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

Percentage Accurate: 98.3% → 98.3%

Time: 15.0s

Alternatives: 19

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: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. +-commutative 97.3%

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

   2. fma-define 97.3%

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

3. Simplified 97.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing

5. Final simplification 97.3%

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

Alternative 2: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e-19)
   (+ y x)
   (if (<= z -1.9e-253)
     x
     (if (<= z 1.55e-273)
       (/ (* y t) a)
       (if (<= z 1.12e-153)
         x
         (if (<= z 1.02e-133)
           (* y (/ t (- z)))
           (if (<= z 2.05e-118) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-19) {
		tmp = y + x;
	} else if (z <= -1.9e-253) {
		tmp = x;
	} else if (z <= 1.55e-273) {
		tmp = (y * t) / a;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 1.02e-133) {
		tmp = y * (t / -z);
	} else if (z <= 2.05e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d-19)) then
        tmp = y + x
    else if (z <= (-1.9d-253)) then
        tmp = x
    else if (z <= 1.55d-273) then
        tmp = (y * t) / a
    else if (z <= 1.12d-153) then
        tmp = x
    else if (z <= 1.02d-133) then
        tmp = y * (t / -z)
    else if (z <= 2.05d-118) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-19) {
		tmp = y + x;
	} else if (z <= -1.9e-253) {
		tmp = x;
	} else if (z <= 1.55e-273) {
		tmp = (y * t) / a;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 1.02e-133) {
		tmp = y * (t / -z);
	} else if (z <= 2.05e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e-19:
		tmp = y + x
	elif z <= -1.9e-253:
		tmp = x
	elif z <= 1.55e-273:
		tmp = (y * t) / a
	elif z <= 1.12e-153:
		tmp = x
	elif z <= 1.02e-133:
		tmp = y * (t / -z)
	elif z <= 2.05e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e-19)
		tmp = Float64(y + x);
	elseif (z <= -1.9e-253)
		tmp = x;
	elseif (z <= 1.55e-273)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 1.02e-133)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (z <= 2.05e-118)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e-19)
		tmp = y + x;
	elseif (z <= -1.9e-253)
		tmp = x;
	elseif (z <= 1.55e-273)
		tmp = (y * t) / a;
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 1.02e-133)
		tmp = y * (t / -z);
	elseif (z <= 2.05e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e-19], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.9e-253], x, If[LessEqual[z, 1.55e-273], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.12e-153], x, If[LessEqual[z, 1.02e-133], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-118], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0000000000000004e-19 or 2.0500000000000002e-118 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -5.0000000000000004e-19 < z < -1.90000000000000006e-253 or 1.54999999999999994e-273 < z < 1.12000000000000005e-153 or 1.02e-133 < z < 2.0500000000000002e-118

