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

Percentage Accurate: 98.1% → 98.1%

Time: 9.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% 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 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a - z}\\ t_2 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-151}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t (- a z))))) (t_2 (+ x (* y (/ (- z t) z)))))
   (if (<= z -9.2e+69)
     t_2
     (if (<= z -2.2e-63)
       t_1
       (if (<= z -2.9e-109)
         t_2
         (if (<= z -1.95e-151)
           (- x (* t (/ y z)))
           (if (<= z 1.52e-89) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / (a - z)));
	double t_2 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -9.2e+69) {
		tmp = t_2;
	} else if (z <= -2.2e-63) {
		tmp = t_1;
	} else if (z <= -2.9e-109) {
		tmp = t_2;
	} else if (z <= -1.95e-151) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.52e-89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + (y * (t / (a - z)))
    t_2 = x + (y * ((z - t) / z))
    if (z <= (-9.2d+69)) then
        tmp = t_2
    else if (z <= (-2.2d-63)) then
        tmp = t_1
    else if (z <= (-2.9d-109)) then
        tmp = t_2
    else if (z <= (-1.95d-151)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.52d-89) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / (a - z)));
	double t_2 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -9.2e+69) {
		tmp = t_2;
	} else if (z <= -2.2e-63) {
		tmp = t_1;
	} else if (z <= -2.9e-109) {
		tmp = t_2;
	} else if (z <= -1.95e-151) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.52e-89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / (a - z)))
	t_2 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -9.2e+69:
		tmp = t_2
	elif z <= -2.2e-63:
		tmp = t_1
	elif z <= -2.9e-109:
		tmp = t_2
	elif z <= -1.95e-151:
		tmp = x - (t * (y / z))
	elif z <= 1.52e-89:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / Float64(a - z))))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -9.2e+69)
		tmp = t_2;
	elseif (z <= -2.2e-63)
		tmp = t_1;
	elseif (z <= -2.9e-109)
		tmp = t_2;
	elseif (z <= -1.95e-151)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.52e-89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / (a - z)));
	t_2 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -9.2e+69)
		tmp = t_2;
	elseif (z <= -2.2e-63)
		tmp = t_1;
	elseif (z <= -2.9e-109)
		tmp = t_2;
	elseif (z <= -1.95e-151)
		tmp = x - (t * (y / z));
	elseif (z <= 1.52e-89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+69], t$95$2, If[LessEqual[z, -2.2e-63], t$95$1, If[LessEqual[z, -2.9e-109], t$95$2, If[LessEqual[z, -1.95e-151], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e-89], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000067e69 or -2.2e-63 < z < -2.9e-109 or 1.52e-89 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 91.9%

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

   if -9.20000000000000067e69 < z < -2.2e-63 or -1.95000000000000003e-151 < z < 1.52e-89

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf 86.6%

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

      1. associate-*r/ 86.6%

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

      2. mul-1-neg 86.6%

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

      3. distribute-lft-neg-out 86.6%

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

      4. *-commutative 86.6%

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

      5. associate-/l* 87.6%

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

      6. distribute-neg-frac 87.6%

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

      7. distribute-neg-frac2 87.6%

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

      8. sub-neg 87.6%

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

      9. distribute-neg-in 87.6%

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

      10. remove-double-neg 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in t around 0 87.6%

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

   if -2.9e-109 < z < -1.95000000000000003e-151

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. mul-1-neg 83.3%

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

      3. distribute-lft-neg-out 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-/l* 74.8%

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

      6. distribute-neg-frac 74.8%

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

      7. distribute-neg-frac2 74.8%

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

      8. sub-neg 74.8%

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

      9. distribute-neg-in 74.8%

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

      10. remove-double-neg 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in z around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

