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

Percentage Accurate: 97.1% → 99.6%

Time: 11.8s

Alternatives: 18

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: 97.1% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (a * ((y - z) / ((-1.0d0) + (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.9%

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

Alternative 2: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-5} \lor \neg \left(z \leq 7.7 \cdot 10^{+18}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -1.95e+149)
     t_1
     (if (<= z -2e+24)
       (- x (* a (/ (- y z) t)))
       (if (or (<= z -3.3e-5) (not (<= z 7.7e+18)))
         t_1
         (+ x (* a (/ y (- -1.0 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -2e+24) {
		tmp = x - (a * ((y - z) / t));
	} else if ((z <= -3.3e-5) || !(z <= 7.7e+18)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-1.95d+149)) then
        tmp = t_1
    else if (z <= (-2d+24)) then
        tmp = x - (a * ((y - z) / t))
    else if ((z <= (-3.3d-5)) .or. (.not. (z <= 7.7d+18))) then
        tmp = t_1
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    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 + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -2e+24) {
		tmp = x - (a * ((y - z) / t));
	} else if ((z <= -3.3e-5) || !(z <= 7.7e+18)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -1.95e+149:
		tmp = t_1
	elif z <= -2e+24:
		tmp = x - (a * ((y - z) / t))
	elif (z <= -3.3e-5) or not (z <= 7.7e+18):
		tmp = t_1
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -2e+24)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	elseif ((z <= -3.3e-5) || !(z <= 7.7e+18))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -2e+24)
		tmp = x - (a * ((y - z) / t));
	elseif ((z <= -3.3e-5) || ~((z <= 7.7e+18)))
		tmp = t_1;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+149], t$95$1, If[LessEqual[z, -2e+24], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.3e-5], N[Not[LessEqual[z, 7.7e+18]], $MachinePrecision]], t$95$1, N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e149 or -2e24 < z < -3.3000000000000003e-5 or 7.7e18 < z

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-neg-frac2 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r/ 88.1%

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

      4. unsub-neg 88.1%

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

      5. associate-*r/ 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-/l* 88.1%

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

   8. Simplified 88.1%

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

   if -1.95e149 < z < -2e24

   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 t around inf 84.0%

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

   if -3.3000000000000003e-5 < z < 7.7e18

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-5} \lor \neg \left(z \leq 7.7 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-5} \lor \neg \left(z \leq 2.55 \cdot 10^{+19}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -1.95e+149)
     t_1
     (if (<= z -1.85e+24)
       (+ x (/ a (/ t (- z y))))
       (if (or (<= z -3.3e-5) (not (<= z 2.55e+19)))
         t_1
         (+ x (* a (/ y (- -1.0 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -1.85e+24) {
		tmp = x + (a / (t / (z - y)));
	} else if ((z <= -3.3e-5) || !(z <= 2.55e+19)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-1.95d+149)) then
        tmp = t_1
    else if (z <= (-1.85d+24)) then
        tmp = x + (a / (t / (z - y)))
    else if ((z <= (-3.3d-5)) .or. (.not. (z <= 2.55d+19))) then
        tmp = t_1
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    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 + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -1.85e+24) {
		tmp = x + (a / (t / (z - y)));
	} else if ((z <= -3.3e-5) || !(z <= 2.55e+19)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -1.95e+149:
		tmp = t_1
	elif z <= -1.85e+24:
		tmp = x + (a / (t / (z - y)))
	elif (z <= -3.3e-5) or not (z <= 2.55e+19):
		tmp = t_1
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -1.85e+24)
		tmp = Float64(x + Float64(a / Float64(t / Float64(z - y))));
	elseif ((z <= -3.3e-5) || !(z <= 2.55e+19))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -1.85e+24)
		tmp = x + (a / (t / (z - y)));
	elseif ((z <= -3.3e-5) || ~((z <= 2.55e+19)))
		tmp = t_1;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+149], t$95$1, If[LessEqual[z, -1.85e+24], N[(x + N[(a / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.3e-5], N[Not[LessEqual[z, 2.55e+19]], $MachinePrecision]], t$95$1, N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e149 or -1.85e24 < z < -3.3000000000000003e-5 or 2.55e19 < z

