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

Percentage Accurate: 98.3% → 98.5%

Time: 11.0s

Alternatives: 20

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: 98.3% 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: 98.5% 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 98.4%

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

   1. clear-num 98.3%

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

   2. un-div-inv 98.8%

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

4. Applied egg-rr 98.8%

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

Alternative 2: 59.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-126}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -8e-126)
     (+ x y)
     (if (<= z -4.4e-203)
       t_1
       (if (<= z -2.4e-228)
         x
         (if (<= z -2e-292)
           (/ (* y t) a)
           (if (<= z 4.5e-251) x (if (<= z 1.65e-111) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -8e-126) {
		tmp = x + y;
	} else if (z <= -4.4e-203) {
		tmp = t_1;
	} else if (z <= -2.4e-228) {
		tmp = x;
	} else if (z <= -2e-292) {
		tmp = (y * t) / a;
	} else if (z <= 4.5e-251) {
		tmp = x;
	} else if (z <= 1.65e-111) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-8d-126)) then
        tmp = x + y
    else if (z <= (-4.4d-203)) then
        tmp = t_1
    else if (z <= (-2.4d-228)) then
        tmp = x
    else if (z <= (-2d-292)) then
        tmp = (y * t) / a
    else if (z <= 4.5d-251) then
        tmp = x
    else if (z <= 1.65d-111) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -8e-126) {
		tmp = x + y;
	} else if (z <= -4.4e-203) {
		tmp = t_1;
	} else if (z <= -2.4e-228) {
		tmp = x;
	} else if (z <= -2e-292) {
		tmp = (y * t) / a;
	} else if (z <= 4.5e-251) {
		tmp = x;
	} else if (z <= 1.65e-111) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -8e-126:
		tmp = x + y
	elif z <= -4.4e-203:
		tmp = t_1
	elif z <= -2.4e-228:
		tmp = x
	elif z <= -2e-292:
		tmp = (y * t) / a
	elif z <= 4.5e-251:
		tmp = x
	elif z <= 1.65e-111:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -8e-126)
		tmp = Float64(x + y);
	elseif (z <= -4.4e-203)
		tmp = t_1;
	elseif (z <= -2.4e-228)
		tmp = x;
	elseif (z <= -2e-292)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 4.5e-251)
		tmp = x;
	elseif (z <= 1.65e-111)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -8e-126)
		tmp = x + y;
	elseif (z <= -4.4e-203)
		tmp = t_1;
	elseif (z <= -2.4e-228)
		tmp = x;
	elseif (z <= -2e-292)
		tmp = (y * t) / a;
	elseif (z <= 4.5e-251)
		tmp = x;
	elseif (z <= 1.65e-111)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-126], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.4e-203], t$95$1, If[LessEqual[z, -2.4e-228], x, If[LessEqual[z, -2e-292], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4.5e-251], x, If[LessEqual[z, 1.65e-111], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9999999999999996e-126 or 1.65e-111 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 68.9%

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

   if -7.9999999999999996e-126 < z < -4.3999999999999999e-203 or 4.49999999999999978e-251 < z < 1.65e-111

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 63.7%

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

   4. Taylor expanded in x around 0 48.4%

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

      1. associate-/l* 72.4%

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

      2. *-commutative 72.4%

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

   6. Applied egg-rr 56.3%

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

   if -4.3999999999999999e-203 < z < -2.40000000000000002e-228 or -2.0000000000000001e-292 < z < 4.49999999999999978e-251

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 87.2%

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

   4. Taylor expanded in x around inf 70.4%

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

   if -2.40000000000000002e-228 < z < -2.0000000000000001e-292

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in x around 0 67.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-126}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+150}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+150)
   (+ x y)
   (if (<= z -7.2e-22)
     (- x (* t (/ y z)))
     (if (<= z 2.1e-17) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+150) {
		tmp = x + y;
	} else if (z <= -7.2e-22) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.1e-17) {
		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 <= (-1.4d+150)) then
        tmp = x + y
    else if (z <= (-7.2d-22)) then
        tmp = x - (t * (y / z))
    else if (z <= 2.1d-17) 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 <= -1.4e+150) {
		tmp = x + y;
	} else if (z <= -7.2e-22) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.1e-17) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+150:
		tmp = x + y
	elif z <= -7.2e-22:
		tmp = x - (t * (y / z))
	elif z <= 2.1e-17:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+150)
		tmp = Float64(x + y);
	elseif (z <= -7.2e-22)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 2.1e-17)
		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 <= -1.4e+150)
		tmp = x + y;
	elseif (z <= -7.2e-22)
		tmp = x - (t * (y / z));
	elseif (z <= 2.1e-17)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+150], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.2e-22], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-17], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000005e150 or 2.09999999999999992e-17 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.8%

