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

Percentage Accurate: 97.2% → 99.6%

Time: 16.2s

Alternatives: 17

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: 97.2% 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

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

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]

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 82.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot a}{1 - z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 0.046:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y a) (- 1.0 z)))))
   (if (<= z -2.5e+24)
     (- x a)
     (if (<= z 9.5e-126)
       (- x (* a (/ y (+ t 1.0))))
       (if (<= z 3.6e-34)
         (+ x (* z (/ a (+ t 1.0))))
         (if (<= z 0.046)
           (+ x (* y (/ a (- -1.0 t))))
           (if (<= z 1.5e+95)
             t_1
             (if (<= z 4.4e+95)
               (* a (/ (- y) t))
               (if (<= z 2.2e+105) t_1 (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * a) / (1.0 - z));
	double tmp;
	if (z <= -2.5e+24) {
		tmp = x - a;
	} else if (z <= 9.5e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.6e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 0.046) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else if (z <= 1.5e+95) {
		tmp = t_1;
	} else if (z <= 4.4e+95) {
		tmp = a * (-y / t);
	} else if (z <= 2.2e+105) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y * a) / (1.0d0 - z))
    if (z <= (-2.5d+24)) then
        tmp = x - a
    else if (z <= 9.5d-126) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 3.6d-34) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= 0.046d0) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else if (z <= 1.5d+95) then
        tmp = t_1
    else if (z <= 4.4d+95) then
        tmp = a * (-y / t)
    else if (z <= 2.2d+105) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * a) / (1.0 - z));
	double tmp;
	if (z <= -2.5e+24) {
		tmp = x - a;
	} else if (z <= 9.5e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.6e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 0.046) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else if (z <= 1.5e+95) {
		tmp = t_1;
	} else if (z <= 4.4e+95) {
		tmp = a * (-y / t);
	} else if (z <= 2.2e+105) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * a) / (1.0 - z))
	tmp = 0
	if z <= -2.5e+24:
		tmp = x - a
	elif z <= 9.5e-126:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 3.6e-34:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= 0.046:
		tmp = x + (y * (a / (-1.0 - t)))
	elif z <= 1.5e+95:
		tmp = t_1
	elif z <= 4.4e+95:
		tmp = a * (-y / t)
	elif z <= 2.2e+105:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * a) / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -2.5e+24)
		tmp = Float64(x - a);
	elseif (z <= 9.5e-126)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 3.6e-34)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= 0.046)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	elseif (z <= 1.5e+95)
		tmp = t_1;
	elseif (z <= 4.4e+95)
		tmp = Float64(a * Float64(Float64(-y) / t));
	elseif (z <= 2.2e+105)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * a) / (1.0 - z));
	tmp = 0.0;
	if (z <= -2.5e+24)
		tmp = x - a;
	elseif (z <= 9.5e-126)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 3.6e-34)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= 0.046)
		tmp = x + (y * (a / (-1.0 - t)));
	elseif (z <= 1.5e+95)
		tmp = t_1;
	elseif (z <= 4.4e+95)
		tmp = a * (-y / t);
	elseif (z <= 2.2e+105)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+24], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.5e-126], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-34], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.046], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+95], t$95$1, If[LessEqual[z, 4.4e+95], N[(a * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+105], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.50000000000000023e24 or 2.20000000000000007e105 < z

   1. Initial program 93.3%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 87.7%

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

   if -2.50000000000000023e24 < z < 9.5000000000000003e-126

   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 90.8%

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

   if 9.5000000000000003e-126 < z < 3.60000000000000008e-34

   1. Initial program 99.9%

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

      1. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. *-commutative 91.1%

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

      3. associate--l+ 91.1%

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

      4. +-commutative 91.1%

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

      5. associate-*r/ 91.2%

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

      6. distribute-rgt-neg-in 91.2%

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

      7. distribute-neg-frac2 91.2%

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

      8. +-commutative 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. metadata-eval 91.2%

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

      11. unsub-neg 91.2%

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

      12. associate--r- 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   10. Simplified 91.2%

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

   if 3.60000000000000008e-34 < z < 0.045999999999999999

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   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 z around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

   if 0.045999999999999999 < z < 1.49999999999999996e95 or 4.3999999999999998e95 < z < 2.20000000000000007e105

