) (not (<= z 1.05e-6)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+58) || !(z <= 1.05e-6)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / (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 <= (-4.5d+58)) .or. (.not. (z <= 1.05d-6))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (t * (y / (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 <= -4.5e+58) || !(z <= 1.05e-6)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+58) or not (z <= 1.05e-6):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+58) || !(z <= 1.05e-6))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+58) || ~((z <= 1.05e-6)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+58], N[Not[LessEqual[z, 1.05e-6]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e58 or 1.0499999999999999e-6 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 86.9%

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

   if -4.4999999999999998e58 < z < 1.0499999999999999e-6

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+58} \lor \neg \left(z \leq 1.05 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+30) (not (<= z 8.5e-5)))
   (+ x (* y (/ (- z t) z)))
   (+ x (/ t (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+30) || !(z <= 8.5e-5)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t / ((a - z) / 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 <= (-1.15d+30)) .or. (.not. (z <= 8.5d-5))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (t / ((a - z) / 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 <= -1.15e+30) || !(z <= 8.5e-5)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+30) or not (z <= 8.5e-5):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+30) || !(z <= 8.5e-5))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+30) || ~((z <= 8.5e-5)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+30], N[Not[LessEqual[z, 8.5e-5]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e30 or 8.500000000000001e-5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 87.3%

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

   if -1.15e30 < z < 8.500000000000001e-5

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf 90.7%

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

      1. mul-1-neg 90.7%

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

      2. associate-/l* 94.9%

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

   5. Simplified 94.9%

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

      1. unsub-neg 94.9%

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

      2. clear-num 94.9%

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

      3. un-div-inv 94.9%

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

   7. Applied egg-rr 94.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-67} \lor \neg \left(z \leq 2.4 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-67) (not (<= z 2.4e-7)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-67) || !(z <= 2.4e-7)) {
		tmp = x + (y * ((z - t) / z));
	} 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 ((z <= (-1.7d-67)) .or. (.not. (z <= 2.4d-7))) then
        tmp = x + (y * ((z - t) / z))
    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 ((z <= -1.7e-67) || !(z <= 2.4e-7)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e-67) or not (z <= 2.4e-7):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-67) || !(z <= 2.4e-7))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 ((z <= -1.7e-67) || ~((z <= 2.4e-7)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-67], N[Not[LessEqual[z, 2.4e-7]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000005e-67 or 2.39999999999999979e-7 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 85.5%

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

   if -1.70000000000000005e-67 < z < 2.39999999999999979e-7

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-/l* 88.9%

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

   5. Simplified 88.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-67} \lor \neg \left(z \leq 2.4 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-67} \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-67) (not (<= z 1.9e-6)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-67) || !(z <= 1.9e-6)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * ((t - 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 <= (-2.3d-67)) .or. (.not. (z <= 1.9d-6))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (y * ((t - 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 <= -2.3e-67) || !(z <= 1.9e-6)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-67) or not (z <= 1.9e-6):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-67) || !(z <= 1.9e-6))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e-67) || ~((z <= 1.9e-6)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-67], N[Not[LessEqual[z, 1.9e-6]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e-67 or 1.9e-6 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 85.5%

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

   if -2.3e-67 < z < 1.9e-6

   1. Initial program 95.2%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in a around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

      3. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-67} \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-67} \lor \neg \left(z \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e-67) (not (<= z 2.5e-7)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e-67) || !(z <= 2.5e-7)) {
		tmp = x + (y * ((z - t) / z));
	} 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 <= (-1.1d-67)) .or. (.not. (z <= 2.5d-7))) then
        tmp = x + (y * ((z - t) / z))
    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 <= -1.1e-67) || !(z <= 2.5e-7)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e-67) or not (z <= 2.5e-7):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e-67) || !(z <= 2.5e-7))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 <= -1.1e-67) || ~((z <= 2.5e-7)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e-67], N[Not[LessEqual[z, 2.5e-7]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e-67 or 2.49999999999999989e-7 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 85.5%

