Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 96.8% → 99.7%

Time: 13.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + a \cdot \frac{z - y}{\left(t - z\right) + 1} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* a (/ (- z y) (+ (- t z) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

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 + (a * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

Python

def code(x, y, z, t, a):
	return x + (a * ((z - y) / ((t - z) + 1.0)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(a * Float64(Float64(z - y) / Float64(Float64(t - z) + 1.0))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (a * ((z - y) / ((t - z) + 1.0)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

   \[\leadsto x + a \cdot \frac{z - y}{\left(t - z\right) + 1} \]
6. Add Preprocessing

Alternative 2: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x + \frac{y \cdot a}{z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-195}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (+ x (/ (* y a) z))))
   (if (<= z -6.5e+56)
     (- x a)
     (if (<= z -3e-5)
       t_2
       (if (<= z -2.5e-15)
         x
         (if (<= z -3.3e-156)
           t_1
           (if (<= z 1.75e-195)
             (+ x (/ (* z a) t))
             (if (<= z 2e+17) t_1 (if (<= z 4.1e+157) t_2 (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x + ((y * a) / z);
	double tmp;
	if (z <= -6.5e+56) {
		tmp = x - a;
	} else if (z <= -3e-5) {
		tmp = t_2;
	} else if (z <= -2.5e-15) {
		tmp = x;
	} else if (z <= -3.3e-156) {
		tmp = t_1;
	} else if (z <= 1.75e-195) {
		tmp = x + ((z * a) / t);
	} else if (z <= 2e+17) {
		tmp = t_1;
	} else if (z <= 4.1e+157) {
		tmp = t_2;
	} else {
		tmp = x - 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) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x + ((y * a) / z)
    if (z <= (-6.5d+56)) then
        tmp = x - a
    else if (z <= (-3d-5)) then
        tmp = t_2
    else if (z <= (-2.5d-15)) then
        tmp = x
    else if (z <= (-3.3d-156)) then
        tmp = t_1
    else if (z <= 1.75d-195) then
        tmp = x + ((z * a) / t)
    else if (z <= 2d+17) then
        tmp = t_1
    else if (z <= 4.1d+157) then
        tmp = t_2
    else
        tmp = x - 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 - (y * a);
	double t_2 = x + ((y * a) / z);
	double tmp;
	if (z <= -6.5e+56) {
		tmp = x - a;
	} else if (z <= -3e-5) {
		tmp = t_2;
	} else if (z <= -2.5e-15) {
		tmp = x;
	} else if (z <= -3.3e-156) {
		tmp = t_1;
	} else if (z <= 1.75e-195) {
		tmp = x + ((z * a) / t);
	} else if (z <= 2e+17) {
		tmp = t_1;
	} else if (z <= 4.1e+157) {
		tmp = t_2;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x + ((y * a) / z)
	tmp = 0
	if z <= -6.5e+56:
		tmp = x - a
	elif z <= -3e-5:
		tmp = t_2
	elif z <= -2.5e-15:
		tmp = x
	elif z <= -3.3e-156:
		tmp = t_1
	elif z <= 1.75e-195:
		tmp = x + ((z * a) / t)
	elif z <= 2e+17:
		tmp = t_1
	elif z <= 4.1e+157:
		tmp = t_2
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x + Float64(Float64(y * a) / z))
	tmp = 0.0
	if (z <= -6.5e+56)
		tmp = Float64(x - a);
	elseif (z <= -3e-5)
		tmp = t_2;
	elseif (z <= -2.5e-15)
		tmp = x;
	elseif (z <= -3.3e-156)
		tmp = t_1;
	elseif (z <= 1.75e-195)
		tmp = Float64(x + Float64(Float64(z * a) / t));
	elseif (z <= 2e+17)
		tmp = t_1;
	elseif (z <= 4.1e+157)
		tmp = t_2;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x + ((y * a) / z);
	tmp = 0.0;
	if (z <= -6.5e+56)
		tmp = x - a;
	elseif (z <= -3e-5)
		tmp = t_2;
	elseif (z <= -2.5e-15)
		tmp = x;
	elseif (z <= -3.3e-156)
		tmp = t_1;
	elseif (z <= 1.75e-195)
		tmp = x + ((z * a) / t);
	elseif (z <= 2e+17)
		tmp = t_1;
	elseif (z <= 4.1e+157)
		tmp = t_2;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+56], N[(x - a), $MachinePrecision], If[LessEqual[z, -3e-5], t$95$2, If[LessEqual[z, -2.5e-15], x, If[LessEqual[z, -3.3e-156], t$95$1, If[LessEqual[z, 1.75e-195], N[(x + N[(N[(z * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+17], t$95$1, If[LessEqual[z, 4.1e+157], t$95$2, N[(x - a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5000000000000001e56 or 4.10000000000000016e157 < z

   1. Initial program 96.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 83.9%

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

   if -6.5000000000000001e56 < z < -3.00000000000000008e-5 or 2e17 < z < 4.10000000000000016e157

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate--l+ 82.4%

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

      3. +-commutative 82.4%

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

      4. associate-*r/ 86.4%

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

      5. +-commutative 86.4%

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

      6. associate--l+ 86.4%

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

      7. associate--l+ 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in z around inf 76.3%

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

   if -3.00000000000000008e-5 < z < -2.5e-15

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate--l+ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

   if -2.5e-15 < z < -3.2999999999999999e-156 or 1.75000000000000007e-195 < z < 2e17

   1. Initial program 98.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 86.2%

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

   6. Taylor expanded in t around 0 68.8%

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

   if -3.2999999999999999e-156 < z < 1.75000000000000007e-195

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 78.7%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. sub-neg 74.8%