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-neg-frac2 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r/ 88.1%

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

      4. unsub-neg 88.1%

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

      5. associate-*r/ 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-/l* 88.1%

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

   8. Simplified 88.1%

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

   if -1.95e149 < z < -1.85e24

   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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 84.1%

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

   if -3.3000000000000003e-5 < z < 2.55e19

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-5} \lor \neg \left(z \leq 2.55 \cdot 10^{+19}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+149)
   (- x a)
   (if (<= z -2.5e+24)
     (- x (* a (/ (- y z) t)))
     (if (<= z -4.3e-7)
       (+ x (* a (/ y z)))
       (if (<= z 2.3e+86) (+ x (* a (/ y (- -1.0 t)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+149) {
		tmp = x - a;
	} else if (z <= -2.5e+24) {
		tmp = x - (a * ((y - z) / t));
	} else if (z <= -4.3e-7) {
		tmp = x + (a * (y / z));
	} else if (z <= 2.3e+86) {
		tmp = x + (a * (y / (-1.0 - t)));
	} 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 <= (-1.95d+149)) then
        tmp = x - a
    else if (z <= (-2.5d+24)) then
        tmp = x - (a * ((y - z) / t))
    else if (z <= (-4.3d-7)) then
        tmp = x + (a * (y / z))
    else if (z <= 2.3d+86) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    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 <= -1.95e+149) {
		tmp = x - a;
	} else if (z <= -2.5e+24) {
		tmp = x - (a * ((y - z) / t));
	} else if (z <= -4.3e-7) {
		tmp = x + (a * (y / z));
	} else if (z <= 2.3e+86) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+149:
		tmp = x - a
	elif z <= -2.5e+24:
		tmp = x - (a * ((y - z) / t))
	elif z <= -4.3e-7:
		tmp = x + (a * (y / z))
	elif z <= 2.3e+86:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+149)
		tmp = Float64(x - a);
	elseif (z <= -2.5e+24)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	elseif (z <= -4.3e-7)
		tmp = Float64(x + Float64(a * Float64(y / z)));
	elseif (z <= 2.3e+86)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+149)
		tmp = x - a;
	elseif (z <= -2.5e+24)
		tmp = x - (a * ((y - z) / t));
	elseif (z <= -4.3e-7)
		tmp = x + (a * (y / z));
	elseif (z <= 2.3e+86)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+149], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.5e+24], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.3e-7], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+86], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95e149 or 2.2999999999999999e86 < z

   1. Initial program 94.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 85.1%

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

   if -1.95e149 < z < -2.50000000000000023e24

   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 t around inf 84.0%

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

   if -2.50000000000000023e24 < z < -4.3000000000000001e-7

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-neg-frac2 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in y around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. associate-/l* 62.8%