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 95.5%

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

   4. Taylor expanded in y around inf 81.4%

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

   if 1.49999999999999996e95 < z < 4.3999999999999998e95

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf 98.4%

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

   4. Taylor expanded in y around inf 53.0%

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

      1. associate-*r/ 53.0%

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

      2. *-commutative 53.0%

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

      3. neg-mul-1 53.0%

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

      4. distribute-lft-neg-in 53.0%

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

   6. Simplified 53.0%

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

   7. Taylor expanded in y around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \color{blue}{a \cdot \frac{-y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 0.046:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{z \cdot a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+24)
   (- x a)
   (if (<= z 1.0)
     (- x (/ a (/ (+ t 1.0) y)))
     (if (<= z 1.5e+95)
       (- x (/ (* y a) (- 1.0 z)))
       (if (<= z 4.4e+95)
         (* a (/ (- y) t))
         (if (<= z 4.6e+161) (+ x (/ (* z a) (- 1.0 z))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+24) {
		tmp = x - a;
	} else if (z <= 1.0) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 1.5e+95) {
		tmp = x - ((y * a) / (1.0 - z));
	} else if (z <= 4.4e+95) {
		tmp = a * (-y / t);
	} else if (z <= 4.6e+161) {
		tmp = x + ((z * a) / (1.0 - z));
	} 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 <= (-1.6d+24)) then
        tmp = x - a
    else if (z <= 1.0d0) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else if (z <= 1.5d+95) then
        tmp = x - ((y * a) / (1.0d0 - z))
    else if (z <= 4.4d+95) then
        tmp = a * (-y / t)
    else if (z <= 4.6d+161) then
        tmp = x + ((z * a) / (1.0d0 - z))
    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 <= -1.6e+24) {
		tmp = x - a;
	} else if (z <= 1.0) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 1.5e+95) {
		tmp = x - ((y * a) / (1.0 - z));
	} else if (z <= 4.4e+95) {
		tmp = a * (-y / t);
	} else if (z <= 4.6e+161) {
		tmp = x + ((z * a) / (1.0 - z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+24:
		tmp = x - a
	elif z <= 1.0:
		tmp = x - (a / ((t + 1.0) / y))
	elif z <= 1.5e+95:
		tmp = x - ((y * a) / (1.0 - z))
	elif z <= 4.4e+95:
		tmp = a * (-y / t)
	elif z <= 4.6e+161:
		tmp = x + ((z * a) / (1.0 - z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+24)
		tmp = Float64(x - a);
	elseif (z <= 1.0)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	elseif (z <= 1.5e+95)
		tmp = Float64(x - Float64(Float64(y * a) / Float64(1.0 - z)));
	elseif (z <= 4.4e+95)
		tmp = Float64(a * Float64(Float64(-y) / t));
	elseif (z <= 4.6e+161)
		tmp = Float64(x + Float64(Float64(z * a) / Float64(1.0 - z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+24)
		tmp = x - a;
	elseif (z <= 1.0)
		tmp = x - (a / ((t + 1.0) / y));
	elseif (z <= 1.5e+95)
		tmp = x - ((y * a) / (1.0 - z));
	elseif (z <= 4.4e+95)
		tmp = a * (-y / t);
	elseif (z <= 4.6e+161)
		tmp = x + ((z * a) / (1.0 - z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+24], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.0], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+95], N[(x - N[(N[(y * a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+95], N[(a * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+161], N[(x + N[(N[(z * a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5999999999999999e24 or 4.5999999999999999e161 < z