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

      2. mul-1-neg 74.8%

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

      3. remove-double-neg 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-195}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.037:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 85000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -5.2e+135)
     (- x a)
     (if (<= z -0.037)
       (+ x (* a (/ y z)))
       (if (<= z -2.25e-250)
         t_1
         (if (<= z 7e-172)
           x
           (if (<= z 85000.0)
             t_1
             (if (<= z 5.5e+66) (+ x (/ a (/ z y))) (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -5.2e+135) {
		tmp = x - a;
	} else if (z <= -0.037) {
		tmp = x + (a * (y / z));
	} else if (z <= -2.25e-250) {
		tmp = t_1;
	} else if (z <= 7e-172) {
		tmp = x;
	} else if (z <= 85000.0) {
		tmp = t_1;
	} else if (z <= 5.5e+66) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - 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 - (y * a)
    if (z <= (-5.2d+135)) then
        tmp = x - a
    else if (z <= (-0.037d0)) then
        tmp = x + (a * (y / z))
    else if (z <= (-2.25d-250)) then
        tmp = t_1
    else if (z <= 7d-172) then
        tmp = x
    else if (z <= 85000.0d0) then
        tmp = t_1
    else if (z <= 5.5d+66) then
        tmp = x + (a / (z / y))
    else
        tmp = x - 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 - (y * a);
	double tmp;
	if (z <= -5.2e+135) {
		tmp = x - a;
	} else if (z <= -0.037) {
		tmp = x + (a * (y / z));
	} else if (z <= -2.25e-250) {
		tmp = t_1;
	} else if (z <= 7e-172) {
		tmp = x;
	} else if (z <= 85000.0) {
		tmp = t_1;
	} else if (z <= 5.5e+66) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -5.2e+135:
		tmp = x - a
	elif z <= -0.037:
		tmp = x + (a * (y / z))
	elif z <= -2.25e-250:
		tmp = t_1
	elif z <= 7e-172:
		tmp = x
	elif z <= 85000.0:
		tmp = t_1
	elif z <= 5.5e+66:
		tmp = x + (a / (z / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -5.2e+135)
		tmp = Float64(x - a);
	elseif (z <= -0.037)
		tmp = Float64(x + Float64(a * Float64(y / z)));
	elseif (z <= -2.25e-250)
		tmp = t_1;
	elseif (z <= 7e-172)
		tmp = x;
	elseif (z <= 85000.0)
		tmp = t_1;
	elseif (z <= 5.5e+66)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -5.2e+135)
		tmp = x - a;
	elseif (z <= -0.037)
		tmp = x + (a * (y / z));
	elseif (z <= -2.25e-250)
		tmp = t_1;
	elseif (z <= 7e-172)
		tmp = x;
	elseif (z <= 85000.0)
		tmp = t_1;
	elseif (z <= 5.5e+66)
		tmp = x + (a / (z / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+135], N[(x - a), $MachinePrecision], If[LessEqual[z, -0.037], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-250], t$95$1, If[LessEqual[z, 7e-172], x, If[LessEqual[z, 85000.0], t$95$1, If[LessEqual[z, 5.5e+66], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.2e135 or 5.5e66 < z

   1. Initial program 96.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -5.2e135 < z < -0.0369999999999999982

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate--l+ 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-*r/ 88.0%

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

      5. +-commutative 88.0%

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

      6. associate--l+ 88.0%

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

      7. associate--l+ 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 76.7%

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

   10. Simplified 76.7%

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

   if -0.0369999999999999982 < z < -2.24999999999999997e-250 or 7.00000000000000057e-172 < z < 85000

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 88.9%

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

   6. Taylor expanded in t around 0 69.0%

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

   if -2.24999999999999997e-250 < z < 7.00000000000000057e-172

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate--l+ 87.2%

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

      3. +-commutative 87.2%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate--l+ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 78.6%

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

   if 85000 < z < 5.5e66

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate--l+ 75.0%

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

      3. +-commutative 75.0%

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

      4. associate-*r/ 79.2%

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

      5. +-commutative 79.2%

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

      6. associate--l+ 79.2%

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

      7. associate--l+ 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in z around inf 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

       1. clear-num 79.1%

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

       2. un-div-inv 79.1%

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

   12. Applied egg-rr 79.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.037:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-250}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 85000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x + a \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.028:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (+ x (* a (/ y z)))))
   (if (<= z -6e+135)
     (- x a)
     (if (<= z -0.028)
       t_2
       (if (<= z -3.8e-248)
         t_1
         (if (<= z 1.5e-166)
           x
           (if (<= z 58000.0) t_1 (if (<= z 2.15e+67) t_2 (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x + (a * (y / z));
	double tmp;
	if (z <= -6e+135) {
		tmp = x - a;
	} else if (z <= -0.028) {
		tmp = t_2;
	} else if (z <= -3.8e-248) {
		tmp = t_1;
	} else if (z <= 1.5e-166) {
		tmp = x;
	} else if (z <= 58000.0) {
		tmp = t_1;
	} else if (z <= 2.15e+67) {
		tmp = t_2;
	} else {
		tmp = x - 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) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x + (a * (y / z))
    if (z <= (-6d+135)) then
        tmp = x - a
    else if (z <= (-0.028d0)) then
        tmp = t_2
    else if (z <= (-3.8d-248)) then
        tmp = t_1
    else if (z <= 1.5d-166) then
        tmp = x
    else if (z <= 58000.0d0) then
        tmp = t_1
    else if (z <= 2.15d+67) then
        tmp = t_2
    else
        tmp = x - 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 - (y * a);
	double t_2 = x + (a * (y / z));
	double tmp;
	if (z <= -6e+135) {
		tmp = x - a;
	} else if (z <= -0.028) {
		tmp = t_2;
	} else if (z <= -3.8e-248) {
		tmp = t_1;
	} else if (z <= 1.5e-166) {
		tmp = x;
	} else if (z <= 58000.0) {
		tmp = t_1;
	} else if (z <= 2.15e+67) {
		tmp = t_2;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x + (a * (y / z))
	tmp = 0
	if z <= -6e+135:
		tmp = x - a
	elif z <= -0.028:
		tmp = t_2
	elif z <= -3.8e-248:
		tmp = t_1
	elif z <= 1.5e-166:
		tmp = x
	elif z <= 58000.0:
		tmp = t_1
	elif z <= 2.15e+67:
		tmp = t_2
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x + Float64(a * Float64(y / z)))
	tmp = 0.0
	if (z <= -6e+135)
		tmp = Float64(x - a);
	elseif (z <= -0.028)
		tmp = t_2;
	elseif (z <= -3.8e-248)
		tmp = t_1;
	elseif (z <= 1.5e-166)
		tmp = x;
	elseif (z <= 58000.0)
		tmp = t_1;
	elseif (z <= 2.15e+67)
		tmp = t_2;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x + (a * (y / z));
	tmp = 0.0;
	if (z <= -6e+135)
		tmp = x - a;
	elseif (z <= -0.028)
		tmp = t_2;
	elseif (z <= -3.8e-248)
		tmp = t_1;
	elseif (z <= 1.5e-166)
		tmp = x;
	elseif (z <= 58000.0)
		tmp = t_1;
	elseif (z <= 2.15e+67)
		tmp = t_2;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+135], N[(x - a), $MachinePrecision], If[LessEqual[z, -0.028], t$95$2, If[LessEqual[z, -3.8e-248], t$95$1, If[LessEqual[z, 1.5e-166], x, If[LessEqual[z, 58000.0], t$95$1, If[LessEqual[z, 2.15e+67], t$95$2, N[(x - a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e135 or 2.1500000000000001e67 < z