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

   if -1.40000000000000005e150 < z < -7.1999999999999996e-22

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac2 80.1%

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

   6. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. add-sqr-sqrt 79.9%

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

      3. sqrt-unprod 80.1%

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

      4. sqr-neg 80.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 56.8%

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

      7. cancel-sign-sub 56.8%

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

      8. distribute-frac-neg2 56.8%

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

      9. *-commutative 56.8%

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

      10. add-sqr-sqrt 56.8%

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

      11. sqrt-unprod 56.8%

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

      12. sqr-neg 56.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 80.1%

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

   8. Applied egg-rr 80.1%

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

      1. add-sqr-sqrt 44.7%

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

      2. sqrt-unprod 68.7%

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

      3. sqr-neg 68.7%

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

      4. sqrt-unprod 28.2%

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

      5. add-sqr-sqrt 56.8%

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

      6. associate-*r/ 56.8%

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

      7. associate-*l/ 56.8%

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

      8. add-sqr-sqrt 28.2%

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

      9. sqrt-unprod 68.8%

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

      10. sqr-neg 68.8%

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

      11. sqrt-unprod 44.7%

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

      12. add-sqr-sqrt 80.2%

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

   10. Applied egg-rr 80.2%

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

   if -7.1999999999999996e-22 < z < 2.09999999999999992e-17

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 71.4%

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

      1. associate-/l* 75.0%

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

      2. *-commutative 75.0%

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

   5. Applied egg-rr 75.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+150}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-20}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+151)
   (+ x y)
   (if (<= z -2.3e-20)
     (- x (* y (/ t z)))
     (if (<= z 8.2e-16) (+ x (* t (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+151) {
		tmp = x + y;
	} else if (z <= -2.3e-20) {
		tmp = x - (y * (t / z));
	} else if (z <= 8.2e-16) {
		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 <= (-1.2d+151)) then
        tmp = x + y
    else if (z <= (-2.3d-20)) then
        tmp = x - (y * (t / z))
    else if (z <= 8.2d-16) 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 <= -1.2e+151) {
		tmp = x + y;
	} else if (z <= -2.3e-20) {
		tmp = x - (y * (t / z));
	} else if (z <= 8.2e-16) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+151:
		tmp = x + y
	elif z <= -2.3e-20:
		tmp = x - (y * (t / z))
	elif z <= 8.2e-16:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+151)
		tmp = Float64(x + y);
	elseif (z <= -2.3e-20)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 8.2e-16)
		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 <= -1.2e+151)
		tmp = x + y;
	elseif (z <= -2.3e-20)
		tmp = x - (y * (t / z));
	elseif (z <= 8.2e-16)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+151], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.3e-20], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-16], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000005e151 or 8.20000000000000012e-16 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.8%

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

   if -1.20000000000000005e151 < z < -2.2999999999999999e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac2 80.1%