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 87.7%

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

   if -1.5999999999999999e24 < z < 1

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. clear-num 87.2%

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

      3. un-div-inv 87.2%

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

      4. +-commutative 87.2%

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

   7. Applied egg-rr 87.2%

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

   if 1 < z < 1.49999999999999996e95

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.9%

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

   4. Taylor expanded in y around inf 78.3%

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

   if 1.49999999999999996e95 < z < 4.3999999999999998e95

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf 98.4%

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

   4. Taylor expanded in y around inf 53.0%

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

      1. associate-*r/ 53.0%

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

      2. *-commutative 53.0%

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

      3. neg-mul-1 53.0%

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

      4. distribute-lft-neg-in 53.0%

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

   6. Simplified 53.0%

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

   7. Taylor expanded in y around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

   9. Simplified 100.0%

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

   if 4.3999999999999998e95 < z < 4.5999999999999999e161

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. *-commutative 91.7%

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

      3. associate--l+ 91.7%

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

      4. +-commutative 91.7%

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

      5. associate-*r/ 85.0%

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

      6. distribute-rgt-neg-in 85.0%

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

      7. distribute-neg-frac2 85.0%

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

      8. +-commutative 85.0%

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

      9. distribute-neg-in 85.0%

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

      10. metadata-eval 85.0%

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

      11. unsub-neg 85.0%

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

      12. associate--r- 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in t around 0 90.0%

      \[\leadsto x - \color{blue}{\frac{a \cdot z}{z - 1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;x - \frac{y \cdot a}{1 - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{z \cdot a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (* y (/ a t)))))
   (if (<= z -8.5e+18)
     (- x a)
     (if (<= z -2.5e-169)
       t_2
       (if (<= z -1.45e-267)
         t_1
         (if (<= z 6.5e-225) t_2 (if (<= z 5.5e-31) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (y * (a / t));
	double tmp;
	if (z <= -8.5e+18) {
		tmp = x - a;
	} else if (z <= -2.5e-169) {
		tmp = t_2;
	} else if (z <= -1.45e-267) {
		tmp = t_1;
	} else if (z <= 6.5e-225) {
		tmp = t_2;
	} else if (z <= 5.5e-31) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x - (y * (a / t))
    if (z <= (-8.5d+18)) then
        tmp = x - a
    else if (z <= (-2.5d-169)) then
        tmp = t_2
    else if (z <= (-1.45d-267)) then
        tmp = t_1
    else if (z <= 6.5d-225) then
        tmp = t_2
    else if (z <= 5.5d-31) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (y * (a / t));
	double tmp;
	if (z <= -8.5e+18) {
		tmp = x - a;
	} else if (z <= -2.5e-169) {
		tmp = t_2;
	} else if (z <= -1.45e-267) {
		tmp = t_1;
	} else if (z <= 6.5e-225) {
		tmp = t_2;
	} else if (z <= 5.5e-31) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (y * (a / t))
	tmp = 0
	if z <= -8.5e+18:
		tmp = x - a
	elif z <= -2.5e-169:
		tmp = t_2
	elif z <= -1.45e-267:
		tmp = t_1
	elif z <= 6.5e-225:
		tmp = t_2
	elif z <= 5.5e-31:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (z <= -8.5e+18)
		tmp = Float64(x - a);
	elseif (z <= -2.5e-169)
		tmp = t_2;
	elseif (z <= -1.45e-267)
		tmp = t_1;
	elseif (z <= 6.5e-225)
		tmp = t_2;
	elseif (z <= 5.5e-31)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x - (y * (a / t));
	tmp = 0.0;
	if (z <= -8.5e+18)
		tmp = x - a;
	elseif (z <= -2.5e-169)
		tmp = t_2;
	elseif (z <= -1.45e-267)
		tmp = t_1;
	elseif (z <= 6.5e-225)
		tmp = t_2;
	elseif (z <= 5.5e-31)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+18], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.5e-169], t$95$2, If[LessEqual[z, -1.45e-267], t$95$1, If[LessEqual[z, 6.5e-225], t$95$2, If[LessEqual[z, 5.5e-31], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e18 or 5.49999999999999958e-31 < z

   1. Initial program 94.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.5%

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

   if -8.5e18 < z < -2.5000000000000001e-169 or -1.45000000000000011e-267 < z < 6.5000000000000005e-225

   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 z around 0 90.3%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-*r/ 79.8%

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

   8. Simplified 79.8%

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

   if -2.5000000000000001e-169 < z < -1.45000000000000011e-267 or 6.5000000000000005e-225 < z < 5.49999999999999958e-31