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

      3. distribute-rgt-neg-in 62.8%

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

      4. distribute-frac-neg 62.8%

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

   8. Simplified 62.8%

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

   if -4.3000000000000001e-7 < z < 2.2999999999999999e86

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 89.6%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -1.95e+149)
     t_1
     (if (<= z -2.5e+24)
       (+ x (/ a (/ t (- z y))))
       (if (<= z -2.1e-12)
         (- x (/ (* y a) (- 1.0 z)))
         (if (<= z 8.2e+18) (+ x (* a (/ y (- -1.0 t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -2.5e+24) {
		tmp = x + (a / (t / (z - y)));
	} else if (z <= -2.1e-12) {
		tmp = x - ((y * a) / (1.0 - z));
	} else if (z <= 8.2e+18) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-1.95d+149)) then
        tmp = t_1
    else if (z <= (-2.5d+24)) then
        tmp = x + (a / (t / (z - y)))
    else if (z <= (-2.1d-12)) then
        tmp = x - ((y * a) / (1.0d0 - z))
    else if (z <= 8.2d+18) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.95e+149) {
		tmp = t_1;
	} else if (z <= -2.5e+24) {
		tmp = x + (a / (t / (z - y)));
	} else if (z <= -2.1e-12) {
		tmp = x - ((y * a) / (1.0 - z));
	} else if (z <= 8.2e+18) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -1.95e+149:
		tmp = t_1
	elif z <= -2.5e+24:
		tmp = x + (a / (t / (z - y)))
	elif z <= -2.1e-12:
		tmp = x - ((y * a) / (1.0 - z))
	elif z <= 8.2e+18:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -2.5e+24)
		tmp = Float64(x + Float64(a / Float64(t / Float64(z - y))));
	elseif (z <= -2.1e-12)
		tmp = Float64(x - Float64(Float64(y * a) / Float64(1.0 - z)));
	elseif (z <= 8.2e+18)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -1.95e+149)
		tmp = t_1;
	elseif (z <= -2.5e+24)
		tmp = x + (a / (t / (z - y)));
	elseif (z <= -2.1e-12)
		tmp = x - ((y * a) / (1.0 - z));
	elseif (z <= 8.2e+18)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+149], t$95$1, If[LessEqual[z, -2.5e+24], N[(x + N[(a / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-12], N[(x - N[(N[(y * a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+18], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95e149 or 8.2e18 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-neg-frac2 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r/ 90.0%

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

      4. unsub-neg 90.0%

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

      5. associate-*r/ 79.6%

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

      6. *-commutative 79.6%

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

      7. associate-/l* 90.0%

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

   8. Simplified 90.0%

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

   if -1.95e149 < z < -2.50000000000000023e24

   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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 84.1%

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

   if -2.50000000000000023e24 < z < -2.09999999999999994e-12

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 71.9%

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

   6. Taylor expanded in t around 0 71.9%

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

   if -2.09999999999999994e-12 < z < 8.2e18

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.3%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -350000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+19}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -2e+149)
     t_1
     (if (<= z -350000.0)
       (+ x (/ (- z y) (/ t a)))
       (if (<= z 6.6e+19) (+ x (* a (/ y (- -1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -2e+149) {
		tmp = t_1;
	} else if (z <= -350000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 6.6e+19) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-2d+149)) then
        tmp = t_1
    else if (z <= (-350000.0d0)) then
        tmp = x + ((z - y) / (t / a))
    else if (z <= 6.6d+19) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -2e+149) {
		tmp = t_1;
	} else if (z <= -350000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 6.6e+19) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -2e+149:
		tmp = t_1
	elif z <= -350000.0:
		tmp = x + ((z - y) / (t / a))
	elif z <= 6.6e+19:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -2e+149)
		tmp = t_1;
	elseif (z <= -350000.0)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (z <= 6.6e+19)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -2e+149)
		tmp = t_1;
	elseif (z <= -350000.0)
		tmp = x + ((z - y) / (t / a));
	elseif (z <= 6.6e+19)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+149], t$95$1, If[LessEqual[z, -350000.0], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+19], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e149 or 6.6e19 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-neg-frac2 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r/ 90.0%

