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

Percentage Accurate: 85.7% → 99.7%

Time: 12.9s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+304)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+304)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+304)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+304):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+304))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+304)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+304]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 4.9999999999999997e304 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999997e304

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+278} \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -5e+278) (not (<= t_1 1e+307)))
     (+ x (/ y (/ z (- z t))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+278) || !(t_1 <= 1e+307)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_1 + 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-5d+278)) .or. (.not. (t_1 <= 1d+307))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+278) || !(t_1 <= 1e+307)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -5e+278) or not (t_1 <= 1e+307):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -5e+278) || !(t_1 <= 1e+307))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -5e+278) || ~((t_1 <= 1e+307)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+278], N[Not[LessEqual[t$95$1, 1e+307]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -5.00000000000000029e278 or 9.99999999999999986e306 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 40.9%

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

   3. Taylor expanded in a around 0 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   if -5.00000000000000029e278 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.99999999999999986e306

   1. Initial program 99.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+278} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+307}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - z}{a}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;a \leq 3800:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t z) a)))))
   (if (<= a -5.5e+80)
     t_1
     (if (<= a 1.9e-90)
       (+ x (/ y (/ z (- z t))))
       (if (<= a 3.8e-15)
         (/ (* y (- z t)) (- z a))
         (if (<= a 3800.0) t_1 (+ x (/ y (/ (- z a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -5.5e+80) {
		tmp = t_1;
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 3.8e-15) {
		tmp = (y * (z - t)) / (z - a);
	} else if (a <= 3800.0) {
		tmp = t_1;
	} else {
		tmp = x + (y / ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((t - z) / a))
    if (a <= (-5.5d+80)) then
        tmp = t_1
    else if (a <= 1.9d-90) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 3.8d-15) then
        tmp = (y * (z - t)) / (z - a)
    else if (a <= 3800.0d0) then
        tmp = t_1
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -5.5e+80) {
		tmp = t_1;
	} else if (a <= 1.9e-90) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 3.8e-15) {
		tmp = (y * (z - t)) / (z - a);
	} else if (a <= 3800.0) {
		tmp = t_1;
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - z) / a))
	tmp = 0
	if a <= -5.5e+80:
		tmp = t_1
	elif a <= 1.9e-90:
		tmp = x + (y / (z / (z - t)))
	elif a <= 3.8e-15:
		tmp = (y * (z - t)) / (z - a)
	elif a <= 3800.0:
		tmp = t_1
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - z) / a)))
	tmp = 0.0
	if (a <= -5.5e+80)
		tmp = t_1;
	elseif (a <= 1.9e-90)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 3.8e-15)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(z - a));
	elseif (a <= 3800.0)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - z) / a));
	tmp = 0.0;
	if (a <= -5.5e+80)
		tmp = t_1;
	elseif (a <= 1.9e-90)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 3.8e-15)
		tmp = (y * (z - t)) / (z - a);
	elseif (a <= 3800.0)
		tmp = t_1;
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+80], t$95$1, If[LessEqual[a, 1.9e-90], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-15], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3800.0], t$95$1, N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.49999999999999967e80 or 3.8000000000000002e-15 < a < 3800