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 57.7%

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

   if -1.90000000000000006e-253 < z < 1.54999999999999994e-273

   1. Initial program 82.1%

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

   3. Taylor expanded in y around inf 69.6%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. associate-*r/ 76.4%

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

   6. Applied egg-rr 76.4%

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

   if 1.12000000000000005e-153 < z < 1.02e-133

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.0%

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

   4. Taylor expanded in t around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-frac-neg2 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in z around inf 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e-19)
   (+ y x)
   (if (<= z -4.8e-252)
     x
     (if (<= z 2.3e-275)
       (/ (* y t) a)
       (if (<= z 1.06e-153)
         x
         (if (<= z 1.15e-133)
           (/ (* y (- t)) z)
           (if (<= z 1.35e-118) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e-19) {
		tmp = y + x;
	} else if (z <= -4.8e-252) {
		tmp = x;
	} else if (z <= 2.3e-275) {
		tmp = (y * t) / a;
	} else if (z <= 1.06e-153) {
		tmp = x;
	} else if (z <= 1.15e-133) {
		tmp = (y * -t) / z;
	} else if (z <= 1.35e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d-19)) then
        tmp = y + x
    else if (z <= (-4.8d-252)) then
        tmp = x
    else if (z <= 2.3d-275) then
        tmp = (y * t) / a
    else if (z <= 1.06d-153) then
        tmp = x
    else if (z <= 1.15d-133) then
        tmp = (y * -t) / z
    else if (z <= 1.35d-118) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e-19) {
		tmp = y + x;
	} else if (z <= -4.8e-252) {
		tmp = x;
	} else if (z <= 2.3e-275) {
		tmp = (y * t) / a;
	} else if (z <= 1.06e-153) {
		tmp = x;
	} else if (z <= 1.15e-133) {
		tmp = (y * -t) / z;
	} else if (z <= 1.35e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e-19:
		tmp = y + x
	elif z <= -4.8e-252:
		tmp = x
	elif z <= 2.3e-275:
		tmp = (y * t) / a
	elif z <= 1.06e-153:
		tmp = x
	elif z <= 1.15e-133:
		tmp = (y * -t) / z
	elif z <= 1.35e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e-19)
		tmp = Float64(y + x);
	elseif (z <= -4.8e-252)
		tmp = x;
	elseif (z <= 2.3e-275)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.06e-153)
		tmp = x;
	elseif (z <= 1.15e-133)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (z <= 1.35e-118)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e-19)
		tmp = y + x;
	elseif (z <= -4.8e-252)
		tmp = x;
	elseif (z <= 2.3e-275)
		tmp = (y * t) / a;
	elseif (z <= 1.06e-153)
		tmp = x;
	elseif (z <= 1.15e-133)
		tmp = (y * -t) / z;
	elseif (z <= 1.35e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e-19], N[(y + x), $MachinePrecision], If[LessEqual[z, -4.8e-252], x, If[LessEqual[z, 2.3e-275], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.06e-153], x, If[LessEqual[z, 1.15e-133], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.35e-118], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.94999999999999998e-19 or 1.34999999999999997e-118 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -1.94999999999999998e-19 < z < -4.8000000000000003e-252 or 2.2999999999999999e-275 < z < 1.06e-153 or 1.15e-133 < z < 1.34999999999999997e-118

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 57.7%

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

   if -4.8000000000000003e-252 < z < 2.2999999999999999e-275

   1. Initial program 82.1%

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

   3. Taylor expanded in y around inf 69.6%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. associate-*r/ 76.4%

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

   6. Applied egg-rr 76.4%

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

   if 1.06e-153 < z < 1.15e-133

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.0%

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

   4. Taylor expanded in t around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-frac-neg2 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in z around inf 68.9%

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

      1. associate-*r/ 68.9%

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

      2. mul-1-neg 68.9%

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

      3. distribute-lft-neg-out 68.9%

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

      4. *-commutative 68.9%

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

   9. Simplified 68.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-185}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+92}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.02e+157)
   x
   (if (<= a -6.5e-185)
     (+ y x)
     (if (<= a 1.14e-305)
       (* y (- 1.0 (/ t z)))
       (if (<= a 1.9e-193)
         (+ y x)
         (if (<= a 3e-126)
           (/ (* y (- t)) z)
           (if (<= a 2.35e+92) (+ y x) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e+157) {
		tmp = x;
	} else if (a <= -6.5e-185) {
		tmp = y + x;
	} else if (a <= 1.14e-305) {
		tmp = y * (1.0 - (t / z));
	} else if (a <= 1.9e-193) {
		tmp = y + x;
	} else if (a <= 3e-126) {
		tmp = (y * -t) / z;
	} else if (a <= 2.35e+92) {
		tmp = y + x;
	} 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 (a <= (-1.02d+157)) then
        tmp = x
    else if (a <= (-6.5d-185)) then
        tmp = y + x
    else if (a <= 1.14d-305) then
        tmp = y * (1.0d0 - (t / z))
    else if (a <= 1.9d-193) then
        tmp = y + x
    else if (a <= 3d-126) then
        tmp = (y * -t) / z
    else if (a <= 2.35d+92) then
        tmp = y + x
    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 (a <= -1.02e+157) {
		tmp = x;
	} else if (a <= -6.5e-185) {
		tmp = y + x;
	} else if (a <= 1.14e-305) {
		tmp = y * (1.0 - (t / z));
	} else if (a <= 1.9e-193) {
		tmp = y + x;
	} else if (a <= 3e-126) {
		tmp = (y * -t) / z;
	} else if (a <= 2.35e+92) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.02e+157:
		tmp = x
	elif a <= -6.5e-185:
		tmp = y + x
	elif a <= 1.14e-305:
		tmp = y * (1.0 - (t / z))
	elif a <= 1.9e-193:
		tmp = y + x
	elif a <= 3e-126:
		tmp = (y * -t) / z
	elif a <= 2.35e+92:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.02e+157)
		tmp = x;
	elseif (a <= -6.5e-185)
		tmp = Float64(y + x);
	elseif (a <= 1.14e-305)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (a <= 1.9e-193)
		tmp = Float64(y + x);
	elseif (a <= 3e-126)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (a <= 2.35e+92)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.02e+157)
		tmp = x;
	elseif (a <= -6.5e-185)
		tmp = y + x;
	elseif (a <= 1.14e-305)
		tmp = y * (1.0 - (t / z));
	elseif (a <= 1.9e-193)
		tmp = y + x;
	elseif (a <= 3e-126)
		tmp = (y * -t) / z;
	elseif (a <= 2.35e+92)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.02e+157], x, If[LessEqual[a, -6.5e-185], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.14e-305], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-193], N[(y + x), $MachinePrecision], If[LessEqual[a, 3e-126], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e+92], N[(y + x), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.02000000000000003e157 or 2.35e92 < a