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 85.2%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-225}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -1.25e+17)
     (- x a)
     (if (<= z -1.2e-167)
       (- x (* a (/ y t)))
       (if (<= z -2.8e-265)
         t_1
         (if (<= z 7e-225)
           (- x (* y (/ a t)))
           (if (<= z 5.5e-31) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -1.25e+17) {
		tmp = x - a;
	} else if (z <= -1.2e-167) {
		tmp = x - (a * (y / t));
	} else if (z <= -2.8e-265) {
		tmp = t_1;
	} else if (z <= 7e-225) {
		tmp = x - (y * (a / t));
	} else if (z <= 5.5e-31) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-1.25d+17)) then
        tmp = x - a
    else if (z <= (-1.2d-167)) then
        tmp = x - (a * (y / t))
    else if (z <= (-2.8d-265)) then
        tmp = t_1
    else if (z <= 7d-225) then
        tmp = x - (y * (a / t))
    else if (z <= 5.5d-31) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -1.25e+17) {
		tmp = x - a;
	} else if (z <= -1.2e-167) {
		tmp = x - (a * (y / t));
	} else if (z <= -2.8e-265) {
		tmp = t_1;
	} else if (z <= 7e-225) {
		tmp = x - (y * (a / t));
	} else if (z <= 5.5e-31) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -1.25e+17:
		tmp = x - a
	elif z <= -1.2e-167:
		tmp = x - (a * (y / t))
	elif z <= -2.8e-265:
		tmp = t_1
	elif z <= 7e-225:
		tmp = x - (y * (a / t))
	elif z <= 5.5e-31:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -1.25e+17)
		tmp = Float64(x - a);
	elseif (z <= -1.2e-167)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -2.8e-265)
		tmp = t_1;
	elseif (z <= 7e-225)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 5.5e-31)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -1.25e+17)
		tmp = x - a;
	elseif (z <= -1.2e-167)
		tmp = x - (a * (y / t));
	elseif (z <= -2.8e-265)
		tmp = t_1;
	elseif (z <= 7e-225)
		tmp = x - (y * (a / t));
	elseif (z <= 5.5e-31)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+17], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.2e-167], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-265], t$95$1, If[LessEqual[z, 7e-225], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-31], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e17 or 5.49999999999999958e-31 < z

   1. Initial program 94.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.5%

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

   if -1.25e17 < z < -1.19999999999999997e-167

   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 z around 0 85.3%

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

   6. Taylor expanded in t around inf 75.1%

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

   if -1.19999999999999997e-167 < z < -2.80000000000000023e-265 or 6.9999999999999994e-225 < z < 5.49999999999999958e-31

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 85.2%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

   8. Simplified 75.8%

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

   if -2.80000000000000023e-265 < z < 6.9999999999999994e-225

   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 z around 0 99.8%

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

   6. Taylor expanded in t around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*r/ 90.4%

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

   8. Simplified 90.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-265}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-225}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 260000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ z a)))))
   (if (<= z -1.05e+14)
     t_1
     (if (<= z 1.6e-126)
       (- x (* a (/ y (+ t 1.0))))
       (if (<= z 3.7e-34)
         (+ x (* z (/ a (+ t 1.0))))
         (if (<= z 260000.0) (+ x (* y (/ a (- -1.0 t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (z / a));
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= 1.6e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.7e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 260000.0) {
		tmp = x + (y * (a / (-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 + ((y - z) / (z / a))
    if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= 1.6d-126) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 3.7d-34) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= 260000.0d0) then
        tmp = x + (y * (a / ((-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 + ((y - z) / (z / a));
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= 1.6e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 3.7e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 260000.0) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (z / a))
	tmp = 0
	if z <= -1.05e+14:
		tmp = t_1
	elif z <= 1.6e-126:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 3.7e-34:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= 260000.0:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(z / a)))
	tmp = 0.0
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= 1.6e-126)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 3.7e-34)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= 260000.0)
		tmp = Float64(x + Float64(y * Float64(a / 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 + ((y - z) / (z / a));
	tmp = 0.0;
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= 1.6e-126)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 3.7e-34)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= 260000.0)
		tmp = x + (y * (a / (-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[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, 1.6e-126], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-34], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 260000.0], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e14 or 2.6e5 < 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 87.9%