   1. Initial program 96.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -6.0000000000000001e135 < z < -0.0280000000000000006 or 58000 < z < 2.1500000000000001e67

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. associate--l+ 76.0%

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

      3. +-commutative 76.0%

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

      4. associate-*r/ 84.0%

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

      5. +-commutative 84.0%

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

      6. associate--l+ 84.0%

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

      7. associate--l+ 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-/l* 77.8%

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

   10. Simplified 77.8%

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

   if -0.0280000000000000006 < z < -3.7999999999999999e-248 or 1.5000000000000001e-166 < z < 58000

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 88.9%

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

   6. Taylor expanded in t around 0 69.0%

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

   if -3.7999999999999999e-248 < z < 1.5000000000000001e-166

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate--l+ 87.2%

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

      3. +-commutative 87.2%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate--l+ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.028:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x + \frac{y \cdot a}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.000415:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (+ x (/ (* y a) z))))
   (if (<= z -1.75e+55)
     (- x a)
     (if (<= z -0.000415)
       t_2
       (if (<= z -2.8e-249)
         t_1
         (if (<= z 7e-172)
           x
           (if (<= z 58000.0) t_1 (if (<= z 4.7e+72) t_2 (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x + ((y * a) / z);
	double tmp;
	if (z <= -1.75e+55) {
		tmp = x - a;
	} else if (z <= -0.000415) {
		tmp = t_2;
	} else if (z <= -2.8e-249) {
		tmp = t_1;
	} else if (z <= 7e-172) {
		tmp = x;
	} else if (z <= 58000.0) {
		tmp = t_1;
	} else if (z <= 4.7e+72) {
		tmp = t_2;
	} else {
		tmp = x - 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) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x + ((y * a) / z)
    if (z <= (-1.75d+55)) then
        tmp = x - a
    else if (z <= (-0.000415d0)) then
        tmp = t_2
    else if (z <= (-2.8d-249)) then
        tmp = t_1
    else if (z <= 7d-172) then
        tmp = x
    else if (z <= 58000.0d0) then
        tmp = t_1
    else if (z <= 4.7d+72) then
        tmp = t_2
    else
        tmp = x - 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 - (y * a);
	double t_2 = x + ((y * a) / z);
	double tmp;
	if (z <= -1.75e+55) {
		tmp = x - a;
	} else if (z <= -0.000415) {
		tmp = t_2;
	} else if (z <= -2.8e-249) {
		tmp = t_1;
	} else if (z <= 7e-172) {
		tmp = x;
	} else if (z <= 58000.0) {
		tmp = t_1;
	} else if (z <= 4.7e+72) {
		tmp = t_2;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x + ((y * a) / z)
	tmp = 0
	if z <= -1.75e+55:
		tmp = x - a
	elif z <= -0.000415:
		tmp = t_2
	elif z <= -2.8e-249:
		tmp = t_1
	elif z <= 7e-172:
		tmp = x
	elif z <= 58000.0:
		tmp = t_1
	elif z <= 4.7e+72:
		tmp = t_2
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x + Float64(Float64(y * a) / z))
	tmp = 0.0
	if (z <= -1.75e+55)
		tmp = Float64(x - a);
	elseif (z <= -0.000415)
		tmp = t_2;
	elseif (z <= -2.8e-249)
		tmp = t_1;
	elseif (z <= 7e-172)
		tmp = x;
	elseif (z <= 58000.0)
		tmp = t_1;
	elseif (z <= 4.7e+72)
		tmp = t_2;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x + ((y * a) / z);
	tmp = 0.0;
	if (z <= -1.75e+55)
		tmp = x - a;
	elseif (z <= -0.000415)
		tmp = t_2;
	elseif (z <= -2.8e-249)
		tmp = t_1;
	elseif (z <= 7e-172)
		tmp = x;
	elseif (z <= 58000.0)
		tmp = t_1;
	elseif (z <= 4.7e+72)
		tmp = t_2;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+55], N[(x - a), $MachinePrecision], If[LessEqual[z, -0.000415], t$95$2, If[LessEqual[z, -2.8e-249], t$95$1, If[LessEqual[z, 7e-172], x, If[LessEqual[z, 58000.0], t$95$1, If[LessEqual[z, 4.7e+72], t$95$2, N[(x - a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.75000000000000005e55 or 4.70000000000000034e72 < z

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.0%

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

   if -1.75000000000000005e55 < z < -4.15e-4 or 58000 < z < 4.70000000000000034e72

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate--l+ 83.0%

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

      3. +-commutative 83.0%

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

      4. associate-*r/ 85.8%

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

      5. +-commutative 85.8%

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

      6. associate--l+ 85.8%

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

      7. associate--l+ 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in z around inf 74.0%