      3. associate-/l* 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-151}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+291}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= t -2.9e+53)
     t_1
     (if (<= t 3.8e+20)
       (+ y x)
       (if (<= t 7e+207)
         (+ x (/ y (/ a t)))
         (if (<= t 1.02e+291) t_1 (+ x (/ (* y t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (t <= -2.9e+53) {
		tmp = t_1;
	} else if (t <= 3.8e+20) {
		tmp = y + x;
	} else if (t <= 7e+207) {
		tmp = x + (y / (a / t));
	} else if (t <= 1.02e+291) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (t <= (-2.9d+53)) then
        tmp = t_1
    else if (t <= 3.8d+20) then
        tmp = y + x
    else if (t <= 7d+207) then
        tmp = x + (y / (a / t))
    else if (t <= 1.02d+291) then
        tmp = t_1
    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 t_1 = x - (t * (y / z));
	double tmp;
	if (t <= -2.9e+53) {
		tmp = t_1;
	} else if (t <= 3.8e+20) {
		tmp = y + x;
	} else if (t <= 7e+207) {
		tmp = x + (y / (a / t));
	} else if (t <= 1.02e+291) {
		tmp = t_1;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if t <= -2.9e+53:
		tmp = t_1
	elif t <= 3.8e+20:
		tmp = y + x
	elif t <= 7e+207:
		tmp = x + (y / (a / t))
	elif t <= 1.02e+291:
		tmp = t_1
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (t <= -2.9e+53)
		tmp = t_1;
	elseif (t <= 3.8e+20)
		tmp = Float64(y + x);
	elseif (t <= 7e+207)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (t <= 1.02e+291)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (t <= -2.9e+53)
		tmp = t_1;
	elseif (t <= 3.8e+20)
		tmp = y + x;
	elseif (t <= 7e+207)
		tmp = x + (y / (a / t));
	elseif (t <= 1.02e+291)
		tmp = t_1;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+53], t$95$1, If[LessEqual[t, 3.8e+20], N[(y + x), $MachinePrecision], If[LessEqual[t, 7e+207], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+291], t$95$1, N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9000000000000002e53 or 7.00000000000000056e207 < t < 1.02000000000000005e291

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. associate-*r/ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. distribute-lft-neg-out 82.8%

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

      4. *-commutative 82.8%

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

      5. associate-/l* 90.7%

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

      6. distribute-neg-frac 90.7%

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

      7. distribute-neg-frac2 90.7%

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

      8. sub-neg 90.7%

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

      9. distribute-neg-in 90.7%

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

      10. remove-double-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. associate-/l* 73.4%

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

   8. Simplified 73.4%

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

   if -2.9000000000000002e53 < t < 3.8e20

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 3.8e20 < t < 7.00000000000000056e207

   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 z around 0 80.6%

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

   if 1.02000000000000005e291 < t

   1. Initial program 76.4%

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

   3. Taylor expanded in z around 0 100.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+291}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+280}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+53)
   (- x (/ y (/ z t)))
   (if (<= t 9e+17)
     (+ y x)
     (if (<= t 5e+205)
       (+ x (/ y (/ a t)))
       (if (<= t 6.7e+280) (- x (* t (/ y z))) (+ x (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+53) {
		tmp = x - (y / (z / t));
	} else if (t <= 9e+17) {
		tmp = y + x;
	} else if (t <= 5e+205) {
		tmp = x + (y / (a / t));
	} else if (t <= 6.7e+280) {
		tmp = x - (t * (y / z));
	} 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 (t <= (-2d+53)) then
        tmp = x - (y / (z / t))
    else if (t <= 9d+17) then
        tmp = y + x
    else if (t <= 5d+205) then
        tmp = x + (y / (a / t))
    else if (t <= 6.7d+280) then
        tmp = x - (t * (y / z))
    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 (t <= -2e+53) {
		tmp = x - (y / (z / t));
	} else if (t <= 9e+17) {
		tmp = y + x;
	} else if (t <= 5e+205) {
		tmp = x + (y / (a / t));
	} else if (t <= 6.7e+280) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+53:
		tmp = x - (y / (z / t))
	elif t <= 9e+17:
		tmp = y + x
	elif t <= 5e+205:
		tmp = x + (y / (a / t))
	elif t <= 6.7e+280:
		tmp = x - (t * (y / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+53)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (t <= 9e+17)
		tmp = Float64(y + x);
	elseif (t <= 5e+205)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (t <= 6.7e+280)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+53)
		tmp = x - (y / (z / t));
	elseif (t <= 9e+17)
		tmp = y + x;
	elseif (t <= 5e+205)
		tmp = x + (y / (a / t));
	elseif (t <= 6.7e+280)
		tmp = x - (t * (y / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+53], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+17], N[(y + x), $MachinePrecision], If[LessEqual[t, 5e+205], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.7e+280], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2e53