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

      4. unsub-neg 90.0%

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

      5. associate-*r/ 79.6%

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

      6. *-commutative 79.6%

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

      7. associate-/l* 90.0%

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

   8. Simplified 90.0%

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

   if -2.0000000000000001e149 < z < -3.5e5

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 80.3%

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

   if -3.5e5 < z < 6.6e19

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+149}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -350000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+19}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+19}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -2e+160)
     t_1
     (if (<= z -1.3e-6)
       (- x (* z (/ a (+ z (- -1.0 t)))))
       (if (<= z 5.1e+19) (+ x (* a (/ y (- -1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -2e+160) {
		tmp = t_1;
	} else if (z <= -1.3e-6) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if (z <= 5.1e+19) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-2d+160)) then
        tmp = t_1
    else if (z <= (-1.3d-6)) then
        tmp = x - (z * (a / (z + ((-1.0d0) - t))))
    else if (z <= 5.1d+19) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -2e+160) {
		tmp = t_1;
	} else if (z <= -1.3e-6) {
		tmp = x - (z * (a / (z + (-1.0 - t))));
	} else if (z <= 5.1e+19) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -2e+160:
		tmp = t_1
	elif z <= -1.3e-6:
		tmp = x - (z * (a / (z + (-1.0 - t))))
	elif z <= 5.1e+19:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -2e+160)
		tmp = t_1;
	elseif (z <= -1.3e-6)
		tmp = Float64(x - Float64(z * Float64(a / Float64(z + Float64(-1.0 - t)))));
	elseif (z <= 5.1e+19)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -2e+160)
		tmp = t_1;
	elseif (z <= -1.3e-6)
		tmp = x - (z * (a / (z + (-1.0 - t))));
	elseif (z <= 5.1e+19)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+160], t$95$1, If[LessEqual[z, -1.3e-6], N[(x - N[(z * N[(a / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+19], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000001e160 or 5.1e19 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-neg-frac2 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r/ 90.5%

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

      4. unsub-neg 90.5%

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

      5. associate-*r/ 79.6%

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

      6. *-commutative 79.6%

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

      7. associate-/l* 90.5%

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

   8. Simplified 90.5%

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

   if -2.00000000000000001e160 < z < -1.30000000000000005e-6

   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 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. *-commutative 65.7%

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

      3. associate--l+ 65.7%

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

      4. +-commutative 65.7%

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

      5. associate-*r/ 78.0%

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

      6. distribute-rgt-neg-in 78.0%

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

      7. distribute-neg-frac2 78.0%

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

      8. +-commutative 78.0%

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

      9. distribute-neg-in 78.0%

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

      10. metadata-eval 78.0%

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

      11. unsub-neg 78.0%

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

      12. associate--r- 78.0%

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

   7. Simplified 78.0%

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

   if -1.30000000000000005e-6 < z < 5.1e19

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+160}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+19}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(-1 - t\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-15} \lor \neg \left(y \leq 0.000235\right):\\ \;\;\;\;x + a \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ z (- -1.0 t))))
   (if (or (<= y -4.2e-15) (not (<= y 0.000235)))
     (+ x (* a (/ y t_1)))
     (- x (* z (/ a t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -4.2e-15) || !(y <= 0.000235)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (z * (a / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((-1.0d0) - t)
    if ((y <= (-4.2d-15)) .or. (.not. (y <= 0.000235d0))) then
        tmp = x + (a * (y / t_1))
    else
        tmp = x - (z * (a / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -4.2e-15) || !(y <= 0.000235)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (z * (a / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z + (-1.0 - t)
	tmp = 0
	if (y <= -4.2e-15) or not (y <= 0.000235):
		tmp = x + (a * (y / t_1))
	else:
		tmp = x - (z * (a / t_1))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z + Float64(-1.0 - t))
	tmp = 0.0
	if ((y <= -4.2e-15) || !(y <= 0.000235))
		tmp = Float64(x + Float64(a * Float64(y / t_1)));
	else
		tmp = Float64(x - Float64(z * Float64(a / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z + (-1.0 - t);
	tmp = 0.0;
	if ((y <= -4.2e-15) || ~((y <= 0.000235)))
		tmp = x + (a * (y / t_1));
	else
		tmp = x - (z * (a / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -4.2e-15], N[Not[LessEqual[y, 0.000235]], $MachinePrecision]], N[(x + N[(a * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.19999999999999962e-15 or 2.34999999999999993e-4 < y