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

   if -4.15e-4 < z < -2.7999999999999999e-249 or 7.00000000000000057e-172 < z < 58000

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 89.5%

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

   6. Taylor expanded in t around 0 69.3%

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

   if -2.7999999999999999e-249 < z < 7.00000000000000057e-172

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate--l+ 87.2%

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

      3. +-commutative 87.2%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate--l+ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.000415:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-249}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+155} \lor \neg \left(z \leq 1.15 \cdot 10^{+158}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+54)
   (- x a)
   (if (<= z -5.6e-70)
     x
     (if (<= z -7.1e-112)
       (* a (- y))
       (if (<= z 8e-13)
         (+ x (* z a))
         (if (or (<= z 1.45e+155) (not (<= z 1.15e+158)))
           (- x a)
           (* y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-70) {
		tmp = x;
	} else if (z <= -7.1e-112) {
		tmp = a * -y;
	} else if (z <= 8e-13) {
		tmp = x + (z * a);
	} else if ((z <= 1.45e+155) || !(z <= 1.15e+158)) {
		tmp = x - a;
	} else {
		tmp = y * (a / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+54)) then
        tmp = x - a
    else if (z <= (-5.6d-70)) then
        tmp = x
    else if (z <= (-7.1d-112)) then
        tmp = a * -y
    else if (z <= 8d-13) then
        tmp = x + (z * a)
    else if ((z <= 1.45d+155) .or. (.not. (z <= 1.15d+158))) then
        tmp = x - a
    else
        tmp = y * (a / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+54) {
		tmp = x - a;
	} else if (z <= -5.6e-70) {
		tmp = x;
	} else if (z <= -7.1e-112) {
		tmp = a * -y;
	} else if (z <= 8e-13) {
		tmp = x + (z * a);
	} else if ((z <= 1.45e+155) || !(z <= 1.15e+158)) {
		tmp = x - a;
	} else {
		tmp = y * (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+54:
		tmp = x - a
	elif z <= -5.6e-70:
		tmp = x
	elif z <= -7.1e-112:
		tmp = a * -y
	elif z <= 8e-13:
		tmp = x + (z * a)
	elif (z <= 1.45e+155) or not (z <= 1.15e+158):
		tmp = x - a
	else:
		tmp = y * (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+54)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-70)
		tmp = x;
	elseif (z <= -7.1e-112)
		tmp = Float64(a * Float64(-y));
	elseif (z <= 8e-13)
		tmp = Float64(x + Float64(z * a));
	elseif ((z <= 1.45e+155) || !(z <= 1.15e+158))
		tmp = Float64(x - a);
	else
		tmp = Float64(y * Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+54)
		tmp = x - a;
	elseif (z <= -5.6e-70)
		tmp = x;
	elseif (z <= -7.1e-112)
		tmp = a * -y;
	elseif (z <= 8e-13)
		tmp = x + (z * a);
	elseif ((z <= 1.45e+155) || ~((z <= 1.15e+158)))
		tmp = x - a;
	else
		tmp = y * (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-70], x, If[LessEqual[z, -7.1e-112], N[(a * (-y)), $MachinePrecision], If[LessEqual[z, 8e-13], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.45e+155], N[Not[LessEqual[z, 1.15e+158]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.50000000000000042e54 or 8.0000000000000002e-13 < z < 1.45e155 or 1.14999999999999993e158 < z

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 77.9%

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

   if -7.50000000000000042e54 < z < -5.5999999999999998e-70

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.5%

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

      1. *-commutative 94.5%

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

      2. associate--l+ 94.5%

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

      3. +-commutative 94.5%

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

      4. associate-*r/ 94.4%

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

      5. +-commutative 94.4%

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

      6. associate--l+ 94.4%

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

      7. associate--l+ 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in x around inf 62.0%

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

   if -5.5999999999999998e-70 < z < -7.09999999999999957e-112

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in z around 0 84.4%

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

   6. Taylor expanded in x around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*r/ 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

      4. distribute-neg-frac2 60.1%

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

      5. distribute-neg-in 60.1%

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

      6. metadata-eval 60.1%

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

      7. sub-neg 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in t around 0 51.5%

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

       1. associate-*r* 51.5%

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

       2. neg-mul-1 51.5%

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

       3. *-commutative 51.5%

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

   11. Simplified 51.5%

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

   if -7.09999999999999957e-112 < z < 8.0000000000000002e-13

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 72.6%

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

   6. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-neg-frac2 64.8%

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

      3. neg-sub0 64.8%

         \[\leadsto x - \frac{a \cdot z}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 64.8%

         \[\leadsto x - \frac{a \cdot z}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in z around 0 64.8%

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

       1. +-commutative 64.8%

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

   11. Simplified 64.8%

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

   if 1.45e155 < z < 1.14999999999999993e158

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. associate--l+ 69.9%

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

      3. +-commutative 69.9%

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

      4. associate-*r/ 99.5%

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

      5. +-commutative 99.5%

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

      6. associate--l+ 99.5%

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

      7. associate--l+ 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around 0 99.5%

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

   9. Taylor expanded in x around 0 39.8%

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

       1. mul-1-neg 39.8%

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

       2. distribute-frac-neg2 39.8%

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

       3. *-commutative 39.8%

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

       4. associate-*r/ 52.3%

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

       5. neg-sub0 52.3%

          \[\leadsto y \cdot \frac{a}{\color{blue}{0 - \left(1 - z\right)}} \]

       6. associate--r- 52.3%

          \[\leadsto y \cdot \frac{a}{\color{blue}{\left(0 - 1\right) + z}} \]