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

      1. mul-1-neg 87.9%

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

      2. distribute-neg-frac2 87.9%

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

   5. Simplified 87.9%

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

   if -1.05e14 < z < 1.6e-126

   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 92.4%

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

   if 1.6e-126 < z < 3.69999999999999988e-34

   1. Initial program 99.9%

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

      1. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. *-commutative 91.1%

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

      3. associate--l+ 91.1%

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

      4. +-commutative 91.1%

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

      5. associate-*r/ 91.2%

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

      6. distribute-rgt-neg-in 91.2%

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

      7. distribute-neg-frac2 91.2%

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

      8. +-commutative 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. metadata-eval 91.2%

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

      11. unsub-neg 91.2%

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

      12. associate--r- 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   10. Simplified 91.2%

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

   if 3.69999999999999988e-34 < z < 2.6e5

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   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 z around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 260000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+25}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 500000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+25)
   (+ x (* z (/ a (- (+ t 1.0) z))))
   (if (<= z 9.5e-126)
     (- x (* a (/ y (+ t 1.0))))
     (if (<= z 2.9e-31)
       (+ x (* z (/ a (+ t 1.0))))
       (if (<= z 500000.0)
         (+ x (* y (/ a (- -1.0 t))))
         (+ x (/ (- y z) (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+25) {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	} else if (z <= 9.5e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 2.9e-31) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 500000.0) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+25)) then
        tmp = x + (z * (a / ((t + 1.0d0) - z)))
    else if (z <= 9.5d-126) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 2.9d-31) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= 500000.0d0) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+25) {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	} else if (z <= 9.5e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 2.9e-31) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 500000.0) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+25:
		tmp = x + (z * (a / ((t + 1.0) - z)))
	elif z <= 9.5e-126:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 2.9e-31:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= 500000.0:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+25)
		tmp = Float64(x + Float64(z * Float64(a / Float64(Float64(t + 1.0) - z))));
	elseif (z <= 9.5e-126)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 2.9e-31)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= 500000.0)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+25)
		tmp = x + (z * (a / ((t + 1.0) - z)));
	elseif (z <= 9.5e-126)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 2.9e-31)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= 500000.0)
		tmp = x + (y * (a / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+25], N[(x + N[(z * N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-126], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-31], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 500000.0], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.49999999999999993e25

   1. Initial program 92.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. associate--l+ 78.1%

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

      4. +-commutative 78.1%

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

      5. associate-*r/ 89.2%

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

      6. distribute-rgt-neg-in 89.2%

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

      7. distribute-neg-frac2 89.2%

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

      8. +-commutative 89.2%

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

      9. distribute-neg-in 89.2%

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

      10. metadata-eval 89.2%

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

      11. unsub-neg 89.2%

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

      12. associate--r- 89.2%

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

   7. Simplified 89.2%

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

   if -7.49999999999999993e25 < z < 9.5000000000000003e-126

   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 90.8%

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

   if 9.5000000000000003e-126 < z < 2.9000000000000001e-31

   1. Initial program 99.9%

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

      1. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. *-commutative 91.1%

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

      3. associate--l+ 91.1%

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

      4. +-commutative 91.1%

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

      5. associate-*r/ 91.2%

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

      6. distribute-rgt-neg-in 91.2%

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

      7. distribute-neg-frac2 91.2%

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

      8. +-commutative 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. metadata-eval 91.2%

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

      11. unsub-neg 91.2%

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

      12. associate--r- 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   10. Simplified 91.2%

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

   if 2.9000000000000001e-31 < z < 5e5

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   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 z around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

   if 5e5 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-neg-frac2 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+25}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 500000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+21)
   (- x (* a (/ z (+ z (- -1.0 t)))))
   (if (<= z 5.6e-126)
     (- x (* a (/ y (+ t 1.0))))
     (if (<= z 1.65e-34)
       (+ x (* z (/ a (+ t 1.0))))
       (if (<= z 255000.0)
         (+ x (* y (/ a (- -1.0 t))))
         (+ x (/ (- y z) (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+21) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 5.6e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 1.65e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 255000.0) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+21)) then
        tmp = x - (a * (z / (z + ((-1.0d0) - t))))
    else if (z <= 5.6d-126) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 1.65d-34) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= 255000.0d0) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+21) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 5.6e-126) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 1.65e-34) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 255000.0) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+21:
		tmp = x - (a * (z / (z + (-1.0 - t))))
	elif z <= 5.6e-126:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 1.65e-34:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= 255000.0:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+21)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + Float64(-1.0 - t)))));
	elseif (z <= 5.6e-126)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 1.65e-34)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= 255000.0)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+21)
		tmp = x - (a * (z / (z + (-1.0 - t))));
	elseif (z <= 5.6e-126)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 1.65e-34)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= 255000.0)
		tmp = x + (y * (a / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+21], N[(x - N[(a * N[(z / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-126], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-34], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 255000.0], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5e21

