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

Percentage Accurate: 85.4% → 96.8%

Time: 10.4s

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: 85.4% 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: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{-192}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 2.6e-192)
   (+ (/ (- z t) (/ (- a t) y)) x)
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.6e-192) {
		tmp = ((z - t) / ((a - t) / y)) + x;
	} else {
		tmp = x + (y / ((a - t) / (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 (y <= 2.6d-192) then
        tmp = ((z - t) / ((a - t) / y)) + x
    else
        tmp = x + (y / ((a - t) / (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 (y <= 2.6e-192) {
		tmp = ((z - t) / ((a - t) / y)) + x;
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.6e-192:
		tmp = ((z - t) / ((a - t) / y)) + x
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.6e-192)
		tmp = Float64(Float64(Float64(z - t) / Float64(Float64(a - t) / y)) + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.6e-192)
		tmp = ((z - t) / ((a - t) / y)) + x;
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.6e-192], N[(N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.6000000000000002e-192

   1. Initial program 89.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 99.2%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 99.3%

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

   if 2.6000000000000002e-192 < y

   1. Initial program 87.7%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{a - t}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a - t}{z - t}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a - t}{z - t}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - t}{z - t}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(a - t\right), \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \left(\color{blue}{z} - t\right)\right)\right)\right) \]

      7. --lowering--.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   4. Applied egg-rr 98.6%

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

Alternative 2: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-189}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+136)
   (+ y x)
   (if (<= t -1.52e-189)
     (- x (/ (* y z) t))
     (if (<= t 2.3e+58) (+ x (* z (/ y a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+136) {
		tmp = y + x;
	} else if (t <= -1.52e-189) {
		tmp = x - ((y * z) / t);
	} else if (t <= 2.3e+58) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+136)) then
        tmp = y + x
    else if (t <= (-1.52d-189)) then
        tmp = x - ((y * z) / t)
    else if (t <= 2.3d+58) then
        tmp = x + (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+136) {
		tmp = y + x;
	} else if (t <= -1.52e-189) {
		tmp = x - ((y * z) / t);
	} else if (t <= 2.3e+58) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+136:
		tmp = y + x
	elif t <= -1.52e-189:
		tmp = x - ((y * z) / t)
	elif t <= 2.3e+58:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+136)
		tmp = Float64(y + x);
	elseif (t <= -1.52e-189)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	elseif (t <= 2.3e+58)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+136)
		tmp = y + x;
	elseif (t <= -1.52e-189)
		tmp = x - ((y * z) / t);
	elseif (t <= 2.3e+58)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+136], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.52e-189], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+58], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000002e136 or 2.30000000000000002e58 < t

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 83.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 83.7%

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

   if -2.8000000000000002e136 < t < -1.5199999999999999e-189

   1. Initial program 91.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]
   8. Step-by-step derivation

   9. Simplified 90.7%

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

   10. Taylor expanded in a around 0

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

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(\frac{y \cdot z}{t}\right)\right) \]

       2. unsub-neg N/A

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

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

       5. *-lowering-*.f64 71.3%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   12. Simplified 71.3%

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

   if -1.5199999999999999e-189 < t < 2.30000000000000002e58

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 75.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 75.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 77.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 77.1%

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

Alternative 3: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+192)
   (+ y x)
   (if (<= t -1.7e-236) x (if (<= t 7.5e-247) (/ (* y z) a) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= -1.7e-236) {
		tmp = x;
	} else if (t <= 7.5e-247) {
		tmp = (y * z) / a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+192)) then
        tmp = y + x
    else if (t <= (-1.7d-236)) then
        tmp = x
    else if (t <= 7.5d-247) then
        tmp = (y * z) / a
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= -1.7e-236) {
		tmp = x;
	} else if (t <= 7.5e-247) {
		tmp = (y * z) / a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+192:
		tmp = y + x
	elif t <= -1.7e-236:
		tmp = x
	elif t <= 7.5e-247:
		tmp = (y * z) / a
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+192)
		tmp = Float64(y + x);
	elseif (t <= -1.7e-236)
		tmp = x;
	elseif (t <= 7.5e-247)
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+192)
		tmp = y + x;
	elseif (t <= -1.7e-236)
		tmp = x;
	elseif (t <= 7.5e-247)
		tmp = (y * z) / a;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+192], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.7e-236], x, If[LessEqual[t, 7.5e-247], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999976e192 or 7.5e-247 < t