       7. metadata-eval 52.3%

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

   11. Simplified 52.3%

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

   12. Taylor expanded in z around inf 52.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+155} \lor \neg \left(z \leq 1.15 \cdot 10^{+158}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -6.8e+55)
     (- x a)
     (if (<= z -3.7e-57)
       x
       (if (<= z -2.25e-250)
         t_1
         (if (<= z 1.35e-171) x (if (<= z 9.8e-55) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -6.8e+55) {
		tmp = x - a;
	} else if (z <= -3.7e-57) {
		tmp = x;
	} else if (z <= -2.25e-250) {
		tmp = t_1;
	} else if (z <= 1.35e-171) {
		tmp = x;
	} else if (z <= 9.8e-55) {
		tmp = t_1;
	} else {
		tmp = x - 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 - (y * a)
    if (z <= (-6.8d+55)) then
        tmp = x - a
    else if (z <= (-3.7d-57)) then
        tmp = x
    else if (z <= (-2.25d-250)) then
        tmp = t_1
    else if (z <= 1.35d-171) then
        tmp = x
    else if (z <= 9.8d-55) then
        tmp = t_1
    else
        tmp = x - 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 - (y * a);
	double tmp;
	if (z <= -6.8e+55) {
		tmp = x - a;
	} else if (z <= -3.7e-57) {
		tmp = x;
	} else if (z <= -2.25e-250) {
		tmp = t_1;
	} else if (z <= 1.35e-171) {
		tmp = x;
	} else if (z <= 9.8e-55) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -6.8e+55:
		tmp = x - a
	elif z <= -3.7e-57:
		tmp = x
	elif z <= -2.25e-250:
		tmp = t_1
	elif z <= 1.35e-171:
		tmp = x
	elif z <= 9.8e-55:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -6.8e+55)
		tmp = Float64(x - a);
	elseif (z <= -3.7e-57)
		tmp = x;
	elseif (z <= -2.25e-250)
		tmp = t_1;
	elseif (z <= 1.35e-171)
		tmp = x;
	elseif (z <= 9.8e-55)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -6.8e+55)
		tmp = x - a;
	elseif (z <= -3.7e-57)
		tmp = x;
	elseif (z <= -2.25e-250)
		tmp = t_1;
	elseif (z <= 1.35e-171)
		tmp = x;
	elseif (z <= 9.8e-55)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+55], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.7e-57], x, If[LessEqual[z, -2.25e-250], t$95$1, If[LessEqual[z, 1.35e-171], x, If[LessEqual[z, 9.8e-55], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999996e55 or 9.80000000000000071e-55 < z

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 73.2%

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

   if -6.7999999999999996e55 < z < -3.7e-57 or -2.24999999999999997e-250 < z < 1.35000000000000007e-171

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. associate--l+ 89.1%

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

      3. +-commutative 89.1%

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

      4. associate-*r/ 98.3%

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

      5. +-commutative 98.3%

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

      6. associate--l+ 98.3%

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

      7. associate--l+ 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around inf 73.3%

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

   if -3.7e-57 < z < -2.24999999999999997e-250 or 1.35000000000000007e-171 < z < 9.80000000000000071e-55

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 94.2%

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

   6. Taylor expanded in t around 0 74.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-250}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-55}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{y \cdot a}{z}\right) - a\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x (/ (* y a) z)) a)))
   (if (<= z -1.7e+136)
     t_1
     (if (<= z 4100000.0)
       (- x (* a (/ y (+ t 1.0))))
       (if (<= z 8.6e+102)
         (+ x (/ a (/ z y)))
         (if (<= z 1.2e+155) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + ((y * a) / z)) - a;
	double tmp;
	if (z <= -1.7e+136) {
		tmp = t_1;
	} else if (z <= 4100000.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 8.6e+102) {
		tmp = x + (a / (z / y));
	} else if (z <= 1.2e+155) {
		tmp = t_1;
	} else {
		tmp = x - 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 + ((y * a) / z)) - a
    if (z <= (-1.7d+136)) then
        tmp = t_1
    else if (z <= 4100000.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 8.6d+102) then
        tmp = x + (a / (z / y))
    else if (z <= 1.2d+155) then
        tmp = t_1
    else
        tmp = x - 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 + ((y * a) / z)) - a;
	double tmp;
	if (z <= -1.7e+136) {
		tmp = t_1;
	} else if (z <= 4100000.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 8.6e+102) {
		tmp = x + (a / (z / y));
	} else if (z <= 1.2e+155) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + ((y * a) / z)) - a
	tmp = 0
	if z <= -1.7e+136:
		tmp = t_1
	elif z <= 4100000.0:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 8.6e+102:
		tmp = x + (a / (z / y))
	elif z <= 1.2e+155:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + Float64(Float64(y * a) / z)) - a)
	tmp = 0.0
	if (z <= -1.7e+136)
		tmp = t_1;
	elseif (z <= 4100000.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 8.6e+102)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	elseif (z <= 1.2e+155)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + ((y * a) / z)) - a;
	tmp = 0.0;
	if (z <= -1.7e+136)
		tmp = t_1;
	elseif (z <= 4100000.0)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 8.6e+102)
		tmp = x + (a / (z / y));
	elseif (z <= 1.2e+155)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]}, If[LessEqual[z, -1.7e+136], t$95$1, If[LessEqual[z, 4100000.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+102], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+155], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.69999999999999998e136 or 8.6000000000000002e102 < z < 1.2000000000000001e155

   1. Initial program 93.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. distribute-neg-frac2 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around 0 86.3%