   1. Initial program 92.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. associate--l+ 93.7%

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

      3. +-commutative 93.7%

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

      4. distribute-neg-frac2 93.7%

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

      5. +-commutative 93.7%

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

      6. distribute-neg-in 93.7%

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

      7. metadata-eval 93.7%

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

      8. unsub-neg 93.7%

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

      9. associate--r- 93.7%

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

   7. Simplified 93.7%

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

   if -4.5e21 < z < 5.59999999999999983e-126

   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 90.8%

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

   if 5.59999999999999983e-126 < z < 1.64999999999999991e-34

   1. Initial program 99.9%

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

      1. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. *-commutative 91.1%

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

      3. associate--l+ 91.1%

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

      4. +-commutative 91.1%

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

      5. associate-*r/ 91.2%

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

      6. distribute-rgt-neg-in 91.2%

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

      7. distribute-neg-frac2 91.2%

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

      8. +-commutative 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. metadata-eval 91.2%

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

      11. unsub-neg 91.2%

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

      12. associate--r- 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   10. Simplified 91.2%

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

   if 1.64999999999999991e-34 < z < 255000

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   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 z around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

   if 255000 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-neg-frac2 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+24)
   (- x (* a (/ z (+ z (- -1.0 t)))))
   (if (<= z 255000.0)
     (+ x (/ (- y z) (/ (- -1.0 t) a)))
     (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+24) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 255000.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+24)) then
        tmp = x - (a * (z / (z + ((-1.0d0) - t))))
    else if (z <= 255000.0d0) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+24) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 255000.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+24:
		tmp = x - (a * (z / (z + (-1.0 - t))))
	elif z <= 255000.0:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+24)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + Float64(-1.0 - t)))));
	elseif (z <= 255000.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+24)
		tmp = x - (a * (z / (z + (-1.0 - t))));
	elseif (z <= 255000.0)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+24], N[(x - N[(a * N[(z / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 255000.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e24

   1. Initial program 92.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. associate--l+ 93.7%

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

      3. +-commutative 93.7%

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

      4. distribute-neg-frac2 93.7%

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

      5. +-commutative 93.7%

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

      6. distribute-neg-in 93.7%

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

      7. metadata-eval 93.7%

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

      8. unsub-neg 93.7%

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

      9. associate--r- 93.7%

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

   7. Simplified 93.7%

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

   if -2.2999999999999999e24 < z < 255000

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 97.1%

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

   if 255000 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-neg-frac2 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 820:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+23)
   (- x (* a (/ z (+ z (- -1.0 t)))))
   (if (<= z 820.0)
     (+ x (/ (- y z) (/ (- -1.0 t) a)))
     (- x (/ (- y z) (/ (- 1.0 z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+23) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 820.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+23)) then
        tmp = x - (a * (z / (z + ((-1.0d0) - t))))
    else if (z <= 820.0d0) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else
        tmp = x - ((y - z) / ((1.0d0 - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+23) {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	} else if (z <= 820.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+23:
		tmp = x - (a * (z / (z + (-1.0 - t))))
	elif z <= 820.0:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	else:
		tmp = x - ((y - z) / ((1.0 - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+23)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + Float64(-1.0 - t)))));
	elseif (z <= 820.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(1.0 - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+23)
		tmp = x - (a * (z / (z + (-1.0 - t))));
	elseif (z <= 820.0)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	else
		tmp = x - ((y - z) / ((1.0 - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+23], N[(x - N[(a * N[(z / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 820.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999993e23

