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

Percentage Accurate: 85.1% → 98.3%

Time: 10.2s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 99.3%

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

4. Applied egg-rr 99.3%

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

Alternative 2: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -17500:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+78)
   (+ x y)
   (if (<= z -17500.0)
     (* y (- 1.0 (/ t z)))
     (if (<= z -5.2e-298) x (if (<= z 6e-148) (* t (/ y (- a z))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+78) {
		tmp = x + y;
	} else if (z <= -17500.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= -5.2e-298) {
		tmp = x;
	} else if (z <= 6e-148) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+78)) then
        tmp = x + y
    else if (z <= (-17500.0d0)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= (-5.2d-298)) then
        tmp = x
    else if (z <= 6d-148) then
        tmp = t * (y / (a - z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+78) {
		tmp = x + y;
	} else if (z <= -17500.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= -5.2e-298) {
		tmp = x;
	} else if (z <= 6e-148) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+78:
		tmp = x + y
	elif z <= -17500.0:
		tmp = y * (1.0 - (t / z))
	elif z <= -5.2e-298:
		tmp = x
	elif z <= 6e-148:
		tmp = t * (y / (a - z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+78)
		tmp = Float64(x + y);
	elseif (z <= -17500.0)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= -5.2e-298)
		tmp = x;
	elseif (z <= 6e-148)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+78)
		tmp = x + y;
	elseif (z <= -17500.0)
		tmp = y * (1.0 - (t / z));
	elseif (z <= -5.2e-298)
		tmp = x;
	elseif (z <= 6e-148)
		tmp = t * (y / (a - z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+78], N[(x + y), $MachinePrecision], If[LessEqual[z, -17500.0], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-298], x, If[LessEqual[z, 6e-148], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1999999999999999e78 or 5.99999999999999996e-148 < z

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.2%

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

   5. Simplified 79.2%

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

   if -1.1999999999999999e78 < z < -17500

   1. Initial program 92.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

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

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

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

      2. --lowering--.f64 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 68.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 68.6%

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

   if -17500 < z < -5.1999999999999998e-298

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.9%

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

   if -5.1999999999999998e-298 < z < 5.99999999999999996e-148

   1. Initial program 97.7%

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

      1. frac-2neg N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. associate-*l* N/A

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

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

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

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

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

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

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\left(0 - y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right)\right)\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \color{blue}{\left(z - a\right)}\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(a\right)\right) + \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      15. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(a\right)\right)\right) - \color{blue}{z}\right)\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) - z\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(a - z\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(0 - y\right) \cdot \frac{1}{a - z}\right)} \]

   5. Taylor expanded in t around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 57.9%

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

   7. Simplified 57.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 60.0%

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

   9. Applied egg-rr 60.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -17500:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e-22)
   (+ x y)
   (if (<= z -1.6e-298) x (if (<= z 4.4e-149) (* t (/ y (- a z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e-22) {
		tmp = x + y;
	} else if (z <= -1.6e-298) {
		tmp = x;
	} else if (z <= 4.4e-149) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d-22)) then
        tmp = x + y
    else if (z <= (-1.6d-298)) then
        tmp = x
    else if (z <= 4.4d-149) then
        tmp = t * (y / (a - z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e-22) {
		tmp = x + y;
	} else if (z <= -1.6e-298) {
		tmp = x;
	} else if (z <= 4.4e-149) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e-22:
		tmp = x + y
	elif z <= -1.6e-298:
		tmp = x
	elif z <= 4.4e-149:
		tmp = t * (y / (a - z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e-22)
		tmp = Float64(x + y);
	elseif (z <= -1.6e-298)
		tmp = x;
	elseif (z <= 4.4e-149)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e-22)
		tmp = x + y;
	elseif (z <= -1.6e-298)
		tmp = x;
	elseif (z <= 4.4e-149)
		tmp = t * (y / (a - z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e-22], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.6e-298], x, If[LessEqual[z, 4.4e-149], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999996e-22 or 4.3999999999999996e-149 < z

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 75.1%

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

   5. Simplified 75.1%

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

   if -7.1999999999999996e-22 < z < -1.59999999999999999e-298

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 66.1%

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

   if -1.59999999999999999e-298 < z < 4.3999999999999996e-149

   1. Initial program 97.7%

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

      1. frac-2neg N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. associate-*l* N/A

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

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

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

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

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

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

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\left(0 - y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right)\right)\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \color{blue}{\left(z - a\right)}\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(a\right)\right) + \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      15. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(a\right)\right)\right) - \color{blue}{z}\right)\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) - z\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(a - z\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(0 - y\right) \cdot \frac{1}{a - z}\right)} \]