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. *-lft-identity 82.0%

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

      4. times-frac 87.4%

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

      5. /-rgt-identity 87.4%

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

   5. Simplified 87.4%

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

   if -5.49999999999999967e80 < a < 1.9e-90

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

   if 1.9e-90 < a < 3.8000000000000002e-15

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 78.7%

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

   if 3800 < a

   1. Initial program 67.6%

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

   3. Taylor expanded in t around 0 63.5%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;a \leq 3800:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 65:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+137} \lor \neg \left(z \leq 1.1 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e-40)
   (+ y x)
   (if (<= z 65.0)
     (+ x (* t (/ y a)))
     (if (or (<= z 7.8e+137) (not (<= z 1.1e+181)))
       (+ y x)
       (- x (* y (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-40) {
		tmp = y + x;
	} else if (z <= 65.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 7.8e+137) || !(z <= 1.1e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (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 <= (-1.2d-40)) then
        tmp = y + x
    else if (z <= 65.0d0) then
        tmp = x + (t * (y / a))
    else if ((z <= 7.8d+137) .or. (.not. (z <= 1.1d+181))) then
        tmp = y + x
    else
        tmp = x - (y * (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 <= -1.2e-40) {
		tmp = y + x;
	} else if (z <= 65.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 7.8e+137) || !(z <= 1.1e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e-40:
		tmp = y + x
	elif z <= 65.0:
		tmp = x + (t * (y / a))
	elif (z <= 7.8e+137) or not (z <= 1.1e+181):
		tmp = y + x
	else:
		tmp = x - (y * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e-40)
		tmp = Float64(y + x);
	elseif (z <= 65.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 7.8e+137) || !(z <= 1.1e+181))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(y * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e-40)
		tmp = y + x;
	elseif (z <= 65.0)
		tmp = x + (t * (y / a));
	elseif ((z <= 7.8e+137) || ~((z <= 1.1e+181)))
		tmp = y + x;
	else
		tmp = x - (y * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e-40], N[(y + x), $MachinePrecision], If[LessEqual[z, 65.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.8e+137], N[Not[LessEqual[z, 1.1e+181]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996e-40 or 65 < z < 7.80000000000000059e137 or 1.1000000000000001e181 < z

   1. Initial program 74.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -1.19999999999999996e-40 < z < 65

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. *-lft-identity 71.8%

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

      3. times-frac 72.3%

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

      4. /-rgt-identity 72.3%

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

   5. Simplified 72.3%

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

   if 7.80000000000000059e137 < z < 1.1000000000000001e181

   1. Initial program 67.4%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-neg-in 86.4%

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

      4. distribute-neg-frac 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 86.6%

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

   8. Simplified 86.6%

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

      1. associate-/r/ 86.4%

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

   10. Applied egg-rr 86.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 65:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+137} \lor \neg \left(z \leq 1.1 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3100000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+135} \lor \neg \left(z \leq 1.35 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e-41)
   (+ y x)
   (if (<= z 3100000.0)
     (+ x (* t (/ y a)))
     (if (or (<= z 7.5e+135) (not (<= z 1.35e+181)))
       (+ y x)
       (- x (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e-41) {
		tmp = y + x;
	} else if (z <= 3100000.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 7.5e+135) || !(z <= 1.35e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t / (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 <= (-5.8d-41)) then
        tmp = y + x
    else if (z <= 3100000.0d0) then
        tmp = x + (t * (y / a))
    else if ((z <= 7.5d+135) .or. (.not. (z <= 1.35d+181))) then
        tmp = y + x
    else
        tmp = x - (t / (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 <= -5.8e-41) {
		tmp = y + x;
	} else if (z <= 3100000.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 7.5e+135) || !(z <= 1.35e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e-41:
		tmp = y + x
	elif z <= 3100000.0:
		tmp = x + (t * (y / a))
	elif (z <= 7.5e+135) or not (z <= 1.35e+181):
		tmp = y + x
	else:
		tmp = x - (t / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e-41)
		tmp = Float64(y + x);
	elseif (z <= 3100000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 7.5e+135) || !(z <= 1.35e+181))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(t / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e-41)
		tmp = y + x;
	elseif (z <= 3100000.0)
		tmp = x + (t * (y / a));
	elseif ((z <= 7.5e+135) || ~((z <= 1.35e+181)))
		tmp = y + x;
	else
		tmp = x - (t / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e-41], N[(y + x), $MachinePrecision], If[LessEqual[z, 3100000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.5e+135], N[Not[LessEqual[z, 1.35e+181]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999955e-41 or 3.1e6 < z < 7.49999999999999947e135 or 1.35000000000000004e181 < z