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 64.2%

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

   if -1.02000000000000003e157 < a < -6.49999999999999946e-185 or 1.14e-305 < a < 1.90000000000000002e-193 or 3.0000000000000002e-126 < a < 2.35e92

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 70.2%

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

      1. +-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -6.49999999999999946e-185 < a < 1.14e-305

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 87.2%

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

   4. Taylor expanded in a around 0 80.7%

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

   if 1.90000000000000002e-193 < a < 3.0000000000000002e-126

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 75.0%

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

   4. Taylor expanded in t around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-frac-neg2 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in z around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-neg-out 65.3%

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

      4. *-commutative 65.3%

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

   9. Simplified 65.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-185}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+92}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-143}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))) (t_2 (* y (/ t (- a z)))))
   (if (<= x -4.5e-143)
     (+ y x)
     (if (<= x -3.55e-186)
       t_2
       (if (<= x -4.2e-254)
         t_1
         (if (<= x 1.85e-230) t_2 (if (<= x 1.95e-14) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = y * (t / (a - z));
	double tmp;
	if (x <= -4.5e-143) {
		tmp = y + x;
	} else if (x <= -3.55e-186) {
		tmp = t_2;
	} else if (x <= -4.2e-254) {
		tmp = t_1;
	} else if (x <= 1.85e-230) {
		tmp = t_2;
	} else if (x <= 1.95e-14) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    t_2 = y * (t / (a - z))
    if (x <= (-4.5d-143)) then
        tmp = y + x
    else if (x <= (-3.55d-186)) then
        tmp = t_2
    else if (x <= (-4.2d-254)) then
        tmp = t_1
    else if (x <= 1.85d-230) then
        tmp = t_2
    else if (x <= 1.95d-14) then
        tmp = t_1
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = y * (t / (a - z));
	double tmp;
	if (x <= -4.5e-143) {
		tmp = y + x;
	} else if (x <= -3.55e-186) {
		tmp = t_2;
	} else if (x <= -4.2e-254) {
		tmp = t_1;
	} else if (x <= 1.85e-230) {
		tmp = t_2;
	} else if (x <= 1.95e-14) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	t_2 = y * (t / (a - z))
	tmp = 0
	if x <= -4.5e-143:
		tmp = y + x
	elif x <= -3.55e-186:
		tmp = t_2
	elif x <= -4.2e-254:
		tmp = t_1
	elif x <= 1.85e-230:
		tmp = t_2
	elif x <= 1.95e-14:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	t_2 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (x <= -4.5e-143)
		tmp = Float64(y + x);
	elseif (x <= -3.55e-186)
		tmp = t_2;
	elseif (x <= -4.2e-254)
		tmp = t_1;
	elseif (x <= 1.85e-230)
		tmp = t_2;
	elseif (x <= 1.95e-14)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	t_2 = y * (t / (a - z));
	tmp = 0.0;
	if (x <= -4.5e-143)
		tmp = y + x;
	elseif (x <= -3.55e-186)
		tmp = t_2;
	elseif (x <= -4.2e-254)
		tmp = t_1;
	elseif (x <= 1.85e-230)
		tmp = t_2;
	elseif (x <= 1.95e-14)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e-143], N[(y + x), $MachinePrecision], If[LessEqual[x, -3.55e-186], t$95$2, If[LessEqual[x, -4.2e-254], t$95$1, If[LessEqual[x, 1.85e-230], t$95$2, If[LessEqual[x, 1.95e-14], t$95$1, N[(y + x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e-143 or 1.9499999999999999e-14 < x

