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

Percentage Accurate: 98.1% → 98.2%

Time: 14.9s

Alternatives: 17

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: 98.1% 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: 98.2% 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 98.0%

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

   2. un-div-inv 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= z -9e+143)
     (+ x y)
     (if (<= z -6.3e-9)
       t_1
       (if (<= z -1.72e-18)
         (+ x y)
         (if (<= z 5.4e-40)
           (+ x (/ y (/ a t)))
           (if (<= z 6.2e+196) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -9e+143) {
		tmp = x + y;
	} else if (z <= -6.3e-9) {
		tmp = t_1;
	} else if (z <= -1.72e-18) {
		tmp = x + y;
	} else if (z <= 5.4e-40) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (z <= (-9d+143)) then
        tmp = x + y
    else if (z <= (-6.3d-9)) then
        tmp = t_1
    else if (z <= (-1.72d-18)) then
        tmp = x + y
    else if (z <= 5.4d-40) then
        tmp = x + (y / (a / t))
    else if (z <= 6.2d+196) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -9e+143) {
		tmp = x + y;
	} else if (z <= -6.3e-9) {
		tmp = t_1;
	} else if (z <= -1.72e-18) {
		tmp = x + y;
	} else if (z <= 5.4e-40) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if z <= -9e+143:
		tmp = x + y
	elif z <= -6.3e-9:
		tmp = t_1
	elif z <= -1.72e-18:
		tmp = x + y
	elif z <= 5.4e-40:
		tmp = x + (y / (a / t))
	elif z <= 6.2e+196:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -9e+143)
		tmp = Float64(x + y);
	elseif (z <= -6.3e-9)
		tmp = t_1;
	elseif (z <= -1.72e-18)
		tmp = Float64(x + y);
	elseif (z <= 5.4e-40)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -9e+143)
		tmp = x + y;
	elseif (z <= -6.3e-9)
		tmp = t_1;
	elseif (z <= -1.72e-18)
		tmp = x + y;
	elseif (z <= 5.4e-40)
		tmp = x + (y / (a / t));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+143], N[(x + y), $MachinePrecision], If[LessEqual[z, -6.3e-9], t$95$1, If[LessEqual[z, -1.72e-18], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.4e-40], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+196], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999993e143 or -6.3000000000000002e-9 < z < -1.72e-18 or 6.2000000000000002e196 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. +-commutative 90.5%

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

   5. Simplified 90.5%

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

   if -8.9999999999999993e143 < z < -6.3000000000000002e-9 or 5.4e-40 < z < 6.2000000000000002e196

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 71.5%

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

      3. distribute-lft-neg-in 71.5%

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

   8. Simplified 71.5%

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

      1. +-commutative 71.5%

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

      2. distribute-lft-neg-out 71.5%

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

      3. unsub-neg 71.5%

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

   10. Applied egg-rr 71.5%

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

   if -1.72e-18 < z < 5.4e-40

   1. Initial program 96.3%

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

      1. clear-num 96.3%

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

      2. un-div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in z around 0 80.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-9}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -6e+143)
     (+ x y)
     (if (<= z -3.6e-5)
       t_1
       (if (<= z -2.6e-18)
         (+ x y)
         (if (<= z 3.1e-40)
           (+ x (/ y (/ a t)))
           (if (<= z 6.2e+196) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -6e+143) {
		tmp = x + y;
	} else if (z <= -3.6e-5) {
		tmp = t_1;
	} else if (z <= -2.6e-18) {
		tmp = x + y;
	} else if (z <= 3.1e-40) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (z <= (-6d+143)) then
        tmp = x + y
    else if (z <= (-3.6d-5)) then
        tmp = t_1
    else if (z <= (-2.6d-18)) then
        tmp = x + y
    else if (z <= 3.1d-40) then
        tmp = x + (y / (a / t))
    else if (z <= 6.2d+196) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -6e+143) {
		tmp = x + y;
	} else if (z <= -3.6e-5) {
		tmp = t_1;
	} else if (z <= -2.6e-18) {
		tmp = x + y;
	} else if (z <= 3.1e-40) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -6e+143:
		tmp = x + y
	elif z <= -3.6e-5:
		tmp = t_1
	elif z <= -2.6e-18:
		tmp = x + y
	elif z <= 3.1e-40:
		tmp = x + (y / (a / t))
	elif z <= 6.2e+196:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -6e+143)
		tmp = Float64(x + y);
	elseif (z <= -3.6e-5)
		tmp = t_1;
	elseif (z <= -2.6e-18)
		tmp = Float64(x + y);
	elseif (z <= 3.1e-40)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (z <= -6e+143)
		tmp = x + y;
	elseif (z <= -3.6e-5)
		tmp = t_1;
	elseif (z <= -2.6e-18)
		tmp = x + y;
	elseif (z <= 3.1e-40)
		tmp = x + (y / (a / t));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+143], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.6e-5], t$95$1, If[LessEqual[z, -2.6e-18], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.1e-40], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+196], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000001e143 or -3.60000000000000009e-5 < z < -2.6e-18 or 6.2000000000000002e196 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. +-commutative 90.5%