   1. Initial program 74.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -5.79999999999999955e-41 < z < 3.1e6

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. *-lft-identity 71.8%

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

      3. times-frac 72.3%

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

      4. /-rgt-identity 72.3%

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

   5. Simplified 72.3%

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

   if 7.49999999999999947e135 < z < 1.35000000000000004e181

   1. Initial program 67.4%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-neg-in 86.4%

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

      4. distribute-neg-frac 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3100000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+135} \lor \neg \left(z \leq 1.35 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+165} \lor \neg \left(t \leq 1.62 \cdot 10^{+223}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= t -3.25e+183)
     t_1
     (if (<= t 5e+112)
       (+ x (/ y (/ (- z a) z)))
       (if (or (<= t 5.2e+165) (not (<= t 1.62e+223)))
         (+ x (* t (/ y a)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (t <= -3.25e+183) {
		tmp = t_1;
	} else if (t <= 5e+112) {
		tmp = x + (y / ((z - a) / z));
	} else if ((t <= 5.2e+165) || !(t <= 1.62e+223)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (t <= (-3.25d+183)) then
        tmp = t_1
    else if (t <= 5d+112) then
        tmp = x + (y / ((z - a) / z))
    else if ((t <= 5.2d+165) .or. (.not. (t <= 1.62d+223))) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (t <= -3.25e+183) {
		tmp = t_1;
	} else if (t <= 5e+112) {
		tmp = x + (y / ((z - a) / z));
	} else if ((t <= 5.2e+165) || !(t <= 1.62e+223)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if t <= -3.25e+183:
		tmp = t_1
	elif t <= 5e+112:
		tmp = x + (y / ((z - a) / z))
	elif (t <= 5.2e+165) or not (t <= 1.62e+223):
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (t <= -3.25e+183)
		tmp = t_1;
	elseif (t <= 5e+112)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif ((t <= 5.2e+165) || !(t <= 1.62e+223))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (t <= -3.25e+183)
		tmp = t_1;
	elseif (t <= 5e+112)
		tmp = x + (y / ((z - a) / z));
	elseif ((t <= 5.2e+165) || ~((t <= 1.62e+223)))
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.25e+183], t$95$1, If[LessEqual[t, 5e+112], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5.2e+165], N[Not[LessEqual[t, 1.62e+223]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.24999999999999991e183 or 5.2000000000000002e165 < t < 1.61999999999999988e223

   1. Initial program 80.4%

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

   3. Taylor expanded in t around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*r/ 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

      4. distribute-neg-frac 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

      3. associate-/l* 71.6%

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

   8. Simplified 71.6%

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

   if -3.24999999999999991e183 < t < 5e112

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 73.7%

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

      1. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   if 5e112 < t < 5.2000000000000002e165 or 1.61999999999999988e223 < t

   1. Initial program 71.5%

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

   3. Taylor expanded in z around 0 64.3%

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

      1. +-commutative 64.3%

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

      2. *-lft-identity 64.3%

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

      3. times-frac 80.1%

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

      4. /-rgt-identity 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+183}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+165} \lor \neg \left(t \leq 1.62 \cdot 10^{+223}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ t z))))
   (if (<= t -7e+185)
     t_1
     (if (<= t 1.5e+182) (+ y x) (if (<= t 8.2e+238) t_1 (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (t / z);
	double tmp;
	if (t <= -7e+185) {
		tmp = t_1;
	} else if (t <= 1.5e+182) {
		tmp = y + x;
	} else if (t <= 8.2e+238) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = -y * (t / z)
    if (t <= (-7d+185)) then
        tmp = t_1
    else if (t <= 1.5d+182) then
        tmp = y + x
    else if (t <= 8.2d+238) then
        tmp = t_1
    else
        tmp = 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 t_1 = -y * (t / z);
	double tmp;
	if (t <= -7e+185) {
		tmp = t_1;
	} else if (t <= 1.5e+182) {
		tmp = y + x;
	} else if (t <= 8.2e+238) {
		tmp = t_1;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (t / z)
	tmp = 0
	if t <= -7e+185:
		tmp = t_1
	elif t <= 1.5e+182:
		tmp = y + x
	elif t <= 8.2e+238:
		tmp = t_1
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(t / z))
	tmp = 0.0
	if (t <= -7e+185)
		tmp = t_1;
	elseif (t <= 1.5e+182)
		tmp = Float64(y + x);
	elseif (t <= 8.2e+238)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (t / z);
	tmp = 0.0;
	if (t <= -7e+185)
		tmp = t_1;
	elseif (t <= 1.5e+182)
		tmp = y + x;
	elseif (t <= 8.2e+238)
		tmp = t_1;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+185], t$95$1, If[LessEqual[t, 1.5e+182], N[(y + x), $MachinePrecision], If[LessEqual[t, 8.2e+238], t$95$1, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000046e185 or 1.5000000000000001e182 < t < 8.1999999999999998e238