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -4.5e-143 < x < -3.55000000000000007e-186 or -4.19999999999999993e-254 < x < 1.84999999999999991e-230

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 75.3%

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

   4. Taylor expanded in t around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-frac-neg2 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in t around 0 60.6%

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

   if -3.55000000000000007e-186 < x < -4.19999999999999993e-254 or 1.84999999999999991e-230 < x < 1.9499999999999999e-14

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in a around 0 61.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-143}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -3.2e-11)
     (+ y x)
     (if (<= z -8e-255)
       x
       (if (<= z 4.2e-272)
         t_1
         (if (<= z 1.12e-153) x (if (<= z 4e-132) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -3.2e-11) {
		tmp = y + x;
	} else if (z <= -8e-255) {
		tmp = x;
	} else if (z <= 4.2e-272) {
		tmp = t_1;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 4e-132) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (z <= (-3.2d-11)) then
        tmp = y + x
    else if (z <= (-8d-255)) then
        tmp = x
    else if (z <= 4.2d-272) then
        tmp = t_1
    else if (z <= 1.12d-153) then
        tmp = x
    else if (z <= 4d-132) then
        tmp = t_1
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -3.2e-11) {
		tmp = y + x;
	} else if (z <= -8e-255) {
		tmp = x;
	} else if (z <= 4.2e-272) {
		tmp = t_1;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 4e-132) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -3.2e-11:
		tmp = y + x
	elif z <= -8e-255:
		tmp = x
	elif z <= 4.2e-272:
		tmp = t_1
	elif z <= 1.12e-153:
		tmp = x
	elif z <= 4e-132:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -3.2e-11)
		tmp = Float64(y + x);
	elseif (z <= -8e-255)
		tmp = x;
	elseif (z <= 4.2e-272)
		tmp = t_1;
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 4e-132)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -3.2e-11)
		tmp = y + x;
	elseif (z <= -8e-255)
		tmp = x;
	elseif (z <= 4.2e-272)
		tmp = t_1;
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 4e-132)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-11], N[(y + x), $MachinePrecision], If[LessEqual[z, -8e-255], x, If[LessEqual[z, 4.2e-272], t$95$1, If[LessEqual[z, 1.12e-153], x, If[LessEqual[z, 4e-132], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999994e-11 or 3.9999999999999999e-132 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -3.19999999999999994e-11 < z < -8.0000000000000001e-255 or 4.19999999999999974e-272 < z < 1.12000000000000005e-153

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 54.8%

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

   if -8.0000000000000001e-255 < z < 4.19999999999999974e-272 or 1.12000000000000005e-153 < z < 3.9999999999999999e-132