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.8%

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

   if -4.19999999999999962e-15 < y < 2.34999999999999993e-4

   1. Initial program 98.0%

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

      1. associate-/r/ 99.9%

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

   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 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-commutative 81.8%

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

      3. associate--l+ 81.8%

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

      4. +-commutative 81.8%

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

      5. associate-*r/ 93.0%

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

      6. distribute-rgt-neg-in 93.0%

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

      7. distribute-neg-frac2 93.0%

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

      8. +-commutative 93.0%

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

      9. distribute-neg-in 93.0%

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

      10. metadata-eval 93.0%

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

      11. unsub-neg 93.0%

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

      12. associate--r- 93.0%

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

   7. Simplified 93.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-15} \lor \neg \left(y \leq 0.000235\right):\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(-1 - t\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-13} \lor \neg \left(y \leq 1.06 \cdot 10^{+49}\right):\\ \;\;\;\;x + a \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ z (- -1.0 t))))
   (if (or (<= y -1.45e-13) (not (<= y 1.06e+49)))
     (+ x (* a (/ y t_1)))
     (- x (* a (/ z t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -1.45e-13) || !(y <= 1.06e+49)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (a * (z / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((-1.0d0) - t)
    if ((y <= (-1.45d-13)) .or. (.not. (y <= 1.06d+49))) then
        tmp = x + (a * (y / t_1))
    else
        tmp = x - (a * (z / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -1.45e-13) || !(y <= 1.06e+49)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (a * (z / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z + (-1.0 - t)
	tmp = 0
	if (y <= -1.45e-13) or not (y <= 1.06e+49):
		tmp = x + (a * (y / t_1))
	else:
		tmp = x - (a * (z / t_1))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z + Float64(-1.0 - t))
	tmp = 0.0
	if ((y <= -1.45e-13) || !(y <= 1.06e+49))
		tmp = Float64(x + Float64(a * Float64(y / t_1)));
	else
		tmp = Float64(x - Float64(a * Float64(z / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z + (-1.0 - t);
	tmp = 0.0;
	if ((y <= -1.45e-13) || ~((y <= 1.06e+49)))
		tmp = x + (a * (y / t_1));
	else
		tmp = x - (a * (z / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -1.45e-13], N[Not[LessEqual[y, 1.06e+49]], $MachinePrecision]], N[(x + N[(a * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e-13 or 1.06e49 < y

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 88.4%

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

   if -1.4499999999999999e-13 < y < 1.06e49

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. associate--l+ 94.3%

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

      3. +-commutative 94.3%

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

      4. distribute-neg-frac2 94.3%

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

      5. +-commutative 94.3%

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

      6. distribute-neg-in 94.3%

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

      7. metadata-eval 94.3%

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

      8. unsub-neg 94.3%

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

      9. associate--r- 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-13} \lor \neg \left(y \leq 1.06 \cdot 10^{+49}\right):\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 1.7 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+149) (not (<= z 1.7e+18)))
   (+ x (- (* a (/ y z)) a))
   (+ x (/ (- y z) (/ (- -1.0 t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+149) || !(z <= 1.7e+18)) {
		tmp = x + ((a * (y / z)) - a);
	} 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 ((z <= (-1.95d+149)) .or. (.not. (z <= 1.7d+18))) then
        tmp = x + ((a * (y / z)) - a)
    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 ((z <= -1.95e+149) || !(z <= 1.7e+18)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+149) or not (z <= 1.7e+18):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+149) || !(z <= 1.7e+18))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	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 ((z <= -1.95e+149) || ~((z <= 1.7e+18)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+149], N[Not[LessEqual[z, 1.7e+18]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e149 or 1.7e18 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-neg-frac2 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r/ 90.0%