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

   5. Simplified 90.5%

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

   if -6.0000000000000001e143 < z < -3.60000000000000009e-5 or 3.10000000000000011e-40 < z < 6.2000000000000002e196

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 71.5%

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

      3. distribute-lft-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in t around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. *-commutative 65.3%

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

       3. associate-/l* 71.6%

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

       4. distribute-lft-neg-in 71.6%

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

       5. cancel-sign-sub-inv 71.6%

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

   11. Simplified 71.6%

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

   if -2.6e-18 < z < 3.10000000000000011e-40

   1. Initial program 96.3%

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

      1. clear-num 96.3%

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

      2. un-div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in z around 0 80.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -9.8e+143)
     (+ x y)
     (if (<= z -3.35e-6)
       t_1
       (if (<= z -4e-31)
         (- x (* y (/ z a)))
         (if (<= z 8.5e-41)
           (+ x (/ y (/ a t)))
           (if (<= z 6.2e+196) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -9.8e+143) {
		tmp = x + y;
	} else if (z <= -3.35e-6) {
		tmp = t_1;
	} else if (z <= -4e-31) {
		tmp = x - (y * (z / a));
	} else if (z <= 8.5e-41) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (z <= (-9.8d+143)) then
        tmp = x + y
    else if (z <= (-3.35d-6)) then
        tmp = t_1
    else if (z <= (-4d-31)) then
        tmp = x - (y * (z / a))
    else if (z <= 8.5d-41) then
        tmp = x + (y / (a / t))
    else if (z <= 6.2d+196) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -9.8e+143) {
		tmp = x + y;
	} else if (z <= -3.35e-6) {
		tmp = t_1;
	} else if (z <= -4e-31) {
		tmp = x - (y * (z / a));
	} else if (z <= 8.5e-41) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -9.8e+143:
		tmp = x + y
	elif z <= -3.35e-6:
		tmp = t_1
	elif z <= -4e-31:
		tmp = x - (y * (z / a))
	elif z <= 8.5e-41:
		tmp = x + (y / (a / t))
	elif z <= 6.2e+196:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -9.8e+143)
		tmp = Float64(x + y);
	elseif (z <= -3.35e-6)
		tmp = t_1;
	elseif (z <= -4e-31)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= 8.5e-41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (z <= -9.8e+143)
		tmp = x + y;
	elseif (z <= -3.35e-6)
		tmp = t_1;
	elseif (z <= -4e-31)
		tmp = x - (y * (z / a));
	elseif (z <= 8.5e-41)
		tmp = x + (y / (a / t));
	elseif (z <= 6.2e+196)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+143], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.35e-6], t$95$1, If[LessEqual[z, -4e-31], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+196], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.79999999999999971e143 or 6.2000000000000002e196 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. +-commutative 91.2%

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

   5. Simplified 91.2%

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

   if -9.79999999999999971e143 < z < -3.35e-6 or 8.4999999999999996e-41 < z < 6.2000000000000002e196

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 71.5%

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

      3. distribute-lft-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in t around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. *-commutative 65.3%