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 75.9%

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

   4. Taylor expanded in z around 0 66.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e-15)
   (+ y x)
   (if (<= z -6.8e-255)
     x
     (if (<= z 7.6e-266)
       (/ y (/ a t))
       (if (<= z 2.6e-157) x (if (<= z 1.95e-132) (* y (/ t a)) (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e-15) {
		tmp = y + x;
	} else if (z <= -6.8e-255) {
		tmp = x;
	} else if (z <= 7.6e-266) {
		tmp = y / (a / t);
	} else if (z <= 2.6e-157) {
		tmp = x;
	} else if (z <= 1.95e-132) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.8d-15)) then
        tmp = y + x
    else if (z <= (-6.8d-255)) then
        tmp = x
    else if (z <= 7.6d-266) then
        tmp = y / (a / t)
    else if (z <= 2.6d-157) then
        tmp = x
    else if (z <= 1.95d-132) then
        tmp = y * (t / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e-15) {
		tmp = y + x;
	} else if (z <= -6.8e-255) {
		tmp = x;
	} else if (z <= 7.6e-266) {
		tmp = y / (a / t);
	} else if (z <= 2.6e-157) {
		tmp = x;
	} else if (z <= 1.95e-132) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.8e-15:
		tmp = y + x
	elif z <= -6.8e-255:
		tmp = x
	elif z <= 7.6e-266:
		tmp = y / (a / t)
	elif z <= 2.6e-157:
		tmp = x
	elif z <= 1.95e-132:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e-15)
		tmp = Float64(y + x);
	elseif (z <= -6.8e-255)
		tmp = x;
	elseif (z <= 7.6e-266)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 2.6e-157)
		tmp = x;
	elseif (z <= 1.95e-132)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.8e-15)
		tmp = y + x;
	elseif (z <= -6.8e-255)
		tmp = x;
	elseif (z <= 7.6e-266)
		tmp = y / (a / t);
	elseif (z <= 2.6e-157)
		tmp = x;
	elseif (z <= 1.95e-132)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e-15], N[(y + x), $MachinePrecision], If[LessEqual[z, -6.8e-255], x, If[LessEqual[z, 7.6e-266], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-157], x, If[LessEqual[z, 1.95e-132], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.80000000000000053e-15 or 1.94999999999999991e-132 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -7.80000000000000053e-15 < z < -6.79999999999999967e-255 or 7.59999999999999988e-266 < z < 2.59999999999999988e-157

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 54.8%

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

   if -6.79999999999999967e-255 < z < 7.59999999999999988e-266

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 74.0%

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

   4. Taylor expanded in z around 0 72.1%

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

      1. clear-num 72.1%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{t}}} \]

      2. un-div-inv 72.4%

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

   6. Applied egg-rr 72.4%

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

   if 2.59999999999999988e-157 < z < 1.94999999999999991e-132

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.0%

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

   4. Taylor expanded in z around 0 56.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-130}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -1.16e+78)
     t_1
     (if (<= z -2.05e+49)
       (- x (* y (/ z a)))
       (if (<= z -6.8e-130)
         (+ x (* (- z t) (/ y z)))
         (if (<= z 7.5e-49) (+ x (/ t (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.16e+78) {
		tmp = t_1;
	} else if (z <= -2.05e+49) {
		tmp = x - (y * (z / a));
	} else if (z <= -6.8e-130) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 7.5e-49) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-1.16d+78)) then
        tmp = t_1
    else if (z <= (-2.05d+49)) then
        tmp = x - (y * (z / a))
    else if (z <= (-6.8d-130)) then
        tmp = x + ((z - t) * (y / z))
    else if (z <= 7.5d-49) then
        tmp = x + (t / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.16e+78) {
		tmp = t_1;
	} else if (z <= -2.05e+49) {
		tmp = x - (y * (z / a));
	} else if (z <= -6.8e-130) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 7.5e-49) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -1.16e+78:
		tmp = t_1
	elif z <= -2.05e+49:
		tmp = x - (y * (z / a))
	elif z <= -6.8e-130:
		tmp = x + ((z - t) * (y / z))
	elif z <= 7.5e-49:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -1.16e+78)
		tmp = t_1;
	elseif (z <= -2.05e+49)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= -6.8e-130)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	elseif (z <= 7.5e-49)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -1.16e+78)
		tmp = t_1;
	elseif (z <= -2.05e+49)
		tmp = x - (y * (z / a));
	elseif (z <= -6.8e-130)
		tmp = x + ((z - t) * (y / z));
	elseif (z <= 7.5e-49)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+78], t$95$1, If[LessEqual[z, -2.05e+49], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-130], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-49], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1600000000000001e78 or 7.4999999999999998e-49 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 90.3%