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 67.0%

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

   if -2.79999999999999976e192 < t < -1.6999999999999999e-236

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.3%

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

   if -1.6999999999999999e-236 < t < 7.5e-247

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 96.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 96.3%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   8. Simplified 66.3%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 58.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+192)
   (+ y x)
   (if (<= t -3.8e-239) x (if (<= t 3.3e-246) (* y (/ z a)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= -3.8e-239) {
		tmp = x;
	} else if (t <= 3.3e-246) {
		tmp = y * (z / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+192)) then
        tmp = y + x
    else if (t <= (-3.8d-239)) then
        tmp = x
    else if (t <= 3.3d-246) then
        tmp = y * (z / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= -3.8e-239) {
		tmp = x;
	} else if (t <= 3.3e-246) {
		tmp = y * (z / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+192:
		tmp = y + x
	elif t <= -3.8e-239:
		tmp = x
	elif t <= 3.3e-246:
		tmp = y * (z / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+192)
		tmp = Float64(y + x);
	elseif (t <= -3.8e-239)
		tmp = x;
	elseif (t <= 3.3e-246)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+192)
		tmp = y + x;
	elseif (t <= -3.8e-239)
		tmp = x;
	elseif (t <= 3.3e-246)
		tmp = y * (z / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+192], N[(y + x), $MachinePrecision], If[LessEqual[t, -3.8e-239], x, If[LessEqual[t, 3.3e-246], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999976e192 or 3.3000000000000001e-246 < t

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 67.0%

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

   if -2.79999999999999976e192 < t < -3.8000000000000002e-239

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.3%

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

   if -3.8000000000000002e-239 < t < 3.3000000000000001e-246

   1. Initial program 96.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 66.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   7. Simplified 66.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{a - t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(a - t\right)\right), y\right) \]

      5. --lowering--.f64 61.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   9. Applied egg-rr 61.8%

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

   10. Taylor expanded in a around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \color{blue}{a}\right), y\right) \]
   11. Step-by-step derivation

   12. Simplified 61.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.75e+111)
   (+ x (* y (/ t (- t a))))
   (if (<= t 7.7e+59) (+ x (/ z (/ (- a t) y))) (+ x (* y (/ (- t z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.75e+111) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 7.7e+59) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (y * ((t - 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 (t <= (-2.75d+111)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 7.7d+59) then
        tmp = x + (z / ((a - t) / y))
    else
        tmp = x + (y * ((t - 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 (t <= -2.75e+111) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 7.7e+59) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (y * ((t - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.75e+111:
		tmp = x + (y * (t / (t - a)))
	elif t <= 7.7e+59:
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = x + (y * ((t - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.75e+111)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 7.7e+59)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.75e+111)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 7.7e+59)
		tmp = x + (z / ((a - t) / y));
	else
		tmp = x + (y * ((t - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.75e+111], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.7e+59], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7499999999999999e111

   1. Initial program 67.9%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a - t}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot t}{\color{blue}{a} - t}\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a - t}}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a - t}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(a - t\right)}\right)\right)\right) \]

      8. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 99.9%

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

   if -2.7499999999999999e111 < t < 7.69999999999999986e59

   1. Initial program 93.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 97.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 97.1%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 97.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]
   8. Step-by-step derivation

   9. Simplified 88.6%

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

   if 7.69999999999999986e59 < t

   1. Initial program 84.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{t}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{t}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - t}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{t}\right)\right)\right) \]

      7. --lowering--.f64 92.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), t\right)\right)\right) \]

   9. Simplified 92.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.46e-46)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 3.6e-173) (+ x (* y (/ t (- t a)))) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.46e-46) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 3.6e-173) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.46d-46)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 3.6d-173) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.46e-46) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 3.6e-173) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.46e-46:
		tmp = x + (z / ((a - t) / y))
	elif z <= 3.6e-173:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.46e-46)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 3.6e-173)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.46e-46)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 3.6e-173)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.46e-46], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-173], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.46000000000000008e-46

