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

Percentage Accurate: 98.0% → 98.2%

Time: 10.3s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. clear-num 97.6%

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

   2. un-div-inv 97.9%

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

4. Applied egg-rr 97.9%

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

Alternative 2: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+34} \lor \neg \left(t \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+34) (not (<= t 3.1e+21)))
   (+ x (* y (/ t (- t a))))
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+34) || !(t <= 3.1e+21)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z / ((a - t) / 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 ((t <= (-2.5d+34)) .or. (.not. (t <= 3.1d+21))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z / ((a - t) / 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 ((t <= -2.5e+34) || !(t <= 3.1e+21)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+34) or not (t <= 3.1e+21):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+34) || !(t <= 3.1e+21))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+34) || ~((t <= 3.1e+21)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+34], N[Not[LessEqual[t, 3.1e+21]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999999e34 or 3.1e21 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

      3. *-commutative 74.6%

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

      4. associate-/l* 92.4%

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

   5. Simplified 92.4%

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

   if -2.4999999999999999e34 < t < 3.1e21

   1. Initial program 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. add-cube-cbrt 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{\left(\sqrt[3]{\frac{a - t}{z - t}} \cdot \sqrt[3]{\frac{a - t}{z - t}}\right) \cdot \sqrt[3]{\frac{a - t}{z - t}}}} \]

      2. pow3 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   6. Applied egg-rr 96.0%

      \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   7. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.3%

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

       2. un-div-inv 92.9%

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

   11. Applied egg-rr 92.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+34} \lor \neg \left(t \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+32} \lor \neg \left(t \leq 4.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+32) (not (<= t 4.5e+21)))
   (+ x y)
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+32) || !(t <= 4.5e+21)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / 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 ((t <= (-3.2d+32)) .or. (.not. (t <= 4.5d+21))) then
        tmp = x + y
    else
        tmp = x + (z / ((a - t) / 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 ((t <= -3.2e+32) || !(t <= 4.5e+21)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+32) or not (t <= 4.5e+21):
		tmp = x + y
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+32) || !(t <= 4.5e+21))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+32) || ~((t <= 4.5e+21)))
		tmp = x + y;
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+32], N[Not[LessEqual[t, 4.5e+21]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999999e32 or 4.5e21 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -3.1999999999999999e32 < t < 4.5e21

   1. Initial program 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. add-cube-cbrt 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{\left(\sqrt[3]{\frac{a - t}{z - t}} \cdot \sqrt[3]{\frac{a - t}{z - t}}\right) \cdot \sqrt[3]{\frac{a - t}{z - t}}}} \]

      2. pow3 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   6. Applied egg-rr 96.0%

      \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   7. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.3%

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

       2. un-div-inv 92.9%

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

   11. Applied egg-rr 92.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+32} \lor \neg \left(t \leq 4.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 4.45 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.8e+34) (not (<= t 4.45e+21)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.8e+34) || !(t <= 4.45e+21)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (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 ((t <= (-7.8d+34)) .or. (.not. (t <= 4.45d+21))) then
        tmp = x + y
    else
        tmp = x + (z * (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 ((t <= -7.8e+34) || !(t <= 4.45e+21)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.8e+34) or not (t <= 4.45e+21):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.8e+34) || !(t <= 4.45e+21))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.8e+34) || ~((t <= 4.45e+21)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.8e+34], N[Not[LessEqual[t, 4.45e+21]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.80000000000000038e34 or 4.45e21 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -7.80000000000000038e34 < t < 4.45e21

   1. Initial program 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. add-cube-cbrt 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{\left(\sqrt[3]{\frac{a - t}{z - t}} \cdot \sqrt[3]{\frac{a - t}{z - t}}\right) \cdot \sqrt[3]{\frac{a - t}{z - t}}}} \]

      2. pow3 96.0%

         \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   6. Applied egg-rr 96.0%

      \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   7. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 92.3%

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

   9. Simplified 92.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 4.45 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 1.6 \cdot 10^{+201}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.8e+34) (not (<= t 1.6e+201)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.8e+34) || !(t <= 1.6e+201)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.8d+34)) .or. (.not. (t <= 1.6d+201))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.8e+34) || !(t <= 1.6e+201)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.8e+34) or not (t <= 1.6e+201):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.8e+34) || !(t <= 1.6e+201))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.8e+34) || ~((t <= 1.6e+201)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.8e+34], N[Not[LessEqual[t, 1.6e+201]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.80000000000000038e34 or 1.6e201 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.4%