   1. Initial program 81.5%

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

   3. Taylor expanded in t around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. associate-*r/ 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

      4. distribute-neg-frac 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-/l* 73.7%

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

   8. Simplified 73.7%

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

   9. Taylor expanded in x around 0 52.3%

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

       1. associate-*l/ 57.4%

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

       2. associate-*r* 57.4%

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

       3. neg-mul-1 57.4%

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

       4. *-commutative 57.4%

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

       5. distribute-neg-frac 57.4%

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

   11. Simplified 57.4%

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

   if -7.00000000000000046e185 < t < 1.5000000000000001e182

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf 70.9%

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

      1. +-commutative 70.9%

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

   5. Simplified 70.9%

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

   if 8.1999999999999998e238 < t

   1. Initial program 73.2%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. +-commutative 58.5%

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

      2. *-lft-identity 58.5%

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

      3. times-frac 71.9%

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

      4. /-rgt-identity 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in t around 0 58.5%

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

   7. Taylor expanded in t around inf 37.8%

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

      1. associate-*l/ 44.2%

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

      2. *-commutative 44.2%

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

   9. Simplified 44.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+185}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+238}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 3.2 \cdot 10^{+123}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0074) (not (<= t 3.2e+123)))
   (- x (* t (/ y (- z a))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 3.2e+123)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - 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 ((t <= (-0.0074d0)) .or. (.not. (t <= 3.2d+123))) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y / ((z - 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 ((t <= -0.0074) || !(t <= 3.2e+123)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0074) or not (t <= 3.2e+123):
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0074) || !(t <= 3.2e+123))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.0074) || ~((t <= 3.2e+123)))
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0074], N[Not[LessEqual[t, 3.2e+123]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0074000000000000003 or 3.20000000000000005e123 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-*r/ 91.0%

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

      3. distribute-rgt-neg-in 91.0%

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

      4. distribute-neg-frac 91.0%

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

   5. Simplified 91.0%

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

   if -0.0074000000000000003 < t < 3.20000000000000005e123

   1. Initial program 85.0%

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

   3. Taylor expanded in t around 0 74.7%

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

      1. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 3.2 \cdot 10^{+123}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+80)
   (+ x (* t (/ y a)))
   (if (<= a 6.5e-72) (+ x (/ (- z t) (/ z y))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 6.5e-72) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y / ((z - 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 (a <= (-6.8d+80)) then
        tmp = x + (t * (y / a))
    else if (a <= 6.5d-72) then
        tmp = x + ((z - t) / (z / y))
    else
        tmp = x + (y / ((z - 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 (a <= -6.8e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 6.5e-72) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+80:
		tmp = x + (t * (y / a))
	elif a <= 6.5e-72:
		tmp = x + ((z - t) / (z / y))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+80)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 6.5e-72)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e+80)
		tmp = x + (t * (y / a));
	elseif (a <= 6.5e-72)
		tmp = x + ((z - t) / (z / y));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+80], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-72], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.79999999999999984e80

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. *-lft-identity 75.5%

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

      3. times-frac 79.9%

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

      4. /-rgt-identity 79.9%

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

   5. Simplified 79.9%

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

   if -6.79999999999999984e80 < a < 6.4999999999999997e-72

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 84.8%

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

   if 6.4999999999999997e-72 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e+80)
   (+ x (* t (/ y a)))
   (if (<= a 1.26e-71) (+ x (/ y (/ z (- z t)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.26e-71) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((z - 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 (a <= (-8.6d+80)) then
        tmp = x + (t * (y / a))
    else if (a <= 1.26d-71) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (y / ((z - 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 (a <= -8.6e+80) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.26e-71) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e+80:
		tmp = x + (t * (y / a))
	elif a <= 1.26e-71:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+80)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 1.26e-71)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.6e+80)
		tmp = x + (t * (y / a));
	elseif (a <= 1.26e-71)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+80], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.26e-71], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.60000000000000008e80