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

   if -1.1600000000000001e78 < z < -2.05e49

   1. Initial program 99.4%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in t around 0 22.8%

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

      1. +-commutative 22.8%

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

      2. associate-*l/ 99.4%

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

      3. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around 0 22.8%

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

      1. mul-1-neg 22.8%

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

      2. unsub-neg 22.8%

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

      3. associate-/l* 99.4%

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

   10. Simplified 99.4%

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

   if -2.05e49 < z < -6.8000000000000001e-130

   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 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r/ 72.5%

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

   7. Simplified 72.5%

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

   if -6.8000000000000001e-130 < z < 7.4999999999999998e-49

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

      1. clear-num 78.0%

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

      2. un-div-inv 78.0%

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

   7. Applied egg-rr 78.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+78}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-130}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -1.16e+78)
     t_1
     (if (<= z -2.05e+49)
       (- x (* y (/ z a)))
       (if (<= z -2.1e-13)
         (+ x (/ (* y z) (- z a)))
         (if (<= z 2.3e-50) (+ x (* y (/ t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.16e+78) {
		tmp = t_1;
	} else if (z <= -2.05e+49) {
		tmp = x - (y * (z / a));
	} else if (z <= -2.1e-13) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= 2.3e-50) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-1.16d+78)) then
        tmp = t_1
    else if (z <= (-2.05d+49)) then
        tmp = x - (y * (z / a))
    else if (z <= (-2.1d-13)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= 2.3d-50) then
        tmp = x + (y * (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.16e+78) {
		tmp = t_1;
	} else if (z <= -2.05e+49) {
		tmp = x - (y * (z / a));
	} else if (z <= -2.1e-13) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= 2.3e-50) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -1.16e+78:
		tmp = t_1
	elif z <= -2.05e+49:
		tmp = x - (y * (z / a))
	elif z <= -2.1e-13:
		tmp = x + ((y * z) / (z - a))
	elif z <= 2.3e-50:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -1.16e+78)
		tmp = t_1;
	elseif (z <= -2.05e+49)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= -2.1e-13)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= 2.3e-50)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -1.16e+78)
		tmp = t_1;
	elseif (z <= -2.05e+49)
		tmp = x - (y * (z / a));
	elseif (z <= -2.1e-13)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= 2.3e-50)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+78], t$95$1, If[LessEqual[z, -2.05e+49], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-13], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-50], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1600000000000001e78 or 2.3000000000000002e-50 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 90.3%

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

   if -1.1600000000000001e78 < z < -2.05e49

   1. Initial program 99.4%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in t around 0 22.8%

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

      1. +-commutative 22.8%

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

      2. associate-*l/ 99.4%

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

      3. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around 0 22.8%

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

      1. mul-1-neg 22.8%

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

      2. unsub-neg 22.8%

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

      3. associate-/l* 99.4%

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

   10. Simplified 99.4%

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

   if -2.05e49 < z < -2.09999999999999989e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.6%

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

   if -2.09999999999999989e-13 < z < 2.3000000000000002e-50

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+78}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -8.5e+188)
     t_1
     (if (<= z -9.8e-17)
       (+ x (* z (/ y (- z a))))
       (if (<= z 1.4e-49) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -8.5e+188) {
		tmp = t_1;
	} else if (z <= -9.8e-17) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 1.4e-49) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-8.5d+188)) then
        tmp = t_1
    else if (z <= (-9.8d-17)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 1.4d-49) then
        tmp = x + (y * (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -8.5e+188) {
		tmp = t_1;
	} else if (z <= -9.8e-17) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 1.4e-49) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -8.5e+188:
		tmp = t_1
	elif z <= -9.8e-17:
		tmp = x + (z * (y / (z - a)))
	elif z <= 1.4e-49:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -8.5e+188)
		tmp = t_1;
	elseif (z <= -9.8e-17)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 1.4e-49)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -8.5e+188)
		tmp = t_1;
	elseif (z <= -9.8e-17)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 1.4e-49)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+188], t$95$1, If[LessEqual[z, -9.8e-17], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-49], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.49999999999999958e188 or 1.39999999999999999e-49 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 91.5%

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

   if -8.49999999999999958e188 < z < -9.80000000000000024e-17

   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 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-*l/ 89.8%

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

      3. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   if -9.80000000000000024e-17 < z < 1.39999999999999999e-49