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. *-commutative 83.9%

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

      5. associate-/l* 91.0%

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

      6. distribute-neg-frac 91.0%

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

      7. distribute-neg-frac2 91.0%

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

      8. sub-neg 91.0%

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

      9. distribute-neg-in 91.0%

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

      10. remove-double-neg 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in z around inf 72.8%

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

      1. associate-*r/ 72.8%

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

      2. neg-mul-1 72.8%

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

   8. Simplified 72.8%

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

      1. *-commutative 72.8%

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

      2. add-sqr-sqrt 72.8%

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

      3. sqrt-unprod 39.9%

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

      4. sqr-neg 39.9%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 31.9%

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

      7. cancel-sign-sub 31.9%

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

      8. distribute-frac-neg 31.9%

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

      9. *-commutative 31.9%

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

      10. add-sqr-sqrt 31.9%

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

      11. sqrt-unprod 13.4%

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

      12. sqr-neg 13.4%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 72.8%

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

   10. Applied egg-rr 72.8%

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

       1. clear-num 72.7%

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

       2. un-div-inv 72.8%

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

   12. Applied egg-rr 72.8%

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

   if -2e53 < t < 9e17

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 9e17 < t < 5.0000000000000002e205

   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 z around 0 80.6%

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

   if 5.0000000000000002e205 < t < 6.6999999999999999e280

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. mul-1-neg 79.8%

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

      3. distribute-lft-neg-out 79.8%

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

      4. *-commutative 79.8%

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

      5. associate-/l* 90.1%

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

      6. distribute-neg-frac 90.1%

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

      7. distribute-neg-frac2 90.1%

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

      8. sub-neg 90.1%

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

      9. distribute-neg-in 90.1%

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

      10. remove-double-neg 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in z around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

      3. associate-/l* 74.9%

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

   8. Simplified 74.9%

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

   if 6.6999999999999999e280 < t

   1. Initial program 76.4%

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

   3. Taylor expanded in z around 0 100.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+280}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+116} \lor \neg \left(z \leq 8.7 \cdot 10^{+102}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+116) (not (<= z 8.7e+102)))
   (+ y x)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+116) || !(z <= 8.7e+102)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d+116)) .or. (.not. (z <= 8.7d+102))) then
        tmp = y + x
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+116) || !(z <= 8.7e+102)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+116) or not (z <= 8.7e+102):
		tmp = y + x
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+116) || !(z <= 8.7e+102))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e+116) || ~((z <= 8.7e+102)))
		tmp = y + x;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+116], N[Not[LessEqual[z, 8.7e+102]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e116 or 8.69999999999999974e102 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.7%

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

      1. +-commutative 91.7%

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

   5. Simplified 91.7%

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

   if -1.54999999999999998e116 < z < 8.69999999999999974e102

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 80.4%

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

      1. associate-*r/ 80.4%

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

      2. mul-1-neg 80.4%

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

      3. distribute-lft-neg-out 80.4%

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

      4. *-commutative 80.4%

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

      5. associate-/l* 80.9%

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

      6. distribute-neg-frac 80.9%

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

      7. distribute-neg-frac2 80.9%

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

      8. sub-neg 80.9%

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

      9. distribute-neg-in 80.9%

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

      10. remove-double-neg 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 80.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+116} \lor \neg \left(z \leq 8.7 \cdot 10^{+102}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+28} \lor \neg \left(t \leq 3.4 \cdot 10^{+84}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.05e+28) (not (<= t 3.4e+84)))
   (+ x (* y (/ t (- a z))))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.05e+28) || !(t <= 3.4e+84)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.05d+28)) .or. (.not. (t <= 3.4d+84))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (z * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.05e+28) || !(t <= 3.4e+84)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.05e+28) or not (t <= 3.4e+84):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.05e+28) || !(t <= 3.4e+84))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.05e+28) || ~((t <= 3.4e+84)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.05e+28], N[Not[LessEqual[t, 3.4e+84]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0499999999999999e28 or 3.3999999999999998e84 < t

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate-*r/ 85.4%

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

      2. mul-1-neg 85.4%

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

      3. distribute-lft-neg-out 85.4%

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

      4. *-commutative 85.4%

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

      5. associate-/l* 90.4%

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

      6. distribute-neg-frac 90.4%

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

      7. distribute-neg-frac2 90.4%

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

      8. sub-neg 90.4%

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

      9. distribute-neg-in 90.4%

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

      10. remove-double-neg 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in t around 0 90.4%