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

   6. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. add-sqr-sqrt 79.9%

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

      3. sqrt-unprod 80.1%

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

      4. sqr-neg 80.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 56.8%

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

      7. cancel-sign-sub 56.8%

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

      8. distribute-frac-neg2 56.8%

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

      9. *-commutative 56.8%

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

      10. add-sqr-sqrt 56.8%

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

      11. sqrt-unprod 56.8%

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

      12. sqr-neg 56.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 80.1%

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

   8. Applied egg-rr 80.1%

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

   if -2.2999999999999999e-20 < z < 8.20000000000000012e-16

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 71.4%

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

      1. associate-/l* 75.0%

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

      2. *-commutative 75.0%

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

   5. Applied egg-rr 75.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-20}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+65)
   (+ x y)
   (if (<= t -6e-10)
     (* y (* t (/ 1.0 a)))
     (if (<= t 3.5e+243) (+ x y) (* y (/ t (- z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+65) {
		tmp = x + y;
	} else if (t <= -6e-10) {
		tmp = y * (t * (1.0 / a));
	} else if (t <= 3.5e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d+65)) then
        tmp = x + y
    else if (t <= (-6d-10)) then
        tmp = y * (t * (1.0d0 / a))
    else if (t <= 3.5d+243) then
        tmp = x + y
    else
        tmp = y * (t / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+65) {
		tmp = x + y;
	} else if (t <= -6e-10) {
		tmp = y * (t * (1.0 / a));
	} else if (t <= 3.5e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+65:
		tmp = x + y
	elif t <= -6e-10:
		tmp = y * (t * (1.0 / a))
	elif t <= 3.5e+243:
		tmp = x + y
	else:
		tmp = y * (t / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+65)
		tmp = Float64(x + y);
	elseif (t <= -6e-10)
		tmp = Float64(y * Float64(t * Float64(1.0 / a)));
	elseif (t <= 3.5e+243)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+65)
		tmp = x + y;
	elseif (t <= -6e-10)
		tmp = y * (t * (1.0 / a));
	elseif (t <= 3.5e+243)
		tmp = x + y;
	else
		tmp = y * (t / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+65], N[(x + y), $MachinePrecision], If[LessEqual[t, -6e-10], N[(y * N[(t * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+243], N[(x + y), $MachinePrecision], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3999999999999999e65 or -6e-10 < t < 3.49999999999999988e243

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 63.7%

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

   if -3.3999999999999999e65 < t < -6e-10

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 67.4%

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

   4. Taylor expanded in x around 0 67.3%

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

      1. div-inv 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*l* 67.4%

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

   6. Applied egg-rr 67.4%

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

   if 3.49999999999999988e243 < t

   1. Initial program 88.9%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. neg-mul-1 78.5%

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

      2. distribute-neg-frac2 78.5%

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

   6. Simplified 78.5%

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

      1. *-commutative 78.5%

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

      2. add-sqr-sqrt 39.3%

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

      3. sqrt-unprod 34.8%

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

      4. sqr-neg 34.8%

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

      5. sqrt-unprod 5.9%

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

      6. add-sqr-sqrt 11.8%

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

      7. cancel-sign-sub 11.8%

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

      8. distribute-frac-neg2 11.8%

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

      9. *-commutative 11.8%

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

      10. add-sqr-sqrt 5.9%

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

      11. sqrt-unprod 40.1%

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

      12. sqr-neg 40.1%

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

      13. sqrt-unprod 39.1%

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

      14. add-sqr-sqrt 78.5%

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

   8. Applied egg-rr 78.5%

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

   9. Taylor expanded in x around 0 59.2%

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

       1. mul-1-neg 59.2%

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

       2. associate-*l/ 73.0%

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

       3. distribute-rgt-neg-in 73.0%

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

   11. Simplified 73.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+65)
   (+ x y)
   (if (<= t -6e-10)
     (/ (* y t) a)
     (if (<= t 3.5e+243) (+ x y) (* y (/ t (- z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+65) {
		tmp = x + y;
	} else if (t <= -6e-10) {
		tmp = (y * t) / a;
	} else if (t <= 3.5e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d+65)) then
        tmp = x + y
    else if (t <= (-6d-10)) then
        tmp = (y * t) / a
    else if (t <= 3.5d+243) then
        tmp = x + y
    else
        tmp = y * (t / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+65) {
		tmp = x + y;
	} else if (t <= -6e-10) {
		tmp = (y * t) / a;
	} else if (t <= 3.5e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+65:
		tmp = x + y
	elif t <= -6e-10:
		tmp = (y * t) / a
	elif t <= 3.5e+243:
		tmp = x + y
	else:
		tmp = y * (t / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+65)
		tmp = Float64(x + y);
	elseif (t <= -6e-10)
		tmp = Float64(Float64(y * t) / a);
	elseif (t <= 3.5e+243)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+65)
		tmp = x + y;
	elseif (t <= -6e-10)
		tmp = (y * t) / a;
	elseif (t <= 3.5e+243)
		tmp = x + y;
	else
		tmp = y * (t / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+65], N[(x + y), $MachinePrecision], If[LessEqual[t, -6e-10], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3.5e+243], N[(x + y), $MachinePrecision], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3999999999999999e65 or -6e-10 < t < 3.49999999999999988e243

