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

Percentage Accurate: 98.2% → 98.3%

Time: 10.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $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 99.2%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

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

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

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

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

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

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

   6. --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: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -120000:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e+78)
   (+ x y)
   (if (<= z -120000.0)
     (* y (- 1.0 (/ t z)))
     (if (<= z -5.5e-297) 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 <= -3.7e+78) {
		tmp = x + y;
	} else if (z <= -120000.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= -5.5e-297) {
		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 <= (-3.7d+78)) then
        tmp = x + y
    else if (z <= (-120000.0d0)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= (-5.5d-297)) 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 <= -3.7e+78) {
		tmp = x + y;
	} else if (z <= -120000.0) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= -5.5e-297) {
		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 <= -3.7e+78:
		tmp = x + y
	elif z <= -120000.0:
		tmp = y * (1.0 - (t / z))
	elif z <= -5.5e-297:
		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 <= -3.7e+78)
		tmp = Float64(x + y);
	elseif (z <= -120000.0)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= -5.5e-297)
		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 <= -3.7e+78)
		tmp = x + y;
	elseif (z <= -120000.0)
		tmp = y * (1.0 - (t / z));
	elseif (z <= -5.5e-297)
		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, -3.7e+78], N[(x + y), $MachinePrecision], If[LessEqual[z, -120000.0], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-297], x, If[LessEqual[z, 1.2e-184], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.69999999999999985e78 or 1.20000000000000012e-184 < z

   1. Initial program 99.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 77.2%

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

   5. Simplified 77.2%

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

   if -3.69999999999999985e78 < z < -1.2e5

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. /-lowering-/.f64 68.6%

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

   8. Simplified 68.6%

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

   if -1.2e5 < z < -5.5000000000000003e-297

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -5.5000000000000003e-297 < z < 1.20000000000000012e-184

   1. Initial program 97.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 97.7%

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

   4. Applied egg-rr 97.7%

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

   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 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 54.9%

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

   10. Simplified 54.9%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 57.5%

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

   12. Applied egg-rr 57.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -120000:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.02e-22)
   (+ x y)
   (if (<= z -9.5e-298) 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 <= -1.02e-22) {
		tmp = x + y;
	} else if (z <= -9.5e-298) {
		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 <= (-1.02d-22)) then
        tmp = x + y
    else if (z <= (-9.5d-298)) 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 <= -1.02e-22) {
		tmp = x + y;
	} else if (z <= -9.5e-298) {
		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 <= -1.02e-22:
		tmp = x + y
	elif z <= -9.5e-298:
		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 <= -1.02e-22)
		tmp = Float64(x + y);
	elseif (z <= -9.5e-298)
		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 <= -1.02e-22)
		tmp = x + y;
	elseif (z <= -9.5e-298)
		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, -1.02e-22], N[(x + y), $MachinePrecision], If[LessEqual[z, -9.5e-298], 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 < -1.02000000000000002e-22 or 1.20000000000000012e-184 < z

   1. Initial program 99.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -1.02000000000000002e-22 < z < -9.50000000000000012e-298

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -9.50000000000000012e-298 < z < 1.20000000000000012e-184

   1. Initial program 97.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 97.7%

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

   4. Applied egg-rr 97.7%

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

   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 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 54.9%

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

   10. Simplified 54.9%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 57.5%

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

   12. Applied egg-rr 57.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 98.1%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --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 5: 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 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 98.4%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --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 6: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.00039:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e+20) (+ x y) (if (<= z 0.00039) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e+20) {
		tmp = x + y;
	} else if (z <= 0.00039) {
		tmp = x + (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 <= (-7.8d+20)) then
        tmp = x + y
    else if (z <= 0.00039d0) then
        tmp = x + (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 <= -7.8e+20) {
		tmp = x + y;
	} else if (z <= 0.00039) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.8e+20:
		tmp = x + y
	elif z <= 0.00039:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e+20)
		tmp = Float64(x + y);
	elseif (z <= 0.00039)
		tmp = Float64(x + 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 <= -7.8e+20)
		tmp = x + y;
	elseif (z <= 0.00039)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e+20], N[(x + y), $MachinePrecision], If[LessEqual[z, 0.00039], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e20 or 3.89999999999999993e-4 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -7.8e20 < z < 3.89999999999999993e-4

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.00039:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-17) (+ x y) (if (<= z 8.5e-40) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-17) {
		tmp = x + y;
	} else if (z <= 8.5e-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 <= (-2.2d-17)) then
        tmp = x + y
    else if (z <= 8.5d-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 <= -2.2e-17) {
		tmp = x + y;
	} else if (z <= 8.5e-40) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-17:
		tmp = x + y
	elif z <= 8.5e-40:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-17)
		tmp = Float64(x + y);
	elseif (z <= 8.5e-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 <= -2.2e-17)
		tmp = x + y;
	elseif (z <= 8.5e-40)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-17], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.5e-40], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e-17 or 8.4999999999999998e-40 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -2.2e-17 < z < 8.4999999999999998e-40

   1. Initial program 98.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.5e+132) y (if (<= y 1000.0) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+132) {
		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 <= (-3.5d+132)) 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 <= -3.5e+132) {
		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 <= -3.5e+132:
		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 <= -3.5e+132)
		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 <= -3.5e+132)
		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, -3.5e+132], y, If[LessEqual[y, 1000.0], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000002e132 or 1e3 < y

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -3.5000000000000002e132 < y < 1e3

   1. Initial program 98.7%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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: 98.2% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 99.2%

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

Alternative 10: 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 99.2%

   \[x + y \cdot \frac{z - t}{z - a} \]
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:renderAxisLine 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)))))