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

       3. associate-/l* 71.6%

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

       4. distribute-lft-neg-in 71.6%

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

       5. cancel-sign-sub-inv 71.6%

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

   11. Simplified 71.6%

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

   if -3.35e-6 < z < -4e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.8%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

   if -4e-31 < z < 8.4999999999999996e-41

   1. Initial program 96.2%

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

      1. clear-num 96.1%

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

      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 z around 0 82.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+143)
   (+ x y)
   (if (<= z -7.8e-6)
     (- x (* y (/ t z)))
     (if (<= z -1.45e-31)
       (- x (* y (/ z a)))
       (if (<= z 1.4e-43)
         (+ x (/ y (/ a t)))
         (if (<= z 6.2e+196) (- x (/ y (/ z t))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+143) {
		tmp = x + y;
	} else if (z <= -7.8e-6) {
		tmp = x - (y * (t / z));
	} else if (z <= -1.45e-31) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.4e-43) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = x - (y / (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9d+143)) then
        tmp = x + y
    else if (z <= (-7.8d-6)) then
        tmp = x - (y * (t / z))
    else if (z <= (-1.45d-31)) then
        tmp = x - (y * (z / a))
    else if (z <= 1.4d-43) then
        tmp = x + (y / (a / t))
    else if (z <= 6.2d+196) then
        tmp = x - (y / (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+143) {
		tmp = x + y;
	} else if (z <= -7.8e-6) {
		tmp = x - (y * (t / z));
	} else if (z <= -1.45e-31) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.4e-43) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.2e+196) {
		tmp = x - (y / (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+143:
		tmp = x + y
	elif z <= -7.8e-6:
		tmp = x - (y * (t / z))
	elif z <= -1.45e-31:
		tmp = x - (y * (z / a))
	elif z <= 1.4e-43:
		tmp = x + (y / (a / t))
	elif z <= 6.2e+196:
		tmp = x - (y / (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+143)
		tmp = Float64(x + y);
	elseif (z <= -7.8e-6)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= -1.45e-31)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= 1.4e-43)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.2e+196)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+143)
		tmp = x + y;
	elseif (z <= -7.8e-6)
		tmp = x - (y * (t / z));
	elseif (z <= -1.45e-31)
		tmp = x - (y * (z / a));
	elseif (z <= 1.4e-43)
		tmp = x + (y / (a / t));
	elseif (z <= 6.2e+196)
		tmp = x - (y / (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+143], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.8e-6], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e-31], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-43], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+196], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.9999999999999993e143 or 6.2000000000000002e196 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. +-commutative 91.2%

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

   5. Simplified 91.2%

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

   if -8.9999999999999993e143 < z < -7.7999999999999999e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 69.7%

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

      3. distribute-lft-neg-in 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. *-commutative 65.3%

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

       3. associate-/l* 69.7%

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

       4. distribute-lft-neg-in 69.7%

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

       5. cancel-sign-sub-inv 69.7%

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

   11. Simplified 69.7%

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

   if -7.7999999999999999e-6 < z < -1.45e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.8%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

   if -1.45e-31 < z < 1.3999999999999999e-43

   1. Initial program 96.2%

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

      1. clear-num 96.1%

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

      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 z around 0 82.4%

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

   if 1.3999999999999999e-43 < z < 6.2000000000000002e196

   1. Initial program 99.7%

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

      1. clear-num 98.0%

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

      2. un-div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-neg-frac2 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-neg-frac2 72.3%

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

   10. Simplified 72.3%

       \[\leadsto x + \frac{y}{\color{blue}{\frac{z}{-t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-32} \lor \neg \left(z \leq 2.2 \cdot 10^{-123}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e-32) (not (<= z 2.2e-123)))
   (+ x (* z (/ y (- z a))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e-32) || !(z <= 2.2e-123)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d-32)) .or. (.not. (z <= 2.2d-123))) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e-32) || !(z <= 2.2e-123)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e-32) or not (z <= 2.2e-123):
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e-32) || !(z <= 2.2e-123))
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e-32) || ~((z <= 2.2e-123)))
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e-32], N[Not[LessEqual[z, 2.2e-123]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e-32 or 2.20000000000000006e-123 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   if -9.4999999999999999e-32 < z < 2.20000000000000006e-123