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 63.7%

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

   if -3.3999999999999999e65 < t < -6e-10

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 67.4%

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

   4. Taylor expanded in x around 0 67.3%

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

   if 3.49999999999999988e243 < t

   1. Initial program 88.9%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. neg-mul-1 78.5%

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

      2. distribute-neg-frac2 78.5%

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

   6. Simplified 78.5%

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

      1. *-commutative 78.5%

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

      2. add-sqr-sqrt 39.3%

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

      3. sqrt-unprod 34.8%

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

      4. sqr-neg 34.8%

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

      5. sqrt-unprod 5.9%

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

      6. add-sqr-sqrt 11.8%

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

      7. cancel-sign-sub 11.8%

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

      8. distribute-frac-neg2 11.8%

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

      9. *-commutative 11.8%

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

      10. add-sqr-sqrt 5.9%

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

      11. sqrt-unprod 40.1%

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

      12. sqr-neg 40.1%

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

      13. sqrt-unprod 39.1%

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

      14. add-sqr-sqrt 78.5%

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

   8. Applied egg-rr 78.5%

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

   9. Taylor expanded in x around 0 59.2%

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

       1. mul-1-neg 59.2%

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

       2. associate-*l/ 73.0%

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

       3. distribute-rgt-neg-in 73.0%

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

   11. Simplified 73.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e-45)
   (+ x y)
   (if (<= z 4.2e-251) x (if (<= z 1.7e-111) (* t (/ y a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e-45) {
		tmp = x + y;
	} else if (z <= 4.2e-251) {
		tmp = x;
	} else if (z <= 1.7e-111) {
		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 <= (-1.9d-45)) then
        tmp = x + y
    else if (z <= 4.2d-251) then
        tmp = x
    else if (z <= 1.7d-111) 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 <= -1.9e-45) {
		tmp = x + y;
	} else if (z <= 4.2e-251) {
		tmp = x;
	} else if (z <= 1.7e-111) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e-45:
		tmp = x + y
	elif z <= 4.2e-251:
		tmp = x
	elif z <= 1.7e-111:
		tmp = t * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e-45)
		tmp = Float64(x + y);
	elseif (z <= 4.2e-251)
		tmp = x;
	elseif (z <= 1.7e-111)
		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 <= -1.9e-45)
		tmp = x + y;
	elseif (z <= 4.2e-251)
		tmp = x;
	elseif (z <= 1.7e-111)
		tmp = t * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e-45], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.2e-251], x, If[LessEqual[z, 1.7e-111], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999999e-45 or 1.69999999999999998e-111 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 71.8%

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

   if -1.89999999999999999e-45 < z < 4.19999999999999964e-251

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 81.5%

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

   4. Taylor expanded in x around inf 50.8%

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

   if 4.19999999999999964e-251 < z < 1.69999999999999998e-111

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 55.6%

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

   4. Taylor expanded in x around 0 41.8%

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

      1. associate-/l* 64.4%

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

      2. *-commutative 64.4%

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

   6. Applied egg-rr 50.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-55} \lor \neg \left(t \leq 1.2 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-55) (not (<= t 1.2e+45)))
   (+ x (/ y (/ (- a z) t)))
   (+ x (/ y (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-55) || !(t <= 1.2e+45)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.8d-55)) .or. (.not. (t <= 1.2d+45))) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-55) || !(t <= 1.2e+45)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e-55) or not (t <= 1.2e+45):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-55) || !(t <= 1.2e+45))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e-55) || ~((t <= 1.2e+45)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e-55], N[Not[LessEqual[t, 1.2e+45]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e-55 or 1.19999999999999995e45 < t

   1. Initial program 97.1%

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

      1. clear-num 97.0%

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

      2. un-div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in t around inf 90.9%