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

   if -1.69999999999999998e136 < z < 4.1e6

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 88.1%

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

   if 4.1e6 < z < 8.6000000000000002e102

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate--l+ 78.6%

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

      3. +-commutative 78.6%

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

      4. associate-*r/ 85.0%

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

      5. +-commutative 85.0%

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

      6. associate--l+ 85.0%

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

      7. associate--l+ 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 81.6%

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

   10. Simplified 81.6%

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

       1. clear-num 81.6%

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

       2. un-div-inv 81.7%

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

   12. Applied egg-rr 81.7%

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

   if 1.2000000000000001e155 < z

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.1%

      \[\leadsto x - \color{blue}{a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;\left(x + \frac{y \cdot a}{z}\right) - a\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+155}:\\ \;\;\;\;\left(x + \frac{y \cdot a}{z}\right) - a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -60000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (* y (/ a t)))))
   (if (<= t -60000000000000.0)
     t_2
     (if (<= t -7e-154)
       t_1
       (if (<= t 8.8e-84) (- x a) (if (<= t 4.6e-26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (y * (a / t));
	double tmp;
	if (t <= -60000000000000.0) {
		tmp = t_2;
	} else if (t <= -7e-154) {
		tmp = t_1;
	} else if (t <= 8.8e-84) {
		tmp = x - a;
	} else if (t <= 4.6e-26) {
		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 * a)
    t_2 = x - (y * (a / t))
    if (t <= (-60000000000000.0d0)) then
        tmp = t_2
    else if (t <= (-7d-154)) then
        tmp = t_1
    else if (t <= 8.8d-84) then
        tmp = x - a
    else if (t <= 4.6d-26) 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 * a);
	double t_2 = x - (y * (a / t));
	double tmp;
	if (t <= -60000000000000.0) {
		tmp = t_2;
	} else if (t <= -7e-154) {
		tmp = t_1;
	} else if (t <= 8.8e-84) {
		tmp = x - a;
	} else if (t <= 4.6e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (y * (a / t))
	tmp = 0
	if t <= -60000000000000.0:
		tmp = t_2
	elif t <= -7e-154:
		tmp = t_1
	elif t <= 8.8e-84:
		tmp = x - a
	elif t <= 4.6e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (t <= -60000000000000.0)
		tmp = t_2;
	elseif (t <= -7e-154)
		tmp = t_1;
	elseif (t <= 8.8e-84)
		tmp = Float64(x - a);
	elseif (t <= 4.6e-26)
		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 * a);
	t_2 = x - (y * (a / t));
	tmp = 0.0;
	if (t <= -60000000000000.0)
		tmp = t_2;
	elseif (t <= -7e-154)
		tmp = t_1;
	elseif (t <= 8.8e-84)
		tmp = x - a;
	elseif (t <= 4.6e-26)
		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 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -60000000000000.0], t$95$2, If[LessEqual[t, -7e-154], t$95$1, If[LessEqual[t, 8.8e-84], N[(x - a), $MachinePrecision], If[LessEqual[t, 4.6e-26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e13 or 4.60000000000000018e-26 < t

   1. Initial program 96.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate--l+ 85.9%

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

      3. +-commutative 85.9%

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

      4. associate-*r/ 89.5%

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

      5. +-commutative 89.5%

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

      6. associate--l+ 89.5%

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

      7. associate--l+ 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t around inf 86.7%

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

   if -6e13 < t < -7.0000000000000001e-154 or 8.7999999999999996e-84 < t < 4.60000000000000018e-26

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 76.6%

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

   6. Taylor expanded in t around 0 74.6%

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

   if -7.0000000000000001e-154 < t < 8.7999999999999996e-84

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -60000000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-154}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+55)
   (- x a)
   (if (<= z -3.2e-68)
     x
     (if (<= z -5e-112) (* a (- y)) (if (<= z 8.8e-107) x (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+55) {
		tmp = x - a;
	} else if (z <= -3.2e-68) {
		tmp = x;
	} else if (z <= -5e-112) {
		tmp = a * -y;
	} else if (z <= 8.8e-107) {
		tmp = x;
	} else {
		tmp = x - 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 <= (-4.3d+55)) then
        tmp = x - a
    else if (z <= (-3.2d-68)) then
        tmp = x
    else if (z <= (-5d-112)) then
        tmp = a * -y
    else if (z <= 8.8d-107) then
        tmp = x
    else
        tmp = x - 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 <= -4.3e+55) {
		tmp = x - a;
	} else if (z <= -3.2e-68) {
		tmp = x;
	} else if (z <= -5e-112) {
		tmp = a * -y;
	} else if (z <= 8.8e-107) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+55:
		tmp = x - a
	elif z <= -3.2e-68:
		tmp = x
	elif z <= -5e-112:
		tmp = a * -y
	elif z <= 8.8e-107:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+55)
		tmp = Float64(x - a);
	elseif (z <= -3.2e-68)
		tmp = x;
	elseif (z <= -5e-112)
		tmp = Float64(a * Float64(-y));
	elseif (z <= 8.8e-107)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+55)
		tmp = x - a;
	elseif (z <= -3.2e-68)
		tmp = x;
	elseif (z <= -5e-112)
		tmp = a * -y;
	elseif (z <= 8.8e-107)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+55], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.2e-68], x, If[LessEqual[z, -5e-112], N[(a * (-y)), $MachinePrecision], If[LessEqual[z, 8.8e-107], x, N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2999999999999999e55 or 8.8000000000000005e-107 < z

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 73.2%

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

   if -4.2999999999999999e55 < z < -3.1999999999999999e-68 or -5.00000000000000044e-112 < z < 8.8000000000000005e-107

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. associate--l+ 91.7%

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

      3. +-commutative 91.7%

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

      4. associate-*r/ 95.3%

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

      5. +-commutative 95.3%

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

      6. associate--l+ 95.3%

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

      7. associate--l+ 95.3%

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

   7. Simplified 95.3%

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

   8. Taylor expanded in x around inf 63.3%

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

   if -3.1999999999999999e-68 < z < -5.00000000000000044e-112

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in z around 0 84.4%

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

   6. Taylor expanded in x around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*r/ 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

      4. distribute-neg-frac2 60.1%

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

      5. distribute-neg-in 60.1%

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

      6. metadata-eval 60.1%

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

      7. sub-neg 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in t around 0 51.5%