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

   if -2.0499999999999999e28 < t < 3.3999999999999998e84

   1. Initial program 99.3%

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

      1. clear-num 98.6%

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

      2. un-div-inv 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around 0 80.1%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   7. Simplified 87.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+28} \lor \neg \left(t \leq 3.4 \cdot 10^{+84}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+22} \lor \neg \left(t \leq 2.8 \cdot 10^{+75}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.06e+22) (not (<= t 2.8e+75)))
   (+ x (* y (/ t (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.06e+22) || !(t <= 2.8e+75)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.06d+22)) .or. (.not. (t <= 2.8d+75))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.06e+22) || !(t <= 2.8e+75)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.06e+22) or not (t <= 2.8e+75):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.06e+22) || !(t <= 2.8e+75))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.06e+22) || ~((t <= 2.8e+75)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.06e+22], N[Not[LessEqual[t, 2.8e+75]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.06e22 or 2.80000000000000012e75 < t

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 85.2%

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

      1. associate-*r/ 85.2%

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

      2. mul-1-neg 85.2%

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

      3. distribute-lft-neg-out 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-/l* 90.0%

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

      6. distribute-neg-frac 90.0%

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

      7. distribute-neg-frac2 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-neg-in 90.0%

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

      10. remove-double-neg 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in t around 0 90.0%

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

   if -1.06e22 < t < 2.80000000000000012e75

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+22} \lor \neg \left(t \leq 2.8 \cdot 10^{+75}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+26} \lor \neg \left(z \leq 3.1 \cdot 10^{-144}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+26) (not (<= z 3.1e-144))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+26) || !(z <= 3.1e-144)) {
		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 <= (-4.8d+26)) .or. (.not. (z <= 3.1d-144))) 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 <= -4.8e+26) || !(z <= 3.1e-144)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+26) or not (z <= 3.1e-144):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+26) || !(z <= 3.1e-144))
		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 <= -4.8e+26) || ~((z <= 3.1e-144)))
		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, -4.8e+26], N[Not[LessEqual[z, 3.1e-144]], $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 < -4.80000000000000009e26 or 3.1000000000000001e-144 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -4.80000000000000009e26 < z < 3.1000000000000001e-144

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+26} \lor \neg \left(z \leq 3.1 \cdot 10^{-144}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{-144}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+23) (not (<= z 4.2e-144))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+23) || !(z <= 4.2e-144)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+23)) .or. (.not. (z <= 4.2d-144))) then
        tmp = y + x
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+23) || !(z <= 4.2e-144)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+23) or not (z <= 4.2e-144):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+23) || !(z <= 4.2e-144))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+23) || ~((z <= 4.2e-144)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+23], N[Not[LessEqual[z, 4.2e-144]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e23 or 4.2000000000000002e-144 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -8.5000000000000001e23 < z < 4.2000000000000002e-144

   1. Initial program 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in z around 0 73.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{-144}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+25} \lor \neg \left(z \leq 3.2 \cdot 10^{-168}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+25) (not (<= z 3.2e-168))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+25) || !(z <= 3.2e-168)) {
		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 <= (-1.9d+25)) .or. (.not. (z <= 3.2d-168))) 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 <= -1.9e+25) || !(z <= 3.2e-168)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+25) or not (z <= 3.2e-168):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+25) || !(z <= 3.2e-168))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+25) || ~((z <= 3.2e-168)))
		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, -1.9e+25], N[Not[LessEqual[z, 3.2e-168]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e25 or 3.20000000000000006e-168 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -1.9e25 < z < 3.20000000000000006e-168

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 74.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+25} \lor \neg \left(z \leq 3.2 \cdot 10^{-168}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 12: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -2.9e+162) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+162) {
		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 (a <= (-2.9d+162)) 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 (a <= -2.9e+162) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e+162:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e+162)
		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 (a <= -2.9e+162)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e+162], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.90000000000000006e162

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.1%

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

   if -2.90000000000000006e162 < a

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% 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 98.4%

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

3. Taylor expanded in x around inf 49.5%

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

4. Final simplification 49.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024095 
(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)))))