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

   if -1.1000000000000001e-67 < z < 2.49999999999999989e-7

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. +-commutative 83.2%

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

      2. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-67} \lor \neg \left(z \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-12}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+25) (not (<= z 2.15e-12))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+25) || !(z <= 2.15e-12)) {
		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 <= (-1.3d+25)) .or. (.not. (z <= 2.15d-12))) 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 <= -1.3e+25) || !(z <= 2.15e-12)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+25) or not (z <= 2.15e-12):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+25) || !(z <= 2.15e-12))
		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 <= -1.3e+25) || ~((z <= 2.15e-12)))
		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, -1.3e+25], N[Not[LessEqual[z, 2.15e-12]], $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 < -1.2999999999999999e25 or 2.14999999999999993e-12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -1.2999999999999999e25 < z < 2.14999999999999993e-12

   1. Initial program 95.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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* 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-12}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-66} \lor \neg \left(z \leq 7.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e-66) (not (<= z 7.2e-11))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e-66) || !(z <= 7.2e-11)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2d-66)) .or. (.not. (z <= 7.2d-11))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e-66) || !(z <= 7.2e-11)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e-66) or not (z <= 7.2e-11):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e-66) || !(z <= 7.2e-11))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e-66) || ~((z <= 7.2e-11)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e-66], N[Not[LessEqual[z, 7.2e-11]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e-66 or 7.19999999999999969e-11 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. +-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -2e-66 < z < 7.19999999999999969e-11

   1. Initial program 95.1%

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

      1. clear-num 94.9%

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

      2. un-div-inv 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around 0 86.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-66} \lor \neg \left(z \leq 7.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-66} \lor \neg \left(z \leq 3.15 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.12e-66) (not (<= z 3.15e-9))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.12e-66) || !(z <= 3.15e-9)) {
		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 <= (-1.12d-66)) .or. (.not. (z <= 3.15d-9))) 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 <= -1.12e-66) || !(z <= 3.15e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.12e-66) or not (z <= 3.15e-9):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.12e-66) || !(z <= 3.15e-9))
		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 <= -1.12e-66) || ~((z <= 3.15e-9)))
		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, -1.12e-66], N[Not[LessEqual[z, 3.15e-9]], $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 < -1.12000000000000004e-66 or 3.1500000000000001e-9 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. +-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -1.12000000000000004e-66 < z < 3.1500000000000001e-9

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-66} \lor \neg \left(z \leq 3.15 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{-225}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e-132) x (if (<= x 7.3e-225) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e-132) {
		tmp = x;
	} else if (x <= 7.3e-225) {
		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 <= (-2.4d-132)) then
        tmp = x
    else if (x <= 7.3d-225) 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 <= -2.4e-132) {
		tmp = x;
	} else if (x <= 7.3e-225) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e-132:
		tmp = x
	elif x <= 7.3e-225:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e-132)
		tmp = x;
	elseif (x <= 7.3e-225)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e-132)
		tmp = x;
	elseif (x <= 7.3e-225)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e-132], x, If[LessEqual[x, 7.3e-225], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000015e-132 or 7.29999999999999997e-225 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 62.8%

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

   if -2.40000000000000015e-132 < x < 7.29999999999999997e-225

   1. Initial program 95.4%

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

      1. clear-num 95.1%

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

      2. un-div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in t around 0 38.6%

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

      1. associate-*l/ 52.8%

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

      2. associate-/r/ 51.6%

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

      3. div-sub 51.6%

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

      4. *-inverses 51.6%

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

   7. Simplified 51.6%

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

   8. Taylor expanded in x around 0 43.6%

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

   9. Taylor expanded in a around 0 40.5%

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

Alternative 13: 98.1% 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 97.8%

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

Alternative 14: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.1e+193) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+193) {
		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 <= (-1.1d+193)) 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 <= -1.1e+193) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+193:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+193)
		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 <= -1.1e+193)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+193], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.09999999999999993e193

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 72.5%

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

   if -1.09999999999999993e193 < a

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% 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 97.8%

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

3. Taylor expanded in x around inf 50.9%

   \[\leadsto \color{blue}{x} \]
4. 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 2024108 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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