   1. Initial program 97.7%

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

      1. clear-num 97.6%

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

      2. un-div-inv 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in z around 0 85.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-32} \lor \neg \left(z \leq 2.2 \cdot 10^{-123}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+81} \lor \neg \left(t \leq 5.6 \cdot 10^{+85}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.6e+81) (not (<= t 5.6e+85)))
   (+ x (* t (/ y (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+81) || !(t <= 5.6e+85)) {
		tmp = x + (t * (y / (a - z)));
	} 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 ((t <= (-8.6d+81)) .or. (.not. (t <= 5.6d+85))) then
        tmp = x + (t * (y / (a - z)))
    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 ((t <= -8.6e+81) || !(t <= 5.6e+85)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.6e+81) or not (t <= 5.6e+85):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.6e+81) || !(t <= 5.6e+85))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	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 ((t <= -8.6e+81) || ~((t <= 5.6e+85)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.6e+81], N[Not[LessEqual[t, 5.6e+85]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6000000000000003e81 or 5.5999999999999998e85 < t

   1. Initial program 96.6%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-neg-frac2 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*r/ 85.0%

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

      4. sub-neg 85.0%

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

      5. associate-*r/ 77.6%

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

      6. associate-*l/ 87.0%

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

      7. *-commutative 87.0%

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

   10. Simplified 87.0%

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

   if -8.6000000000000003e81 < t < 5.5999999999999998e85

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+81} \lor \neg \left(t \leq 5.6 \cdot 10^{+85}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-32)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z 3e-123) (+ x (/ y (/ a t))) (+ x (* z (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-32) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 3e-123) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (z * (y / (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 <= (-9.5d-32)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 3d-123) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (z * (y / (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 <= -9.5e-32) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 3e-123) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-32:
		tmp = x + (y / ((z - a) / z))
	elif z <= 3e-123:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-32)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 3e-123)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-32)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 3e-123)
		tmp = x + (y / (a / t));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-32], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-123], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999999e-32

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      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 87.1%

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

   if -9.4999999999999999e-32 < z < 2.99999999999999984e-123

   1. Initial program 97.7%

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

      1. clear-num 97.6%

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

      2. un-div-inv 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in z around 0 85.7%

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

   if 2.99999999999999984e-123 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e-30)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z 8.4e-215) (+ x (/ y (/ a t))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e-30) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 8.4e-215) {
		tmp = x + (y / (a / t));
	} 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 <= (-1.12d-30)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 8.4d-215) then
        tmp = x + (y / (a / t))
    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 <= -1.12e-30) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 8.4e-215) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e-30:
		tmp = x + (y / ((z - a) / z))
	elif z <= 8.4e-215:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e-30)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 8.4e-215)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	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 <= -1.12e-30)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 8.4e-215)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e-30], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e-215], N[(x + N[(y / N[(a / t), $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 < -1.12e-30

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      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 87.1%

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

   if -1.12e-30 < z < 8.4000000000000001e-215

   1. Initial program 97.2%

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

      1. clear-num 97.2%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around 0 87.5%

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

   if 8.4000000000000001e-215 < z

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-31)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z 1.8e-45) (+ x (/ y (/ a t))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-31) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 1.8e-45) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-31)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 1.8d-45) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-31) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 1.8e-45) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-31:
		tmp = x + (y / ((z - a) / z))
	elif z <= 1.8e-45:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-31)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 1.8e-45)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-31)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 1.8e-45)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-31], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-45], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999958e-31

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      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 87.1%

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

   if -5.49999999999999958e-31 < z < 1.8e-45

   1. Initial program 96.2%

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

      1. clear-num 96.1%

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

      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 z around 0 82.4%

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

   if 1.8e-45 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-31)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z 6.8e-40) (+ x (/ y (/ a t))) (+ x (/ y (/ z (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-31) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.8e-40) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d-31)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 6.8d-40) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-31) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.8e-40) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-31:
		tmp = x + (y / ((z - a) / z))
	elif z <= 6.8e-40:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-31)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 6.8e-40)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-31)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 6.8e-40)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-31], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-40], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000008e-31

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      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 87.1%