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+188}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+27}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -9.8e+187)
     t_1
     (if (<= z -9e-8)
       (+ x (* z (/ y (- z a))))
       (if (<= z 4.1e+27) (+ x (* t (/ y (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -9.8e+187) {
		tmp = t_1;
	} else if (z <= -9e-8) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.1e+27) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-9.8d+187)) then
        tmp = t_1
    else if (z <= (-9d-8)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 4.1d+27) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -9.8e+187) {
		tmp = t_1;
	} else if (z <= -9e-8) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.1e+27) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -9.8e+187:
		tmp = t_1
	elif z <= -9e-8:
		tmp = x + (z * (y / (z - a)))
	elif z <= 4.1e+27:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -9.8e+187)
		tmp = t_1;
	elseif (z <= -9e-8)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 4.1e+27)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -9.8e+187)
		tmp = t_1;
	elseif (z <= -9e-8)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 4.1e+27)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+187], t$95$1, If[LessEqual[z, -9e-8], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+27], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8000000000000006e187 or 4.1000000000000002e27 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 94.1%

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

   if -9.8000000000000006e187 < z < -8.99999999999999986e-8

   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 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-*l/ 89.8%

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

      3. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   if -8.99999999999999986e-8 < z < 4.1000000000000002e27

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. associate-*r/ 85.3%

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

      2. mul-1-neg 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

      4. associate-*r/ 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+187}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+27}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-269}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e-18)
   (+ y x)
   (if (<= z -9.5e-254)
     x
     (if (<= z 2.15e-269) (/ (* y t) a) (if (<= z 1.88e-118) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e-18) {
		tmp = y + x;
	} else if (z <= -9.5e-254) {
		tmp = x;
	} else if (z <= 2.15e-269) {
		tmp = (y * t) / a;
	} else if (z <= 1.88e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.85d-18)) then
        tmp = y + x
    else if (z <= (-9.5d-254)) then
        tmp = x
    else if (z <= 2.15d-269) then
        tmp = (y * t) / a
    else if (z <= 1.88d-118) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e-18) {
		tmp = y + x;
	} else if (z <= -9.5e-254) {
		tmp = x;
	} else if (z <= 2.15e-269) {
		tmp = (y * t) / a;
	} else if (z <= 1.88e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e-18:
		tmp = y + x
	elif z <= -9.5e-254:
		tmp = x
	elif z <= 2.15e-269:
		tmp = (y * t) / a
	elif z <= 1.88e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e-18)
		tmp = Float64(y + x);
	elseif (z <= -9.5e-254)
		tmp = x;
	elseif (z <= 2.15e-269)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.88e-118)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e-18)
		tmp = y + x;
	elseif (z <= -9.5e-254)
		tmp = x;
	elseif (z <= 2.15e-269)
		tmp = (y * t) / a;
	elseif (z <= 1.88e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e-18], N[(y + x), $MachinePrecision], If[LessEqual[z, -9.5e-254], x, If[LessEqual[z, 2.15e-269], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.88e-118], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000002e-18 or 1.88000000000000001e-118 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -1.8500000000000002e-18 < z < -9.5000000000000003e-254 or 2.14999999999999994e-269 < z < 1.88000000000000001e-118

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 53.4%

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

   if -9.5000000000000003e-254 < z < 2.14999999999999994e-269

   1. Initial program 82.1%

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

   3. Taylor expanded in y around inf 69.6%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. associate-*r/ 76.4%

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

   6. Applied egg-rr 76.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-269}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+61} \lor \neg \left(a \leq 1060\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e+61) (not (<= a 1060.0)))
   (- x (* (- z t) (/ y a)))
   (+ x (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e+61) || !(a <= 1060.0)) {
		tmp = x - ((z - t) * (y / a));
	} 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 ((a <= (-8.5d+61)) .or. (.not. (a <= 1060.0d0))) then
        tmp = x - ((z - t) * (y / a))
    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 ((a <= -8.5e+61) || !(a <= 1060.0)) {
		tmp = x - ((z - t) * (y / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e+61) or not (a <= 1060.0):
		tmp = x - ((z - t) * (y / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e+61) || !(a <= 1060.0))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	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 ((a <= -8.5e+61) || ~((a <= 1060.0)))
		tmp = x - ((z - t) * (y / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e+61], N[Not[LessEqual[a, 1060.0]], $MachinePrecision]], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000035e61 or 1060 < a