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

      4. unsub-neg 90.0%

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

      5. associate-*r/ 79.6%

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

      6. *-commutative 79.6%

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

      7. associate-/l* 90.0%

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

   8. Simplified 90.0%

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

   if -1.95e149 < z < 1.7e18

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 94.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 1.7 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+149} \lor \neg \left(z \leq 8.5 \cdot 10^{+86}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+149) (not (<= z 8.5e+86)))
   (- x a)
   (+ x (* y (/ a (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+149) || !(z <= 8.5e+86)) {
		tmp = x - a;
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d+149)) .or. (.not. (z <= 8.5d+86))) then
        tmp = x - a
    else
        tmp = x + (y * (a / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+149) || !(z <= 8.5e+86)) {
		tmp = x - a;
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+149) or not (z <= 8.5e+86):
		tmp = x - a
	else:
		tmp = x + (y * (a / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+149) || !(z <= 8.5e+86))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+149) || ~((z <= 8.5e+86)))
		tmp = x - a;
	else
		tmp = x + (y * (a / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+149], N[Not[LessEqual[z, 8.5e+86]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999995e149 or 8.5000000000000005e86 < z

   1. Initial program 94.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 85.1%

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

   if -2.49999999999999995e149 < z < 8.5000000000000005e86

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+149} \lor \neg \left(z \leq 8.5 \cdot 10^{+86}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 2.6 \cdot 10^{+88}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+149) (not (<= z 2.6e+88)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+149) || !(z <= 2.6e+88)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+149)) .or. (.not. (z <= 2.6d+88))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+149) || !(z <= 2.6e+88)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+149) or not (z <= 2.6e+88):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+149) || !(z <= 2.6e+88))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+149) || ~((z <= 2.6e+88)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+149], N[Not[LessEqual[z, 2.6e+88]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e149 or 2.6000000000000001e88 < z

   1. Initial program 94.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 85.1%

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

   if -1.95e149 < z < 2.6000000000000001e88

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 84.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 2.6 \cdot 10^{+88}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16} \lor \neg \left(t \leq 5.7 \cdot 10^{-5}\right):\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+16) (not (<= t 5.7e-5))) (- x (* y (/ a t))) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+16) || !(t <= 5.7e-5)) {
		tmp = x - (y * (a / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2d+16)) .or. (.not. (t <= 5.7d-5))) then
        tmp = x - (y * (a / t))
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+16) || !(t <= 5.7e-5)) {
		tmp = x - (y * (a / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+16) or not (t <= 5.7e-5):
		tmp = x - (y * (a / t))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+16) || !(t <= 5.7e-5))
		tmp = Float64(x - Float64(y * Float64(a / t)));
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e+16) || ~((t <= 5.7e-5)))
		tmp = x - (y * (a / t));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+16], N[Not[LessEqual[t, 5.7e-5]], $MachinePrecision]], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e16 or 5.7000000000000003e-5 < t

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 83.4%

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

   6. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. clear-num 77.0%

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

      3. un-div-inv 77.0%

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

   8. Applied egg-rr 77.0%

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

      1. associate-/r/ 76.2%

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

   10. Simplified 76.2%

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

   if -2e16 < t < 5.7000000000000003e-5

   1. Initial program 97.5%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 71.8%

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

   8. Taylor expanded in t around 0 71.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16} \lor \neg \left(t \leq 5.7 \cdot 10^{-5}\right):\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16} \lor \neg \left(t \leq 5.7 \cdot 10^{-5}\right):\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+16) (not (<= t 5.7e-5))) (- x (* a (/ y t))) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+16) || !(t <= 5.7e-5)) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2d+16)) .or. (.not. (t <= 5.7d-5))) then
        tmp = x - (a * (y / t))
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+16) || !(t <= 5.7e-5)) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+16) or not (t <= 5.7e-5):
		tmp = x - (a * (y / t))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+16) || !(t <= 5.7e-5))
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e+16) || ~((t <= 5.7e-5)))
		tmp = x - (a * (y / t));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+16], N[Not[LessEqual[t, 5.7e-5]], $MachinePrecision]], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e16 or 5.7000000000000003e-5 < t

