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

Percentage Accurate: 85.7% → 98.4%

Time: 10.0s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% 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 86.3%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

   1. clear-num 98.0%

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

   2. un-div-inv 98.1%

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

6. Applied egg-rr 98.1%

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

7. Final simplification 98.1%

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

Alternative 2: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -1.55e+77)
     (+ x y)
     (if (<= t 2.7e-13)
       t_1
       (if (<= t 5.8e+53)
         (/ y (/ t (- z)))
         (if (<= t 5.1e+84) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 2.7e-13) {
		tmp = t_1;
	} else if (t <= 5.8e+53) {
		tmp = y / (t / -z);
	} else if (t <= 5.1e+84) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-1.55d+77)) then
        tmp = x + y
    else if (t <= 2.7d-13) then
        tmp = t_1
    else if (t <= 5.8d+53) then
        tmp = y / (t / -z)
    else if (t <= 5.1d+84) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 2.7e-13) {
		tmp = t_1;
	} else if (t <= 5.8e+53) {
		tmp = y / (t / -z);
	} else if (t <= 5.1e+84) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -1.55e+77:
		tmp = x + y
	elif t <= 2.7e-13:
		tmp = t_1
	elif t <= 5.8e+53:
		tmp = y / (t / -z)
	elif t <= 5.1e+84:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -1.55e+77)
		tmp = Float64(x + y);
	elseif (t <= 2.7e-13)
		tmp = t_1;
	elseif (t <= 5.8e+53)
		tmp = Float64(y / Float64(t / Float64(-z)));
	elseif (t <= 5.1e+84)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -1.55e+77)
		tmp = x + y;
	elseif (t <= 2.7e-13)
		tmp = t_1;
	elseif (t <= 5.8e+53)
		tmp = y / (t / -z);
	elseif (t <= 5.1e+84)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+77], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.7e-13], t$95$1, If[LessEqual[t, 5.8e+53], N[(y / N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+84], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999999e77 or 5.1000000000000001e84 < t

   1. Initial program 69.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -1.54999999999999999e77 < t < 2.70000000000000011e-13 or 5.8000000000000004e53 < t < 5.1000000000000001e84

   1. Initial program 96.6%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.6%

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

      2. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in t around 0 77.7%

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

   if 2.70000000000000011e-13 < t < 5.8000000000000004e53

   1. Initial program 99.9%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around inf 75.3%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in a around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 74.8%

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

   10. Simplified 74.8%

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

   11. Taylor expanded in x around 0 55.5%

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

       1. mul-1-neg 55.5%

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

       2. distribute-frac-neg2 55.5%

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

       3. associate-/l* 55.2%

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

   13. Simplified 55.2%

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

       1. associate-*r/ 55.5%

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

       2. distribute-frac-neg2 55.5%

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

       3. associate-*l/ 55.3%

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

       4. associate-/r/ 55.5%

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

       5. distribute-neg-frac 55.5%

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

   15. Applied egg-rr 55.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+221}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+185} \lor \neg \left(z \leq 9 \cdot 10^{+228}\right) \land z \leq 3.2 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+221)
   (* z (/ y (- t)))
   (if (or (<= z 1.65e+185) (and (not (<= z 9e+228)) (<= z 3.2e+253)))
     (+ x y)
     (* y (/ (- z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+221) {
		tmp = z * (y / -t);
	} else if ((z <= 1.65e+185) || (!(z <= 9e+228) && (z <= 3.2e+253))) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+221)) then
        tmp = z * (y / -t)
    else if ((z <= 1.65d+185) .or. (.not. (z <= 9d+228)) .and. (z <= 3.2d+253)) then
        tmp = x + y
    else
        tmp = y * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+221) {
		tmp = z * (y / -t);
	} else if ((z <= 1.65e+185) || (!(z <= 9e+228) && (z <= 3.2e+253))) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+221:
		tmp = z * (y / -t)
	elif (z <= 1.65e+185) or (not (z <= 9e+228) and (z <= 3.2e+253)):
		tmp = x + y
	else:
		tmp = y * (-z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+221)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif ((z <= 1.65e+185) || (!(z <= 9e+228) && (z <= 3.2e+253)))
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+221)
		tmp = z * (y / -t);
	elseif ((z <= 1.65e+185) || (~((z <= 9e+228)) && (z <= 3.2e+253)))
		tmp = x + y;
	else
		tmp = y * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+221], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.65e+185], And[N[Not[LessEqual[z, 9e+228]], $MachinePrecision], LessEqual[z, 3.2e+253]]], N[(x + y), $MachinePrecision], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e221