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

   if -9.5000000000000008e-31 < z < 6.79999999999999968e-40

   1. Initial program 96.2%

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

      1. clear-num 96.1%

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

      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 z around 0 82.4%

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

   if 6.79999999999999968e-40 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

      1. clear-num 89.8%

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

      2. un-div-inv 89.8%

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

   7. Applied egg-rr 89.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+82)
   (+ x (* y (/ t (- a z))))
   (if (<= t 1.95e+85) (+ x (* y (/ z (- z a)))) (+ x (* t (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+82) {
		tmp = x + (y * (t / (a - z)));
	} else if (t <= 1.95e+85) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / (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 <= (-1.1d+82)) then
        tmp = x + (y * (t / (a - z)))
    else if (t <= 1.95d+85) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (t * (y / (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 <= -1.1e+82) {
		tmp = x + (y * (t / (a - z)));
	} else if (t <= 1.95e+85) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+82:
		tmp = x + (y * (t / (a - z)))
	elif t <= 1.95e+85:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+82)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	elseif (t <= 1.95e+85)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+82)
		tmp = x + (y * (t / (a - z)));
	elseif (t <= 1.95e+85)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+82], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+85], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1000000000000001e82

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.8%

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

      1. associate-*r/ 77.8%

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

      2. mul-1-neg 77.8%

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

      3. distribute-lft-neg-out 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   if -1.1000000000000001e82 < t < 1.95000000000000017e85

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

   if 1.95000000000000017e85 < t

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in t around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-neg-frac2 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r/ 83.0%

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

      4. sub-neg 83.0%

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

      5. associate-*r/ 77.5%

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

      6. associate-*l/ 88.6%

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

      7. *-commutative 88.6%

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

   10. Simplified 88.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+63} \lor \neg \left(z \leq 5 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+63) (not (<= z 5e-42))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+63) || !(z <= 5e-42)) {
		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 <= (-3.1d+63)) .or. (.not. (z <= 5d-42))) 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 <= -3.1e+63) || !(z <= 5e-42)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+63) or not (z <= 5e-42):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+63) || !(z <= 5e-42))
		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 <= -3.1e+63) || ~((z <= 5e-42)))
		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, -3.1e+63], N[Not[LessEqual[z, 5e-42]], $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 < -3.1000000000000001e63 or 5.00000000000000003e-42 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. +-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -3.1000000000000001e63 < z < 5.00000000000000003e-42

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+63} \lor \neg \left(z \leq 5 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+14} \lor \neg \left(z \leq 1.55 \cdot 10^{-41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+14) (not (<= z 1.55e-41))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+14) || !(z <= 1.55e-41)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.45d+14)) .or. (.not. (z <= 1.55d-41))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+14) || !(z <= 1.55e-41)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+14) or not (z <= 1.55e-41):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+14) || !(z <= 1.55e-41))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+14) || ~((z <= 1.55e-41)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+14], N[Not[LessEqual[z, 1.55e-41]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e14 or 1.55e-41 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.3%

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

      1. +-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -1.45e14 < z < 1.55e-41

   1. Initial program 96.5%

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

      1. clear-num 96.5%

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

      2. un-div-inv 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in z around 0 79.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+14} \lor \neg \left(z \leq 1.55 \cdot 10^{-41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-18} \lor \neg \left(z \leq 1.25 \cdot 10^{-48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e-18) (not (<= z 1.25e-48))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e-18) || !(z <= 1.25e-48)) {
		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 <= (-1.9d-18)) .or. (.not. (z <= 1.25d-48))) 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 <= -1.9e-18) || !(z <= 1.25e-48)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e-18) or not (z <= 1.25e-48):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e-18) || !(z <= 1.25e-48))
		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 <= -1.9e-18) || ~((z <= 1.25e-48)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e-18], N[Not[LessEqual[z, 1.25e-48]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-18 or 1.25e-48 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.2%

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

      1. +-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -1.8999999999999999e-18 < z < 1.25e-48

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 59.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-18} \lor \neg \left(z \leq 1.25 \cdot 10^{-48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 98.1% 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. Final simplification 98.4%

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

Alternative 17: 51.2% 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 x around inf 52.8%

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

4. Final simplification 52.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% 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 2024043 
(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)))))