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

      1. associate-*r/ 90.9%

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

      2. mul-1-neg 90.9%

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

      3. sub0-neg 90.9%

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

      4. associate--r- 90.9%

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

      5. neg-sub0 90.9%

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

   7. Simplified 90.9%

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

   if -1.8e-55 < t < 1.19999999999999995e45

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 94.1%

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

      1. div-sub 94.1%

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

      2. *-inverses 94.1%

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

   7. Simplified 94.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-55} \lor \neg \left(t \leq 1.2 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+25) (not (<= z 1.45e-85)))
   (+ x (* y (/ z (- z a))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+25) || !(z <= 1.45e-85)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d+25)) .or. (.not. (z <= 1.45d-85))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+25) || !(z <= 1.45e-85)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+25) or not (z <= 1.45e-85):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+25) || !(z <= 1.45e-85))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+25) || ~((z <= 1.45e-85)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+25], N[Not[LessEqual[z, 1.45e-85]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999999e25 or 1.4500000000000001e-85 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 83.6%

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

   if -3.49999999999999999e25 < z < 1.4500000000000001e-85

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 74.7%

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

      1. associate-/l* 77.1%

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

      2. *-commutative 77.1%

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

   5. Applied egg-rr 77.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e-20)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 8.4e-79) (+ x (/ y (/ a (- t z)))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 8.4e-79) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d-20)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 8.4d-79) then
        tmp = x + (y / (a / (t - z)))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 8.4e-79) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e-20:
		tmp = x + (y / (z / (z - t)))
	elif z <= 8.4e-79:
		tmp = x + (y / (a / (t - z)))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e-20)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 8.4e-79)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e-20)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 8.4e-79)
		tmp = x + (y / (a / (t - z)));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e-20], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e-79], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e-20

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 87.2%

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

   if -3.3e-20 < z < 8.3999999999999998e-79

   1. Initial program 96.7%

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

      1. clear-num 96.6%

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

      2. un-div-inv 97.6%

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in a around inf 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac2 81.7%

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

      3. sub-neg 81.7%

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

      4. +-commutative 81.7%

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

      5. distribute-neg-in 81.7%

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

      6. remove-double-neg 81.7%

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

   7. Simplified 81.7%

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

   if 8.3999999999999998e-79 < z

   1. Initial program 98.9%

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

      1. clear-num 98.7%

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

      2. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. div-sub 83.1%

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

      2. *-inverses 83.1%

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

   7. Simplified 83.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-20)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 4.5e-86) (+ x (* (/ y a) (- t z))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.5e-86) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.4d-20)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 4.5d-86) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.5e-86) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-20:
		tmp = x + (y / (z / (z - t)))
	elif z <= 4.5e-86:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-20)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 4.5e-86)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-20)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 4.5e-86)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-20], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-86], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999982e-20

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 87.2%

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

   if -4.39999999999999982e-20 < z < 4.4999999999999998e-86

   1. Initial program 96.7%

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

      1. clear-num 96.6%

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

      2. un-div-inv 97.6%

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

   4. Applied egg-rr 97.6%

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

      1. associate-/r/ 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-frac-neg2 81.4%

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

   9. Simplified 81.4%

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

   if 4.4999999999999998e-86 < z

   1. Initial program 98.9%

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

      1. clear-num 98.7%

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

      2. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. div-sub 83.1%

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

      2. *-inverses 83.1%

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

   7. Simplified 83.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e-22)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 1.08e-78) (+ x (* y (/ (- t z) a))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-22) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.08e-78) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9d-22)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.08d-78) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-22) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.08e-78) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e-22:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.08e-78:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e-22)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.08e-78)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e-22)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.08e-78)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e-22], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-78], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999973e-22

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 87.2%

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

   if -8.99999999999999973e-22 < z < 1.0800000000000001e-78

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

      4. distribute-frac-neg 80.8%

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

      5. neg-sub0 80.8%

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

      6. associate--r- 80.8%

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

      7. neg-sub0 80.8%

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

   5. Simplified 80.8%

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

   if 1.0800000000000001e-78 < z

   1. Initial program 98.9%

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

      1. clear-num 98.7%

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

      2. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. div-sub 83.1%

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

      2. *-inverses 83.1%

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

   7. Simplified 83.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-89}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e-20)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 7.5e-89) (+ x (* t (/ y a))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 7.5e-89) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d-20)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 7.5d-89) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-20) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 7.5e-89) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e-20:
		tmp = x + (y / (z / (z - t)))
	elif z <= 7.5e-89:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e-20)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 7.5e-89)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e-20)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 7.5e-89)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e-20], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-89], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999945e-21