   1. Initial program 100.0%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 94.9%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

   11. Taylor expanded in x around 0 64.3%

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

       1. associate-*r/ 64.3%

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

       2. associate-*r* 64.3%

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

       3. neg-mul-1 64.3%

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

       4. associate-*l/ 64.2%

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

   13. Simplified 64.2%

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

   if -1.4499999999999999e221 < z < 1.65000000000000006e185 or 8.99999999999999966e228 < z < 3.2000000000000003e253

   1. Initial program 85.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   7. Simplified 68.2%

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

   if 1.65000000000000006e185 < z < 8.99999999999999966e228 or 3.2000000000000003e253 < z

   1. Initial program 81.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 81.7%

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

      1. associate-/l* 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in a around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

      3. associate-/l* 54.7%

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

   10. Simplified 54.7%

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

   11. Taylor expanded in x around 0 47.8%

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

       1. mul-1-neg 47.8%

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

       2. distribute-frac-neg2 47.8%

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

       3. associate-/l* 50.9%

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

   13. Simplified 50.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+221}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+185} \lor \neg \left(z \leq 9 \cdot 10^{+228}\right) \land z \leq 3.2 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+252}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+218)
   (* z (/ y (- t)))
   (if (<= z 4.6e+184)
     (+ x y)
     (if (<= z 5.1e+228)
       (* y (/ (- z) t))
       (if (<= z 6e+252) (+ x y) (/ y (/ t (- z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+218) {
		tmp = z * (y / -t);
	} else if (z <= 4.6e+184) {
		tmp = x + y;
	} else if (z <= 5.1e+228) {
		tmp = y * (-z / t);
	} else if (z <= 6e+252) {
		tmp = x + y;
	} else {
		tmp = 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 <= (-2.9d+218)) then
        tmp = z * (y / -t)
    else if (z <= 4.6d+184) then
        tmp = x + y
    else if (z <= 5.1d+228) then
        tmp = y * (-z / t)
    else if (z <= 6d+252) then
        tmp = x + y
    else
        tmp = 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 <= -2.9e+218) {
		tmp = z * (y / -t);
	} else if (z <= 4.6e+184) {
		tmp = x + y;
	} else if (z <= 5.1e+228) {
		tmp = y * (-z / t);
	} else if (z <= 6e+252) {
		tmp = x + y;
	} else {
		tmp = y / (t / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+218:
		tmp = z * (y / -t)
	elif z <= 4.6e+184:
		tmp = x + y
	elif z <= 5.1e+228:
		tmp = y * (-z / t)
	elif z <= 6e+252:
		tmp = x + y
	else:
		tmp = y / (t / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+218)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= 4.6e+184)
		tmp = Float64(x + y);
	elseif (z <= 5.1e+228)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 6e+252)
		tmp = Float64(x + y);
	else
		tmp = Float64(y / Float64(t / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+218)
		tmp = z * (y / -t);
	elseif (z <= 4.6e+184)
		tmp = x + y;
	elseif (z <= 5.1e+228)
		tmp = y * (-z / t);
	elseif (z <= 6e+252)
		tmp = x + y;
	else
		tmp = y / (t / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+218], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+184], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.1e+228], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+252], N[(x + y), $MachinePrecision], N[(y / N[(t / (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8999999999999999e218

   1. Initial program 100.0%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 94.9%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

   11. Taylor expanded in x around 0 64.3%

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

       1. associate-*r/ 64.3%

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

       2. associate-*r* 64.3%

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

       3. neg-mul-1 64.3%

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

       4. associate-*l/ 64.2%

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

   13. Simplified 64.2%

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

   if -2.8999999999999999e218 < z < 4.6e184 or 5.09999999999999972e228 < z < 5.99999999999999978e252