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 83.4%

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

   6. Taylor expanded in y around inf 77.0%

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

   if -2e16 < t < 5.7000000000000003e-5

   1. Initial program 97.5%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 71.8%

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

   8. Taylor expanded in t around 0 71.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16} \lor \neg \left(t \leq 5.7 \cdot 10^{-5}\right):\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+16)
   (- x (* a (/ y t)))
   (if (<= t 5.7e-5) (- x (* y a)) (- x (/ a (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+16) {
		tmp = x - (a * (y / t));
	} else if (t <= 5.7e-5) {
		tmp = x - (y * a);
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2d+16)) then
        tmp = x - (a * (y / t))
    else if (t <= 5.7d-5) then
        tmp = x - (y * a)
    else
        tmp = x - (a / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+16) {
		tmp = x - (a * (y / t));
	} else if (t <= 5.7e-5) {
		tmp = x - (y * a);
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+16:
		tmp = x - (a * (y / t))
	elif t <= 5.7e-5:
		tmp = x - (y * a)
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+16)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= 5.7e-5)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+16)
		tmp = x - (a * (y / t));
	elseif (t <= 5.7e-5)
		tmp = x - (y * a);
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+16], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e-5], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e16

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 81.4%

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

   6. Taylor expanded in y around inf 72.7%

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

   if -2e16 < t < 5.7000000000000003e-5

   1. Initial program 97.5%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 71.8%

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

   8. Taylor expanded in t around 0 71.4%

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

   if 5.7000000000000003e-5 < t

   1. Initial program 97.5%

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

      1. *-commutative 99.9%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in t around inf 85.2%

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

   8. Taylor expanded in y around inf 80.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 8.8 \cdot 10^{-114}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+149) (not (<= z 8.8e-114))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+149) || !(z <= 8.8e-114)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+149)) .or. (.not. (z <= 8.8d-114))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+149) || !(z <= 8.8e-114)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+149) or not (z <= 8.8e-114):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+149) || !(z <= 8.8e-114))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+149) || ~((z <= 8.8e-114)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+149], N[Not[LessEqual[z, 8.8e-114]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e149 or 8.80000000000000045e-114 < z

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 77.1%

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

   if -1.95e149 < z < 8.80000000000000045e-114

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 83.5%

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

   8. Taylor expanded in t around 0 71.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+149} \lor \neg \left(z \leq 8.8 \cdot 10^{-114}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+93} \lor \neg \left(z \leq 2.3 \cdot 10^{+86}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.05e+93) (not (<= z 2.3e+86))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.05e+93) || !(z <= 2.3e+86)) {
		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 <= (-3.05d+93)) .or. (.not. (z <= 2.3d+86))) 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 <= -3.05e+93) || !(z <= 2.3e+86)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.05e+93) or not (z <= 2.3e+86):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.05e+93) || !(z <= 2.3e+86))
		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 <= -3.05e+93) || ~((z <= 2.3e+86)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.05e+93], N[Not[LessEqual[z, 2.3e+86]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.05e93 or 2.2999999999999999e86 < z

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.6%

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

   if -3.05e93 < z < 2.2999999999999999e86

   1. Initial program 98.8%

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

      1. associate-/r/ 99.9%

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

   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 inf 65.7%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. neg-mul-1 53.8%

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

      2. distribute-neg-frac 53.8%

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

   8. Simplified 53.8%

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

   9. Taylor expanded in x around inf 56.2%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+93} \lor \neg \left(z \leq 2.3 \cdot 10^{+86}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.8% 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 97.5%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 inf 57.6%

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

6. Taylor expanded in y around 0 48.2%

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

   1. neg-mul-1 48.2%

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

   2. distribute-neg-frac 48.2%

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

8. Simplified 48.2%

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

9. Taylor expanded in x around inf 53.9%

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

10. Final simplification 53.9%

    \[\leadsto x \]
11. Add Preprocessing

Developer target: 99.6% 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 2024082 
(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))))