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. *-lft-identity 75.5%

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

      3. times-frac 79.9%

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

      4. /-rgt-identity 79.9%

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

   5. Simplified 79.9%

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

   if -8.60000000000000008e80 < a < 1.2600000000000001e-71

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

   if 1.2600000000000001e-71 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+80}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e+80)
   (+ x (* y (/ (- t z) a)))
   (if (<= a 6.2e-72) (+ x (/ y (/ z (- z t)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e+80) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 6.2e-72) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((z - 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 (a <= (-7.5d+80)) then
        tmp = x + (y * ((t - z) / a))
    else if (a <= 6.2d-72) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (y / ((z - 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 (a <= -7.5e+80) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 6.2e-72) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e+80:
		tmp = x + (y * ((t - z) / a))
	elif a <= 6.2e-72:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e+80)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (a <= 6.2e-72)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e+80)
		tmp = x + (y * ((t - z) / a));
	elseif (a <= 6.2e-72)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e+80], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-72], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999994e80

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

      3. *-lft-identity 81.2%

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

      4. times-frac 87.6%

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

      5. /-rgt-identity 87.6%

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

   5. Simplified 87.6%

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

   if -7.49999999999999994e80 < a < 6.1999999999999996e-72

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

   if 6.1999999999999996e-72 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-40} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e-40) (not (<= z 1.35e+25))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e-40) || !(z <= 1.35e+25)) {
		tmp = y + x;
	} 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 <= (-2.8d-40)) .or. (.not. (z <= 1.35d+25))) then
        tmp = y + x
    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 <= -2.8e-40) || !(z <= 1.35e+25)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e-40) or not (z <= 1.35e+25):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e-40) || !(z <= 1.35e+25))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e-40) || ~((z <= 1.35e+25)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e-40], N[Not[LessEqual[z, 1.35e+25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e-40 or 1.35e25 < z

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. +-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -2.8e-40 < z < 1.35e25

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 71.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-40} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-41} \lor \neg \left(z \leq 42000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e-41) (not (<= z 42000.0))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e-41) || !(z <= 42000.0)) {
		tmp = y + x;
	} 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 <= (-2.4d-41)) .or. (.not. (z <= 42000.0d0))) then
        tmp = y + x
    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 <= -2.4e-41) || !(z <= 42000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e-41) or not (z <= 42000.0):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e-41) || !(z <= 42000.0))
		tmp = Float64(y + x);
	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 <= -2.4e-41) || ~((z <= 42000.0)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e-41], N[Not[LessEqual[z, 42000.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000022e-41 or 42000 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -2.40000000000000022e-41 < z < 42000

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. *-lft-identity 71.8%

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

      3. times-frac 72.3%

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

      4. /-rgt-identity 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-41} \lor \neg \left(z \leq 42000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+246) (* y (/ t a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+246) {
		tmp = y * (t / a);
	} else {
		tmp = y + 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 (t <= (-3.6d+246)) then
        tmp = y * (t / a)
    else
        tmp = y + 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 (t <= -3.6e+246) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+246:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+246)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+246)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+246], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e246

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. *-lft-identity 83.6%

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

      3. times-frac 83.6%

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

      4. /-rgt-identity 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 83.6%

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

   7. Taylor expanded in t around inf 73.8%

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

      1. associate-*l/ 70.6%

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

      2. *-commutative 70.6%

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

   9. Simplified 70.6%

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

   if -3.6e246 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+248) (/ (* y t) a) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+248) {
		tmp = (y * t) / a;
	} else {
		tmp = y + 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 (t <= (-6.2d+248)) then
        tmp = (y * t) / a
    else
        tmp = y + 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 (t <= -6.2e+248) {
		tmp = (y * t) / a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+248:
		tmp = (y * t) / a
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+248)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+248)
		tmp = (y * t) / a;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+248], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000011e248

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. *-lft-identity 83.6%

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

      3. times-frac 83.6%

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

      4. /-rgt-identity 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 83.6%

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

   7. Taylor expanded in t around inf 73.8%

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

   if -6.20000000000000011e248 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.9 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 6.9e+135) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6.9e+135) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 6.9d+135) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6.9e+135) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 6.9e+135:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 6.9e+135)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 6.9e+135)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 6.9e+135], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 6.89999999999999972e135

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. +-commutative 61.5%

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

   5. Simplified 61.5%

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

   if 6.89999999999999972e135 < a

   1. Initial program 62.4%

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

   3. Taylor expanded in x around inf 76.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.9 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.9% 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 83.7%

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

3. Taylor expanded in x around inf 47.1%

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

4. Final simplification 47.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% 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 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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