   1. Initial program 85.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   7. Simplified 68.2%

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

   if 4.6e184 < z < 5.09999999999999972e228

   1. Initial program 82.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate-/l* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in a around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-/l* 55.7%

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

   10. Simplified 55.7%

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

   11. Taylor expanded in x around 0 55.1%

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

       1. mul-1-neg 55.1%

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

       2. distribute-frac-neg2 55.1%

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

       3. associate-/l* 55.3%

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

   13. Simplified 55.3%

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

   if 5.99999999999999978e252 < z

   1. Initial program 81.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 54.0%

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

   10. Simplified 54.0%

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

   11. Taylor expanded in x around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. distribute-frac-neg2 42.4%

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

       3. associate-/l* 47.7%

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

   13. Simplified 47.7%

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

       1. associate-*r/ 42.4%

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

       2. distribute-frac-neg2 42.4%

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

       3. associate-*l/ 47.5%

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

       4. associate-/r/ 47.8%

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

       5. distribute-neg-frac 47.8%

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

   15. Applied egg-rr 47.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+252}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+220}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+220)
   (/ (* y (- z)) t)
   (if (<= z 1.5e+185)
     (+ x y)
     (if (<= z 3.7e+229)
       (* y (/ (- z) t))
       (if (<= z 8e+253) (+ x y) (/ y (/ t (- z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+220) {
		tmp = (y * -z) / t;
	} else if (z <= 1.5e+185) {
		tmp = x + y;
	} else if (z <= 3.7e+229) {
		tmp = y * (-z / t);
	} else if (z <= 8e+253) {
		tmp = x + y;
	} else {
		tmp = 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 <= (-9.5d+220)) then
        tmp = (y * -z) / t
    else if (z <= 1.5d+185) then
        tmp = x + y
    else if (z <= 3.7d+229) then
        tmp = y * (-z / t)
    else if (z <= 8d+253) then
        tmp = x + y
    else
        tmp = 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 <= -9.5e+220) {
		tmp = (y * -z) / t;
	} else if (z <= 1.5e+185) {
		tmp = x + y;
	} else if (z <= 3.7e+229) {
		tmp = y * (-z / t);
	} else if (z <= 8e+253) {
		tmp = x + y;
	} else {
		tmp = y / (t / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+220:
		tmp = (y * -z) / t
	elif z <= 1.5e+185:
		tmp = x + y
	elif z <= 3.7e+229:
		tmp = y * (-z / t)
	elif z <= 8e+253:
		tmp = x + y
	else:
		tmp = y / (t / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+220)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 1.5e+185)
		tmp = Float64(x + y);
	elseif (z <= 3.7e+229)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 8e+253)
		tmp = Float64(x + y);
	else
		tmp = Float64(y / Float64(t / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+220)
		tmp = (y * -z) / t;
	elseif (z <= 1.5e+185)
		tmp = x + y;
	elseif (z <= 3.7e+229)
		tmp = y * (-z / t);
	elseif (z <= 8e+253)
		tmp = x + y;
	else
		tmp = y / (t / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+220], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.5e+185], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.7e+229], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+253], N[(x + y), $MachinePrecision], N[(y / N[(t / (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.50000000000000084e220

   1. Initial program 100.0%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 94.9%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

   11. Taylor expanded in x around 0 64.3%

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

       1. mul-1-neg 64.3%

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

       2. distribute-frac-neg2 64.3%

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

       3. associate-/l* 54.5%

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

   13. Simplified 54.5%

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

       1. associate-*r/ 64.3%

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

       2. frac-2neg 64.3%

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

       3. *-commutative 64.3%

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

       4. distribute-rgt-neg-in 64.3%

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

       5. remove-double-neg 64.3%

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

   15. Applied egg-rr 64.3%

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

   if -9.50000000000000084e220 < z < 1.49999999999999997e185 or 3.70000000000000002e229 < z < 7.9999999999999995e253

   1. Initial program 85.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   7. Simplified 68.2%

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

   if 1.49999999999999997e185 < z < 3.70000000000000002e229

   1. Initial program 82.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate-/l* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in a around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-/l* 55.7%