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 87.2%

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

   if -9.99999999999999945e-21 < z < 7.4999999999999999e-89

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 79.1%

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

      2. *-commutative 79.1%

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

   5. Applied egg-rr 79.1%

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

   if 7.4999999999999999e-89 < z

   1. Initial program 98.9%

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

      1. clear-num 98.7%

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

      2. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. div-sub 83.1%

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

      2. *-inverses 83.1%

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

   7. Simplified 83.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-89}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-21)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 7.2e-92) (+ x (* t (/ y a))) (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-21) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 7.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d-21)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 7.2d-92) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-21) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 7.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-21:
		tmp = x + (y * ((z - t) / z))
	elif z <= 7.2e-92:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-21)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 7.2e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-21)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 7.2e-92)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-21], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 87.1%

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

   if -1.3500000000000001e-21 < z < 7.20000000000000032e-92

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 79.1%

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

      2. *-commutative 79.1%

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

   5. Applied egg-rr 79.1%

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

   if 7.20000000000000032e-92 < z

   1. Initial program 98.9%

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

      1. clear-num 98.7%

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

      2. un-div-inv 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. div-sub 83.1%

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

      2. *-inverses 83.1%

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

   7. Simplified 83.1%

      \[\leadsto x + \frac{y}{\color{blue}{1 - \frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-21)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 2.15e-92) (+ x (* t (/ y a))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-21) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 2.15e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d-21)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 2.15d-92) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-21) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 2.15e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-21:
		tmp = x + (y * ((z - t) / z))
	elif z <= 2.15e-92:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-21)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 2.15e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e-21)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 2.15e-92)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-21], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 87.1%

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

   if -2.9e-21 < z < 2.15000000000000007e-92

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 79.1%

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

      2. *-commutative 79.1%

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

   5. Applied egg-rr 79.1%

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

   if 2.15000000000000007e-92 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 83.1%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+29} \lor \neg \left(z \leq 1.46 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+29) (not (<= z 1.46e-15))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+29) || !(z <= 1.46e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+29)) .or. (.not. (z <= 1.46d-15))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+29) || !(z <= 1.46e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+29) or not (z <= 1.46e-15):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+29) || !(z <= 1.46e-15))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+29) || ~((z <= 1.46e-15)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+29], N[Not[LessEqual[z, 1.46e-15]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e29 or 1.4600000000000001e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.5%

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

   if -2.6e29 < z < 1.4600000000000001e-15

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 70.8%

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

      1. associate-/l* 73.7%

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

      2. *-commutative 73.7%

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

   5. Applied egg-rr 73.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+29} \lor \neg \left(z \leq 1.46 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+39} \lor \neg \left(z \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+39) (not (<= z 2.2e-15))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+39) || !(z <= 2.2e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+39)) .or. (.not. (z <= 2.2d-15))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+39) || !(z <= 2.2e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+39) or not (z <= 2.2e-15):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+39) || !(z <= 2.2e-15))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+39) || ~((z <= 2.2e-15)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+39], N[Not[LessEqual[z, 2.2e-15]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000011e39 or 2.19999999999999986e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.7%

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

   if -9.50000000000000011e39 < z < 2.19999999999999986e-15

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 72.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+39} \lor \neg \left(z \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-42} \lor \neg \left(z \leq 1.95 \cdot 10^{-219}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e-42) (not (<= z 1.95e-219))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-42) || !(z <= 1.95e-219)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d-42)) .or. (.not. (z <= 1.95d-219))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-42) || !(z <= 1.95e-219)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e-42) or not (z <= 1.95e-219):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e-42) || !(z <= 1.95e-219))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e-42) || ~((z <= 1.95e-219)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e-42], N[Not[LessEqual[z, 1.95e-219]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-42 or 1.94999999999999994e-219 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 67.0%

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

   if -2.6e-42 < z < 1.94999999999999994e-219

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 79.5%

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

   4. Taylor expanded in x around inf 48.8%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-42} \lor \neg \left(z \leq 1.95 \cdot 10^{-219}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 98.3% 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 98.4%

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

Alternative 20: 50.3% 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 98.4%

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

3. Taylor expanded in z around 0 56.8%

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

4. Taylor expanded in x around inf 50.5%

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

Developer target: 98.5% 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 2024097 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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