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

       1. associate-*r* 51.5%

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

       2. neg-mul-1 51.5%

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

       3. *-commutative 51.5%

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

   11. Simplified 51.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5500000:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+135)
   (- x a)
   (if (<= z 5500000.0)
     (- x (* a (/ y (+ t 1.0))))
     (if (<= z 3.15e+88) (+ x (/ a (/ z y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+135) {
		tmp = x - a;
	} else if (z <= 5500000.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.15e+88) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - 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 <= (-5.6d+135)) then
        tmp = x - a
    else if (z <= 5500000.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 3.15d+88) then
        tmp = x + (a / (z / y))
    else
        tmp = x - 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 <= -5.6e+135) {
		tmp = x - a;
	} else if (z <= 5500000.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.15e+88) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+135:
		tmp = x - a
	elif z <= 5500000.0:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 3.15e+88:
		tmp = x + (a / (z / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+135)
		tmp = Float64(x - a);
	elseif (z <= 5500000.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 3.15e+88)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+135)
		tmp = x - a;
	elseif (z <= 5500000.0)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 3.15e+88)
		tmp = x + (a / (z / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+135], N[(x - a), $MachinePrecision], If[LessEqual[z, 5500000.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e+88], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000004e135 or 3.15e88 < z

   1. Initial program 96.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   if -5.60000000000000004e135 < z < 5.5e6

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 88.6%

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

   if 5.5e6 < z < 3.15e88

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate--l+ 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-*r/ 81.1%

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

      5. +-commutative 81.1%

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

      6. associate--l+ 81.1%

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

      7. associate--l+ 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 80.9%

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

   10. Simplified 80.9%

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

       1. clear-num 80.9%

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

       2. un-div-inv 80.9%

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

   12. Applied egg-rr 80.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+135}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5500000:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+136)
   (- x a)
   (if (<= z 3400000.0)
     (- x (* y (/ a (+ t 1.0))))
     (if (<= z 2.5e+89) (+ x (/ a (/ z y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+136) {
		tmp = x - a;
	} else if (z <= 3400000.0) {
		tmp = x - (y * (a / (t + 1.0)));
	} else if (z <= 2.5e+89) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - 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 <= (-1.8d+136)) then
        tmp = x - a
    else if (z <= 3400000.0d0) then
        tmp = x - (y * (a / (t + 1.0d0)))
    else if (z <= 2.5d+89) then
        tmp = x + (a / (z / y))
    else
        tmp = x - 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 <= -1.8e+136) {
		tmp = x - a;
	} else if (z <= 3400000.0) {
		tmp = x - (y * (a / (t + 1.0)));
	} else if (z <= 2.5e+89) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+136:
		tmp = x - a
	elif z <= 3400000.0:
		tmp = x - (y * (a / (t + 1.0)))
	elif z <= 2.5e+89:
		tmp = x + (a / (z / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+136)
		tmp = Float64(x - a);
	elseif (z <= 3400000.0)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t + 1.0))));
	elseif (z <= 2.5e+89)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+136)
		tmp = x - a;
	elseif (z <= 3400000.0)
		tmp = x - (y * (a / (t + 1.0)));
	elseif (z <= 2.5e+89)
		tmp = x + (a / (z / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+136], N[(x - a), $MachinePrecision], If[LessEqual[z, 3400000.0], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+89], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000003e136 or 2.49999999999999992e89 < z

   1. Initial program 96.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.5%

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

   if -1.80000000000000003e136 < z < 3.4e6

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

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

   if 3.4e6 < z < 2.49999999999999992e89

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate--l+ 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-*r/ 81.1%

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

      5. +-commutative 81.1%

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

      6. associate--l+ 81.1%

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

      7. associate--l+ 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 80.9%

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

   10. Simplified 80.9%

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

       1. clear-num 80.9%

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

       2. un-div-inv 80.9%

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

   12. Applied egg-rr 80.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+46} \lor \neg \left(y \leq 31000\right):\\ \;\;\;\;x - y \cdot \frac{a}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.9e+46) (not (<= y 31000.0)))
   (- x (* y (/ a (+ (- t z) 1.0))))
   (+ x (* a (/ z (- (+ t 1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e+46) || !(y <= 31000.0)) {
		tmp = x - (y * (a / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (z / ((t + 1.0) - 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 ((y <= (-1.9d+46)) .or. (.not. (y <= 31000.0d0))) then
        tmp = x - (y * (a / ((t - z) + 1.0d0)))
    else
        tmp = x + (a * (z / ((t + 1.0d0) - 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 ((y <= -1.9e+46) || !(y <= 31000.0)) {
		tmp = x - (y * (a / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (z / ((t + 1.0) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.9e+46) or not (y <= 31000.0):
		tmp = x - (y * (a / ((t - z) + 1.0)))
	else:
		tmp = x + (a * (z / ((t + 1.0) - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.9e+46) || !(y <= 31000.0))
		tmp = Float64(x - Float64(y * Float64(a / Float64(Float64(t - z) + 1.0))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t + 1.0) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.9e+46) || ~((y <= 31000.0)))
		tmp = x - (y * (a / ((t - z) + 1.0)));
	else
		tmp = x + (a * (z / ((t + 1.0) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.9e+46], N[Not[LessEqual[y, 31000.0]], $MachinePrecision]], N[(x - N[(y * N[(a / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e46 or 31000 < y