   5. Taylor expanded in t around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 57.9%

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

   7. Simplified 57.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 60.0%

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

   9. Applied egg-rr 60.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e-20)
   (+ x y)
   (if (<= z -7e-299) x (if (<= z 1.2e-184) (* t (/ y a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-20) {
		tmp = x + y;
	} else if (z <= -7e-299) {
		tmp = x;
	} else if (z <= 1.2e-184) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d-20)) then
        tmp = x + y
    else if (z <= (-7d-299)) then
        tmp = x
    else if (z <= 1.2d-184) then
        tmp = t * (y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-20) {
		tmp = x + y;
	} else if (z <= -7e-299) {
		tmp = x;
	} else if (z <= 1.2e-184) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e-20:
		tmp = x + y
	elif z <= -7e-299:
		tmp = x
	elif z <= 1.2e-184:
		tmp = t * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e-20)
		tmp = Float64(x + y);
	elseif (z <= -7e-299)
		tmp = x;
	elseif (z <= 1.2e-184)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e-20)
		tmp = x + y;
	elseif (z <= -7e-299)
		tmp = x;
	elseif (z <= 1.2e-184)
		tmp = t * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e-20], N[(x + y), $MachinePrecision], If[LessEqual[z, -7e-299], x, If[LessEqual[z, 1.2e-184], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e-20 or 1.20000000000000012e-184 < z

   1. Initial program 79.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 73.5%

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

   5. Simplified 73.5%

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

   if -1.4000000000000001e-20 < z < -6.99999999999999981e-299

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 66.1%

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

   if -6.99999999999999981e-299 < z < 1.20000000000000012e-184

   1. Initial program 97.3%

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

      1. frac-2neg N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. associate-*l* N/A

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

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

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

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

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

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

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\left(0 - y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \left(\frac{\color{blue}{1}}{\mathsf{neg}\left(\left(z - a\right)\right)}\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(z - a\right)\right)\right)}\right)\right)\right)\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \color{blue}{\left(z - a\right)}\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(a\right)\right) + \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      15. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(a\right)\right)\right) - \color{blue}{z}\right)\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) - z\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \left(a - z\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, y\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(0 - y\right) \cdot \frac{1}{a - z}\right)} \]

   5. Taylor expanded in t around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 58.1%

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

   7. Simplified 58.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 60.7%

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

   9. Applied egg-rr 60.7%

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

   10. Taylor expanded in a around inf

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

       1. /-lowering-/.f64 57.5%

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

   12. Simplified 57.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -6e-66) t_1 (if (<= z 3.3e-50) (+ x (/ y (/ a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6e-66) {
		tmp = t_1;
	} else if (z <= 3.3e-50) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-6d-66)) then
        tmp = t_1
    else if (z <= 3.3d-50) then
        tmp = x + (y / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6e-66) {
		tmp = t_1;
	} else if (z <= 3.3e-50) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -6e-66:
		tmp = t_1
	elif z <= 3.3e-50:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -6e-66)
		tmp = t_1;
	elseif (z <= 3.3e-50)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -6e-66)
		tmp = t_1;
	elseif (z <= 3.3e-50)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-66], t$95$1, If[LessEqual[z, 3.3e-50], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000004e-66 or 3.2999999999999998e-50 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 88.6%

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

   if -6.0000000000000004e-66 < z < 3.2999999999999998e-50

   1. Initial program 95.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 88.9%

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

   7. Simplified 88.9%

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

Alternative 6: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+16) (+ x y) (if (<= z 0.0012) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+16) {
		tmp = x + y;
	} else if (z <= 0.0012) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+16)) then
        tmp = x + y
    else if (z <= 0.0012d0) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+16) {
		tmp = x + y;
	} else if (z <= 0.0012) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+16:
		tmp = x + y
	elif z <= 0.0012:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+16)
		tmp = Float64(x + y);
	elseif (z <= 0.0012)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+16)
		tmp = x + y;
	elseif (z <= 0.0012)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+16], N[(x + y), $MachinePrecision], If[LessEqual[z, 0.0012], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e16 or 0.00119999999999999989 < z

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.5%

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

   5. Simplified 82.5%

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

   if -1.3e16 < z < 0.00119999999999999989

   1. Initial program 96.0%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 82.9%

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

   7. Simplified 82.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e-23) (+ x y) (if (<= z 4.6e-40) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e-23) {
		tmp = x + y;
	} else if (z <= 4.6e-40) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.22d-23)) then
        tmp = x + y
    else if (z <= 4.6d-40) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e-23) {
		tmp = x + y;
	} else if (z <= 4.6e-40) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.22e-23:
		tmp = x + y
	elif z <= 4.6e-40:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e-23)
		tmp = Float64(x + y);
	elseif (z <= 4.6e-40)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.22e-23)
		tmp = x + y;
	elseif (z <= 4.6e-40)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e-23], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.6e-40], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22000000000000007e-23 or 4.6e-40 < z

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 78.4%

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

   5. Simplified 78.4%

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

   if -1.22000000000000007e-23 < z < 4.6e-40

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e+134) y (if (<= y 1000.0) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e+134) {
		tmp = y;
	} else if (y <= 1000.0) {
		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 <= (-6d+134)) then
        tmp = y
    else if (y <= 1000.0d0) 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 <= -6e+134) {
		tmp = y;
	} else if (y <= 1000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e+134:
		tmp = y
	elif y <= 1000.0:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e+134)
		tmp = y;
	elseif (y <= 1000.0)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e+134)
		tmp = y;
	elseif (y <= 1000.0)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e+134], y, If[LessEqual[y, 1000.0], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999993e134 or 1e3 < y

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 39.7%

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

   if -5.99999999999999993e134 < y < 1e3

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 62.1%

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

Alternative 9: 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 84.8%

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

3. Taylor expanded in x around inf

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

5. Simplified 45.2%

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

Developer Target 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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