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if -8.50000000000000035e61 < a < 1060

   1. Initial program 97.3%

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

   3. Taylor expanded in a around 0 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+61} \lor \neg \left(a \leq 1060\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 780:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+102)
   (- x (* y (/ z a)))
   (if (<= a 780.0) (+ x (* y (/ (- z t) z))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+102) {
		tmp = x - (y * (z / a));
	} else if (a <= 780.0) {
		tmp = x + (y * ((z - t) / z));
	} 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 (a <= (-1.35d+102)) then
        tmp = x - (y * (z / a))
    else if (a <= 780.0d0) then
        tmp = x + (y * ((z - t) / z))
    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 (a <= -1.35e+102) {
		tmp = x - (y * (z / a));
	} else if (a <= 780.0) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+102:
		tmp = x - (y * (z / a))
	elif a <= 780.0:
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+102)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (a <= 780.0)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 (a <= -1.35e+102)
		tmp = x - (y * (z / a));
	elseif (a <= 780.0)
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+102], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 780.0], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3500000000000001e102

   1. Initial program 95.7%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in t around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-*l/ 81.7%

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

      3. *-commutative 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

      3. associate-/l* 77.3%

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

   10. Simplified 77.3%

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

   if -1.3500000000000001e102 < a < 780

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0 84.6%

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

   if 780 < a

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 780:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-16)
   (+ x (* y (/ z (- z a))))
   (if (<= z 1.05e-50) (+ x (* y (/ t a))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-16) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.05e-50) {
		tmp = x + (y * (t / a));
	} 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 <= (-2.4d-16)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 1.05d-50) then
        tmp = x + (y * (t / a))
    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 <= -2.4e-16) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.05e-50) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-16:
		tmp = x + (y * (z / (z - a)))
	elif z <= 1.05e-50:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-16)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 1.05e-50)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	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 <= -2.4e-16)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 1.05e-50)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-16], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-50], N[(x + N[(y * N[(t / a), $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 < -2.40000000000000005e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if -2.40000000000000005e-16 < z < 1.05e-50

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

   if 1.05e-50 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 89.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245 \lor \neg \left(z \leq 6.4 \cdot 10^{-7}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -245.0) (not (<= z 6.4e-7))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -245.0) || !(z <= 6.4e-7)) {
		tmp = y + x;
	} 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 <= (-245.0d0)) .or. (.not. (z <= 6.4d-7))) then
        tmp = y + x
    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 <= -245.0) || !(z <= 6.4e-7)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -245.0) or not (z <= 6.4e-7):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -245.0) || !(z <= 6.4e-7))
		tmp = Float64(y + x);
	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 <= -245.0) || ~((z <= 6.4e-7)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -245.0], N[Not[LessEqual[z, 6.4e-7]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -245 or 6.4000000000000001e-7 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -245 < z < 6.4000000000000001e-7

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245 \lor \neg \left(z \leq 6.4 \cdot 10^{-7}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-17} \lor \neg \left(z \leq 1.9 \cdot 10^{-118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e-17) (not (<= z 1.9e-118))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e-17) || !(z <= 1.9e-118)) {
		tmp = y + x;
	} 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 <= (-9.8d-17)) .or. (.not. (z <= 1.9d-118))) then
        tmp = y + x
    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 <= -9.8e-17) || !(z <= 1.9e-118)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.8e-17) or not (z <= 1.9e-118):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e-17) || !(z <= 1.9e-118))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.8e-17) || ~((z <= 1.9e-118)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e-17], N[Not[LessEqual[z, 1.9e-118]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000024e-17 or 1.9e-118 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -9.80000000000000024e-17 < z < 1.9e-118

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 47.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-17} \lor \neg \left(z \leq 1.9 \cdot 10^{-118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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 97.3%

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

3. Final simplification 97.3%

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

Alternative 19: 49.7% 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 97.3%

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

3. Taylor expanded in x around inf 47.5%

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

4. Final simplification 47.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.4% 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 2024067 
(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)))))