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

   10. Simplified 55.7%

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

   11. Taylor expanded in x around 0 55.1%

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

       1. mul-1-neg 55.1%

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

       2. distribute-frac-neg2 55.1%

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

       3. associate-/l* 55.3%

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

   13. Simplified 55.3%

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

   if 7.9999999999999995e253 < z

   1. Initial program 81.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 54.0%

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

   10. Simplified 54.0%

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

   11. Taylor expanded in x around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. distribute-frac-neg2 42.4%

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

       3. associate-/l* 47.7%

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

   13. Simplified 47.7%

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

       1. associate-*r/ 42.4%

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

       2. distribute-frac-neg2 42.4%

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

       3. associate-*l/ 47.5%

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

       4. associate-/r/ 47.8%

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

       5. distribute-neg-frac 47.8%

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

   15. Applied egg-rr 47.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+220}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+253}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+76)
   (+ x y)
   (if (<= t 1.02e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 1.2e+88) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+76) {
		tmp = x + y;
	} else if (t <= 1.02e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+88) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+76)) then
        tmp = x + y
    else if (t <= 1.02d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 1.2d+88) then
        tmp = x - (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+76) {
		tmp = x + y;
	} else if (t <= 1.02e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+88) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+76:
		tmp = x + y
	elif t <= 1.02e-89:
		tmp = x + (y / (a / z))
	elif t <= 1.2e+88:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+76)
		tmp = Float64(x + y);
	elseif (t <= 1.02e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.2e+88)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+76)
		tmp = x + y;
	elseif (t <= 1.02e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 1.2e+88)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+76], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.02e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+88], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000006e76 or 1.2e88 < t

   1. Initial program 69.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -7.2000000000000006e76 < t < 1.0199999999999999e-89

   1. Initial program 95.9%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in t around 0 80.4%

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

   if 1.0199999999999999e-89 < t < 1.2e88

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in a around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+76)
   (+ x y)
   (if (<= t 1.45e-90)
     (+ x (/ y (/ a z)))
     (if (<= t 1.75e+88) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+76) {
		tmp = x + y;
	} else if (t <= 1.45e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.75e+88) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.2d+76)) then
        tmp = x + y
    else if (t <= 1.45d-90) then
        tmp = x + (y / (a / z))
    else if (t <= 1.75d+88) then
        tmp = x - (y / (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+76) {
		tmp = x + y;
	} else if (t <= 1.45e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.75e+88) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+76:
		tmp = x + y
	elif t <= 1.45e-90:
		tmp = x + (y / (a / z))
	elif t <= 1.75e+88:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+76)
		tmp = Float64(x + y);
	elseif (t <= 1.45e-90)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.75e+88)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e+76)
		tmp = x + y;
	elseif (t <= 1.45e-90)
		tmp = x + (y / (a / z));
	elseif (t <= 1.75e+88)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+76], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.45e-90], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+88], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000005e76 or 1.7499999999999999e88 < t

   1. Initial program 69.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -9.20000000000000005e76 < t < 1.44999999999999992e-90

   1. Initial program 95.9%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in t around 0 80.4%

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

   if 1.44999999999999992e-90 < t < 1.7499999999999999e88

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in a around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

       1. clear-num 79.2%

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

       2. un-div-inv 79.3%

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

   12. Applied egg-rr 79.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+77)
   (+ x y)
   (if (<= t 1.22e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 3.5e+87) (- x (/ (* y z) t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+77) {
		tmp = x + y;
	} else if (t <= 1.22e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.5e+87) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1d+77)) then
        tmp = x + y
    else if (t <= 1.22d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 3.5d+87) then
        tmp = x - ((y * z) / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+77) {
		tmp = x + y;
	} else if (t <= 1.22e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.5e+87) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+77:
		tmp = x + y
	elif t <= 1.22e-89:
		tmp = x + (y / (a / z))
	elif t <= 3.5e+87:
		tmp = x - ((y * z) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+77)
		tmp = Float64(x + y);
	elseif (t <= 1.22e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 3.5e+87)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+77)
		tmp = x + y;
	elseif (t <= 1.22e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 3.5e+87)
		tmp = x - ((y * z) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+77], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.22e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+87], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999983e76 or 3.49999999999999986e87 < t