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

      1. +-commutative 87.4%

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

   5. Simplified 87.4%

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

   if -7.80000000000000038e34 < t < 1.6e201

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 85.0%

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

      1. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 1.6 \cdot 10^{+201}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2500000:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2500000.0)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 1.4e+24) (+ x (* t (/ y (- t a)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2500000.0) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.4e+24) {
		tmp = x + (t * (y / (t - a)));
	} 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 <= (-2500000.0d0)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 1.4d+24) then
        tmp = x + (t * (y / (t - a)))
    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 <= -2500000.0) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.4e+24) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2500000.0:
		tmp = x + (z / ((a - t) / y))
	elif z <= 1.4e+24:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2500000.0)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 1.4e+24)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2500000.0)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 1.4e+24)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2500000.0], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+24], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e6

   1. Initial program 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. add-cube-cbrt 92.9%

         \[\leadsto x + \frac{y}{\color{blue}{\left(\sqrt[3]{\frac{a - t}{z - t}} \cdot \sqrt[3]{\frac{a - t}{z - t}}\right) \cdot \sqrt[3]{\frac{a - t}{z - t}}}} \]

      2. pow3 92.9%

         \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   6. Applied egg-rr 92.9%

      \[\leadsto x + \frac{y}{\color{blue}{{\left(\sqrt[3]{\frac{a - t}{z - t}}\right)}^{3}}} \]

   7. Taylor expanded in z around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*r/ 92.6%

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

   9. Simplified 92.6%

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

       1. clear-num 92.5%

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

       2. un-div-inv 92.7%

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

   11. Applied egg-rr 92.7%

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

   if -2.5e6 < z < 1.4000000000000001e24

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if 1.4000000000000001e24 < z

   1. Initial program 98.0%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in z around inf 93.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2500000:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+32} \lor \neg \left(t \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+32) (not (<= t 4.5e+18))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+32) || !(t <= 4.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (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 ((t <= (-2.1d+32)) .or. (.not. (t <= 4.5d+18))) then
        tmp = x + y
    else
        tmp = x + (z * (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 ((t <= -2.1e+32) || !(t <= 4.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+32) or not (t <= 4.5e+18):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+32) || !(t <= 4.5e+18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+32) || ~((t <= 4.5e+18)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+32], N[Not[LessEqual[t, 4.5e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1000000000000001e32 or 4.5e18 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -2.1000000000000001e32 < t < 4.5e18

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. un-div-inv 79.3%

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

   7. Applied egg-rr 79.3%

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

      1. associate-/r/ 81.8%

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

   9. Simplified 81.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+32} \lor \neg \left(t \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+31} \lor \neg \left(t \leq 7.5 \cdot 10^{+20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e+31) (not (<= t 7.5e+20))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+31) || !(t <= 7.5e+20)) {
		tmp = x + y;
	} else {
		tmp = x + (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 ((t <= (-3.8d+31)) .or. (.not. (t <= 7.5d+20))) then
        tmp = x + y
    else
        tmp = x + (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 ((t <= -3.8e+31) || !(t <= 7.5e+20)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e+31) or not (t <= 7.5e+20):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e+31) || !(t <= 7.5e+20))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.8e+31) || ~((t <= 7.5e+20)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e+31], N[Not[LessEqual[t, 7.5e+20]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000001e31 or 7.5e20 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -3.8000000000000001e31 < t < 7.5e20

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+31} \lor \neg \left(t \leq 7.5 \cdot 10^{+20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+31} \lor \neg \left(t \leq 1.76 \cdot 10^{+19}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+31) (not (<= t 1.76e+19))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+31) || !(t <= 1.76e+19)) {
		tmp = x + y;
	} else {
		tmp = x + ((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 ((t <= (-3.4d+31)) .or. (.not. (t <= 1.76d+19))) then
        tmp = x + y
    else
        tmp = x + ((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 ((t <= -3.4e+31) || !(t <= 1.76e+19)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e+31) or not (t <= 1.76e+19):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e+31) || !(t <= 1.76e+19))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e+31) || ~((t <= 1.76e+19)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e+31], N[Not[LessEqual[t, 1.76e+19]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3999999999999998e31 or 1.76e19 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -3.3999999999999998e31 < t < 1.76e19

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 77.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+31} \lor \neg \left(t \leq 1.76 \cdot 10^{+19}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e+131) x (if (<= a 1.22e+185) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+131) {
		tmp = x;
	} else if (a <= 1.22e+185) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d+131)) then
        tmp = x
    else if (a <= 1.22d+185) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+131) {
		tmp = x;
	} else if (a <= 1.22e+185) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e+131:
		tmp = x
	elif a <= 1.22e+185:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e+131)
		tmp = x;
	elseif (a <= 1.22e+185)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e+131)
		tmp = x;
	elseif (a <= 1.22e+185)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e+131], x, If[LessEqual[a, 1.22e+185], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9e131 or 1.22000000000000002e185 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.6%

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

   if -3.9e131 < a < 1.22000000000000002e185

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 68.0%

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

      1. +-commutative 68.0%

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

   5. Simplified 68.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

Alternative 12: 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 97.6%

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

3. Taylor expanded in x around inf 55.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024094 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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