   1. Initial program 96.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. associate--l+ 79.6%

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

      3. +-commutative 79.6%

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

      4. associate-*r/ 89.0%

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

      5. +-commutative 89.0%

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

      6. associate--l+ 89.0%

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

      7. associate--l+ 89.0%

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

   7. Simplified 89.0%

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

   if -1.9e46 < y < 31000

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 93.1%

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

      1. mul-1-neg 93.1%

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

      2. associate--l+ 93.1%

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

      3. +-commutative 93.1%

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

      4. distribute-neg-frac2 93.1%

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

      5. +-commutative 93.1%

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

      6. distribute-neg-in 93.1%

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

      7. metadata-eval 93.1%

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

      8. unsub-neg 93.1%

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

      9. associate--r- 93.1%

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

   7. Simplified 93.1%

      \[\leadsto x - \color{blue}{\frac{z}{\left(-1 - t\right) + z}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+46} \lor \neg \left(y \leq 31000\right):\\ \;\;\;\;x - y \cdot \frac{a}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+56} \lor \neg \left(z \leq 8.8 \cdot 10^{+102}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+56) (not (<= z 8.8e+102)))
   (+ x (/ (- y z) (/ z a)))
   (- x (* y (/ a (+ (- t z) 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+56) || !(z <= 8.8e+102)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x - (y * (a / ((t - z) + 1.0)));
	}
	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 <= (-1.15d+56)) .or. (.not. (z <= 8.8d+102))) then
        tmp = x + ((y - z) / (z / a))
    else
        tmp = x - (y * (a / ((t - z) + 1.0d0)))
    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 <= -1.15e+56) || !(z <= 8.8e+102)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x - (y * (a / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+56) or not (z <= 8.8e+102):
		tmp = x + ((y - z) / (z / a))
	else:
		tmp = x - (y * (a / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+56) || !(z <= 8.8e+102))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	else
		tmp = Float64(x - Float64(y * Float64(a / Float64(Float64(t - z) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+56) || ~((z <= 8.8e+102)))
		tmp = x + ((y - z) / (z / a));
	else
		tmp = x - (y * (a / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+56], N[Not[LessEqual[z, 8.8e+102]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(a / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000007e56 or 8.8000000000000003e102 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.4%

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

      1. mul-1-neg 91.4%

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

      2. distribute-neg-frac2 91.4%

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

   5. Simplified 91.4%

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

   if -1.15000000000000007e56 < z < 8.8000000000000003e102

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. associate--l+ 87.0%

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

      3. +-commutative 87.0%

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

      4. associate-*r/ 90.8%

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

      5. +-commutative 90.8%

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

      6. associate--l+ 90.8%

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

      7. associate--l+ 90.8%

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

   7. Simplified 90.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+56} \lor \neg \left(z \leq 8.8 \cdot 10^{+102}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 0.0035:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+81)
   (- x (* a (/ y (+ t 1.0))))
   (if (<= t 0.0035)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (+ x (/ (- y z) (/ (- -1.0 t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+81) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 0.0035) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + ((y - z) / ((-1.0 - 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 <= (-5.2d+81)) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (t <= 0.0035d0) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x + ((y - z) / (((-1.0d0) - 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 <= -5.2e+81) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 0.0035) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+81:
		tmp = x - (a * (y / (t + 1.0)))
	elif t <= 0.0035:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+81)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (t <= 0.0035)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+81)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (t <= 0.0035)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+81], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0035], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.19999999999999984e81

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 96.4%

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

   if -5.19999999999999984e81 < t < 0.00350000000000000007

   1. Initial program 98.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 96.4%

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

   if 0.00350000000000000007 < t

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 0.0035:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+83}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 0.045:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+83)
   (- x (* a (/ y (+ t 1.0))))
   (if (<= t 0.045)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (- x (/ (- y z) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+83) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 0.045) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (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 <= (-3.9d+83)) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (t <= 0.045d0) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x - ((y - z) / (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 <= -3.9e+83) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 0.045) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+83:
		tmp = x - (a * (y / (t + 1.0)))
	elif t <= 0.045:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x - ((y - z) / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+83)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (t <= 0.045)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.9e+83)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (t <= 0.045)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x - ((y - z) / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+83], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.045], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9000000000000002e83

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 96.4%

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

   if -3.9000000000000002e83 < t < 0.044999999999999998

   1. Initial program 98.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 96.4%

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

   if 0.044999999999999998 < t

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+83}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 0.045:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+101} \lor \neg \left(z \leq 2400000\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.22e+101) (not (<= z 2400000.0)))
   (+ x (/ (- y z) (/ z a)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+101) || !(z <= 2400000.0)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	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 <= (-1.22d+101)) .or. (.not. (z <= 2400000.0d0))) then
        tmp = x + ((y - z) / (z / a))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    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 <= -1.22e+101) || !(z <= 2400000.0)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.22e+101) or not (z <= 2400000.0):
		tmp = x + ((y - z) / (z / a))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.22e+101) || !(z <= 2400000.0))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.22e+101) || ~((z <= 2400000.0)))
		tmp = x + ((y - z) / (z / a));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.22e+101], N[Not[LessEqual[z, 2400000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e101 or 2.4e6 < z

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-neg-frac2 89.9%

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

   5. Simplified 89.9%

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

   if -1.22e101 < z < 2.4e6

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around 0 90.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+101} \lor \neg \left(z \leq 2400000\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+135} \lor \neg \left(z \leq 1.9 \cdot 10^{-122}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+135) (not (<= z 1.9e-122))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+135) || !(z <= 1.9e-122)) {
		tmp = x - a;
	} 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 <= (-5d+135)) .or. (.not. (z <= 1.9d-122))) then
        tmp = x - a
    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 <= -5e+135) || !(z <= 1.9e-122)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e+135) or not (z <= 1.9e-122):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+135) || !(z <= 1.9e-122))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e+135) || ~((z <= 1.9e-122)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+135], N[Not[LessEqual[z, 1.9e-122]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000029e135 or 1.9e-122 < z

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -5.00000000000000029e135 < z < 1.9e-122

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate--l+ 87.2%

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

      3. +-commutative 87.2%

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

      4. associate-*r/ 92.3%

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

      5. +-commutative 92.3%

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

      6. associate--l+ 92.3%

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

      7. associate--l+ 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in x around inf 61.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+135} \lor \neg \left(z \leq 1.9 \cdot 10^{-122}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.1% accurate, 13.0× 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 98.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in y around inf 78.6%

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

   1. *-commutative 78.6%

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

   2. associate--l+ 78.6%

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

   3. +-commutative 78.6%

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

   4. associate-*r/ 82.6%

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

   5. +-commutative 82.6%

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

   6. associate--l+ 82.6%

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

   7. associate--l+ 82.6%

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

7. Simplified 82.6%

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

8. Taylor expanded in x around inf 58.9%

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

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * 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) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))