   1. Initial program 69.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -9.99999999999999983e76 < t < 1.22e-89

   1. Initial program 95.9%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in t around 0 80.4%

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

   if 1.22e-89 < t < 3.49999999999999986e87

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in a around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in y around 0 79.3%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+77)
   (+ x y)
   (if (<= t 1.25e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 3.2e+87) (- x (/ (* y z) t)) (+ x (/ t (/ t y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 1.25e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.2e+87) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = x + (t / (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 <= (-1.55d+77)) then
        tmp = x + y
    else if (t <= 1.25d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 3.2d+87) then
        tmp = x - ((y * z) / t)
    else
        tmp = x + (t / (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 <= -1.55e+77) {
		tmp = x + y;
	} else if (t <= 1.25e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.2e+87) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = x + (t / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+77:
		tmp = x + y
	elif t <= 1.25e-89:
		tmp = x + (y / (a / z))
	elif t <= 3.2e+87:
		tmp = x - ((y * z) / t)
	else:
		tmp = x + (t / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+77)
		tmp = Float64(x + y);
	elseif (t <= 1.25e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 3.2e+87)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	else
		tmp = Float64(x + Float64(t / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.55e+77)
		tmp = x + y;
	elseif (t <= 1.25e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 3.2e+87)
		tmp = x - ((y * z) / t);
	else
		tmp = x + (t / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+77], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.25e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+87], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.54999999999999999e77

   1. Initial program 63.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.5%

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

      1. +-commutative 83.5%

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

   7. Simplified 83.5%

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

   if -1.54999999999999999e77 < t < 1.24999999999999992e-89

   1. Initial program 95.9%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in t around 0 80.4%

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

   if 1.24999999999999992e-89 < t < 3.2e87

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in a around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in y around 0 79.3%

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

   if 3.2e87 < t

   1. Initial program 74.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 92.7%

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

   7. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.8%

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

   9. Applied egg-rr 92.8%

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

   10. Taylor expanded in a around 0 92.8%

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

       1. neg-mul-1 92.8%

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

       2. distribute-neg-frac2 92.8%

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

   12. Simplified 92.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+77} \lor \neg \left(t \leq 3.35 \cdot 10^{+84}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+77) (not (<= t 3.35e+84)))
   (- x (* y (+ (/ z t) -1.0)))
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+77) || !(t <= 3.35e+84)) {
		tmp = x - (y * ((z / t) + -1.0));
	} 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 <= (-1.3d+77)) .or. (.not. (t <= 3.35d+84))) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 <= -1.3e+77) || !(t <= 3.35e+84)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+77) or not (t <= 3.35e+84):
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x + ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+77) || !(t <= 3.35e+84))
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+77) || ~((t <= 3.35e+84)))
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x + ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+77], N[Not[LessEqual[t, 3.35e+84]], $MachinePrecision]], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e77 or 3.3500000000000002e84 < t

   1. Initial program 69.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. associate-/l* 95.1%

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

      4. div-sub 95.1%

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

      5. sub-neg 95.1%

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

      6. *-inverses 95.1%

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

      7. metadata-eval 95.1%

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

   7. Simplified 95.1%

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

   if -1.3000000000000001e77 < t < 3.3500000000000002e84

   1. Initial program 96.9%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 87.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+77} \lor \neg \left(t \leq 3.35 \cdot 10^{+84}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+180)
   (+ x y)
   (if (<= t 3.3e+89) (+ x (* y (/ z (- a t)))) (+ x (/ t (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+180) {
		tmp = x + y;
	} else if (t <= 3.3e+89) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t / (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 <= (-8d+180)) then
        tmp = x + y
    else if (t <= 3.3d+89) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t / (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 <= -8e+180) {
		tmp = x + y;
	} else if (t <= 3.3e+89) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e+180:
		tmp = x + y
	elif t <= 3.3e+89:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+180)
		tmp = Float64(x + y);
	elseif (t <= 3.3e+89)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8e+180)
		tmp = x + y;
	elseif (t <= 3.3e+89)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+180], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.3e+89], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000001e180