   1. Initial program 90.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 98.6%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]
   8. Step-by-step derivation

   9. Simplified 88.9%

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

   if -1.46000000000000008e-46 < z < 3.59999999999999972e-173

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a - t}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot t}{\color{blue}{a} - t}\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a - t}}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a - t}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(a - t\right)}\right)\right)\right) \]

      8. --lowering--.f64 93.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 93.5%

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

   if 3.59999999999999972e-173 < z

   1. Initial program 90.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 98.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \color{blue}{z}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 89.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+192)
   (+ y x)
   (if (<= t 3.1e+173) (+ x (/ z (/ (- a t) y))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 3.1e+173) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+192)) then
        tmp = y + x
    else if (t <= 3.1d+173) then
        tmp = x + (z / ((a - t) / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 3.1e+173) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+192:
		tmp = y + x
	elif t <= 3.1e+173:
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+192)
		tmp = Float64(y + x);
	elseif (t <= 3.1e+173)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+192)
		tmp = y + x;
	elseif (t <= 3.1e+173)
		tmp = x + (z / ((a - t) / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+192], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.1e+173], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999976e192 or 3.1e173 < t

   1. Initial program 69.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 93.2%

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

   if -2.79999999999999976e192 < t < 3.1e173

   1. Initial program 93.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 97.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 97.1%

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

      1. associate-/r/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{a - t}{z - t}}\right), \color{blue}{x}\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{a - t} \cdot \left(z - t\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{y}{a - t}\right), x\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}\right), x\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{a - t}{y}}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{a - t}{y}\right)\right), x\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(a - t\right), y\right)\right), x\right) \]

      11. --lowering--.f64 97.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), y\right)\right), x\right) \]
   8. Step-by-step derivation

   9. Simplified 85.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+192)
   (+ y x)
   (if (<= t 1.95e+173) (+ x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 1.95e+173) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+192)) then
        tmp = y + x
    else if (t <= 1.95d+173) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 1.95e+173) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+192:
		tmp = y + x
	elif t <= 1.95e+173:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+192)
		tmp = Float64(y + x);
	elseif (t <= 1.95e+173)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+192)
		tmp = y + x;
	elseif (t <= 1.95e+173)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+192], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.95e+173], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999976e192 or 1.9499999999999999e173 < t

   1. Initial program 69.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 93.2%

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

   if -2.79999999999999976e192 < t < 1.9499999999999999e173

   1. Initial program 93.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 97.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \color{blue}{z}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 85.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+135)
   (+ y x)
   (if (<= t 1.05e+62) (+ x (* y (/ (- z t) a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+135) {
		tmp = y + x;
	} else if (t <= 1.05e+62) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.22d+135)) then
        tmp = y + x
    else if (t <= 1.05d+62) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+135) {
		tmp = y + x;
	} else if (t <= 1.05e+62) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e+135:
		tmp = y + x
	elif t <= 1.05e+62:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+135)
		tmp = Float64(y + x);
	elseif (t <= 1.05e+62)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e+135)
		tmp = y + x;
	elseif (t <= 1.05e+62)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+135], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.05e+62], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.21999999999999996e135 or 1.05e62 < t

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 83.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 83.9%

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

   if -1.21999999999999996e135 < t < 1.05e62

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{a}\right)\right)\right) \]

      5. --lowering--.f64 73.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), a\right)\right)\right) \]

   5. Simplified 73.9%

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

Alternative 10: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+59}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e-32) (+ y x) (if (<= t 4.4e+59) (+ x (* z (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e-32) {
		tmp = y + x;
	} else if (t <= 4.4e+59) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9d-32)) then
        tmp = y + x
    else if (t <= 4.4d+59) then
        tmp = x + (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e-32) {
		tmp = y + x;
	} else if (t <= 4.4e+59) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e-32:
		tmp = y + x
	elif t <= 4.4e+59:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e-32)
		tmp = Float64(y + x);
	elseif (t <= 4.4e+59)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e-32)
		tmp = y + x;
	elseif (t <= 4.4e+59)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e-32], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.4e+59], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000009e-32 or 4.3999999999999999e59 < t