   1. Initial program 57.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.0%

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

      1. +-commutative 88.0%

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

   7. Simplified 88.0%

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

   if -8.0000000000000001e180 < t < 3.29999999999999974e89

   1. Initial program 95.5%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 86.7%

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

   7. Simplified 86.7%

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

   if 3.29999999999999974e89 < t

   1. Initial program 74.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 92.7%

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

   7. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.8%

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

   9. Applied egg-rr 92.8%

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

   10. Taylor expanded in a around 0 92.8%

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

       1. neg-mul-1 92.8%

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

       2. distribute-neg-frac2 92.8%

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

   12. Simplified 92.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+62)
   (+ x (* t (/ y (- t a))))
   (if (<= t 1.65e+88) (+ x (/ (* y z) (- a t))) (+ x (/ t (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+62) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 1.65e+88) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t / (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+62)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 1.65d+88) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (t / (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+62) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 1.65e+88) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+62:
		tmp = x + (t * (y / (t - a)))
	elif t <= 1.65e+88:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (t / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+62)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 1.65e+88)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(t / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+62)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 1.65e+88)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (t / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+62], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+88], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.50000000000000014e62

   1. Initial program 66.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if -2.50000000000000014e62 < t < 1.6500000000000002e88

   1. Initial program 96.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 88.9%

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

   if 1.6500000000000002e88 < t

   1. Initial program 74.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 92.7%

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

   7. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.8%

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

   9. Applied egg-rr 92.8%

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

   10. Taylor expanded in a around 0 92.8%

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

       1. neg-mul-1 92.8%

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

       2. distribute-neg-frac2 92.8%

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

   12. Simplified 92.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e+61)
   (+ x (/ y (/ (- t a) t)))
   (if (<= t 1.15e+87)
     (+ x (/ (* y z) (- a t)))
     (- x (* y (+ (/ z t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+61) {
		tmp = x + (y / ((t - a) / t));
	} else if (t <= 1.15e+87) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	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 <= (-8.5d+61)) then
        tmp = x + (y / ((t - a) / t))
    else if (t <= 1.15d+87) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 <= -8.5e+61) {
		tmp = x + (y / ((t - a) / t));
	} else if (t <= 1.15e+87) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e+61:
		tmp = x + (y / ((t - a) / t))
	elif t <= 1.15e+87:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x - (y * ((z / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e+61)
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	elseif (t <= 1.15e+87)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e+61)
		tmp = x + (y / ((t - a) / t));
	elseif (t <= 1.15e+87)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x - (y * ((z / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e+61], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+87], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000035e61

   1. Initial program 66.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}} \]
   4. Add Preprocessing
   5. 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 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 88.4%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

   9. Simplified 88.4%

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

   if -8.50000000000000035e61 < t < 1.1500000000000001e87

   1. Initial program 96.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 88.9%

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

   if 1.1500000000000001e87 < t

   1. Initial program 74.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. associate-/l* 100.0%

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

      4. div-sub 100.0%

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

      5. sub-neg 100.0%

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

      6. *-inverses 100.0%

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

      7. metadata-eval 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x - y \cdot \left(\frac{z}{t} + -1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-114} \lor \neg \left(t \leq 2.7 \cdot 10^{-160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e-114) (not (<= t 2.7e-160))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-114) || !(t <= 2.7e-160)) {
		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 ((t <= (-5.2d-114)) .or. (.not. (t <= 2.7d-160))) 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 ((t <= -5.2e-114) || !(t <= 2.7e-160)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e-114) or not (t <= 2.7e-160):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e-114) || !(t <= 2.7e-160))
		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 ((t <= -5.2e-114) || ~((t <= 2.7e-160)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e-114], N[Not[LessEqual[t, 2.7e-160]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000026e-114 or 2.7000000000000001e-160 < t

   1. Initial program 82.3%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 68.8%

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

      1. +-commutative 68.8%

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

   7. Simplified 68.8%

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

   if -5.20000000000000026e-114 < t < 2.7000000000000001e-160

   1. Initial program 97.1%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 46.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-114} \lor \neg \left(t \leq 2.7 \cdot 10^{-160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 98.3% 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 86.3%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 16: 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 86.3%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in x around inf 48.0%

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

6. Final simplification 48.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.4% 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]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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