   1. Initial program 78.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 77.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 77.2%

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

   if -9.00000000000000009e-32 < t < 4.3999999999999999e59

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 72.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 72.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 74.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 74.5%

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

Alternative 11: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= z -4.4e+119) t_1 (if (<= z 2.8e+178) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -4.4e+119) {
		tmp = t_1;
	} else if (z <= 2.8e+178) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (z <= (-4.4d+119)) then
        tmp = t_1
    else if (z <= 2.8d+178) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -4.4e+119) {
		tmp = t_1;
	} else if (z <= 2.8e+178) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if z <= -4.4e+119:
		tmp = t_1
	elif z <= 2.8e+178:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -4.4e+119)
		tmp = t_1;
	elseif (z <= 2.8e+178)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (z <= -4.4e+119)
		tmp = t_1;
	elseif (z <= 2.8e+178)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+119], t$95$1, If[LessEqual[z, 2.8e+178], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000003e119 or 2.79999999999999993e178 < z

   1. Initial program 89.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a - t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(a - t\right)}\right)\right) \]

      4. --lowering--.f64 69.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 69.4%

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

   if -4.4000000000000003e119 < z < 2.79999999999999993e178

   1. Initial program 88.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 66.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 66.0%

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

Alternative 12: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.9e-193)
   (+ x (* (- z t) (/ y (- a t))))
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.9e-193) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / (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 (y <= 1.9d-193) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = x + (y / ((a - t) / (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 (y <= 1.9e-193) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.9e-193:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.9e-193)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.9e-193)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.9e-193], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.90000000000000002e-193

   1. Initial program 89.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

      7. --lowering--.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 99.2%

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

   if 1.90000000000000002e-193 < y

   1. Initial program 87.7%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{a - t}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a - t}{z - t}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a - t}{z - t}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - t}{z - t}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(a - t\right), \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \left(\color{blue}{z} - t\right)\right)\right)\right) \]

      7. --lowering--.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   4. Applied egg-rr 98.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+192) (+ y x) (if (<= t 3.9e-191) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 3.9e-191) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+192)) then
        tmp = y + x
    else if (t <= 3.9d-191) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+192) {
		tmp = y + x;
	} else if (t <= 3.9e-191) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+192:
		tmp = y + x
	elif t <= 3.9e-191:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+192)
		tmp = Float64(y + x);
	elseif (t <= 3.9e-191)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+192)
		tmp = y + x;
	elseif (t <= 3.9e-191)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+192], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.9e-191], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999976e192 or 3.8999999999999999e-191 < t

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 70.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 70.1%

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

   if -2.79999999999999976e192 < t < 3.8999999999999999e-191

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.7%

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

Alternative 14: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+129}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+212}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.6e+129) y (if (<= y 3e+212) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.6e+129) {
		tmp = y;
	} else if (y <= 3e+212) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-7.6d+129)) then
        tmp = y
    else if (y <= 3d+212) then
        tmp = x
    else
        tmp = 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 (y <= -7.6e+129) {
		tmp = y;
	} else if (y <= 3e+212) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.6e+129:
		tmp = y
	elif y <= 3e+212:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.6e+129)
		tmp = y;
	elseif (y <= 3e+212)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.6e+129)
		tmp = y;
	elseif (y <= 3e+212)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.6e+129], y, If[LessEqual[y, 3e+212], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -7.60000000000000011e129 or 3e212 < y

   1. Initial program 66.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 34.6%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 34.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 30.6%

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

   if -7.60000000000000011e129 < y < 3e212

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.5%

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

Alternative 15: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t}\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a - t} \cdot \color{blue}{\left(z - t\right)}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a - t}\right), \color{blue}{\left(z - t\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a - t\right)\right), \left(\color{blue}{z} - t\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \left(z - t\right)\right)\right) \]

   7. --lowering--.f64 97.3%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

4. Applied egg-rr 97.3%

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

5. Final simplification 97.3%

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

Alternative 16: 51.0% 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 88.5%

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

3. Taylor expanded in x around inf

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

5. Simplified 50.7%

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

Developer Target 1: 98.7% 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 2024152 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- a t) (- z t)))))

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