   1. Initial program 92.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. associate--l+ 93.7%

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

      3. +-commutative 93.7%

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

      4. distribute-neg-frac2 93.7%

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

      5. +-commutative 93.7%

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

      6. distribute-neg-in 93.7%

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

      7. metadata-eval 93.7%

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

      8. unsub-neg 93.7%

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

      9. associate--r- 93.7%

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

   7. Simplified 93.7%

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

   if -7.9999999999999993e23 < z < 820

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 97.1%

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

   if 820 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 91.9%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;z \leq 820:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+30} \lor \neg \left(z \leq 5000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e+30) (not (<= z 5000.0)))
   (- 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 <= -1.02e+30) || !(z <= 5000.0)) {
		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 <= (-1.02d+30)) .or. (.not. (z <= 5000.0d0))) 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 <= -1.02e+30) || !(z <= 5000.0)) {
		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 <= -1.02e+30) or not (z <= 5000.0):
		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 <= -1.02e+30) || !(z <= 5000.0))
		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 <= -1.02e+30) || ~((z <= 5000.0)))
		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, -1.02e+30], N[Not[LessEqual[z, 5000.0]], $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 < -1.02e30 or 5e3 < z

   1. Initial program 94.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 83.1%

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

   if -1.02e30 < z < 5e3

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+30} \lor \neg \left(z \leq 5000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+24} \lor \neg \left(z \leq 1020000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+24) (not (<= z 1020000.0)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+24) || !(z <= 1020000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.25d+24)) .or. (.not. (z <= 1020000.0d0))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+24) || !(z <= 1020000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+24) or not (z <= 1020000.0):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+24) || !(z <= 1020000.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+24) || ~((z <= 1020000.0)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+24], N[Not[LessEqual[z, 1020000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000011e24 or 1.02e6 < z

   1. Initial program 94.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 83.1%

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

   if -1.25000000000000011e24 < z < 1.02e6

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 87.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+24} \lor \neg \left(z \leq 1020000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22} \lor \neg \left(z \leq 400\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+22) (not (<= z 400.0)))
   (- x a)
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+22) || !(z <= 400.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.5d+22)) .or. (.not. (z <= 400.0d0))) then
        tmp = x - a
    else
        tmp = x - (a / ((t + 1.0d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+22) || !(z <= 400.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+22) or not (z <= 400.0):
		tmp = x - a
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+22) || !(z <= 400.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+22) || ~((z <= 400.0)))
		tmp = x - a;
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+22], N[Not[LessEqual[z, 400.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e22 or 400 < z

   1. Initial program 94.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 83.1%

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

   if -4.4999999999999998e22 < z < 400

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. clear-num 87.2%

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

      3. un-div-inv 87.2%

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

      4. +-commutative 87.2%

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

   7. Applied egg-rr 87.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22} \lor \neg \left(z \leq 400\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+22} \lor \neg \left(z \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+22) (not (<= z 2e-10))) (- x a) (+ x (* z a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+22) || !(z <= 2e-10)) {
		tmp = x - a;
	} else {
		tmp = x + (z * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d+22)) .or. (.not. (z <= 2d-10))) then
        tmp = x - a
    else
        tmp = x + (z * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+22) || !(z <= 2e-10)) {
		tmp = x - a;
	} else {
		tmp = x + (z * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+22) or not (z <= 2e-10):
		tmp = x - a
	else:
		tmp = x + (z * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+22) || !(z <= 2e-10))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(z * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+22) || ~((z <= 2e-10)))
		tmp = x - a;
	else
		tmp = x + (z * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+22], N[Not[LessEqual[z, 2e-10]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e22 or 2.00000000000000007e-10 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.9%

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

   if -1.2e22 < z < 2.00000000000000007e-10

   1. Initial program 99.1%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. *-commutative 69.7%

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

      3. associate--l+ 69.7%

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

      4. +-commutative 69.7%

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

      5. associate-*r/ 69.7%

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

      6. distribute-rgt-neg-in 69.7%

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

      7. distribute-neg-frac2 69.7%

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

      8. +-commutative 69.7%

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

      9. distribute-neg-in 69.7%

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

      10. metadata-eval 69.7%

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

      11. unsub-neg 69.7%

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

      12. associate--r- 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in t around 0 63.2%

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

   9. Taylor expanded in z around 0 63.2%

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

       1. +-commutative 63.2%

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

   11. Simplified 63.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+22} \lor \neg \left(z \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+26} \lor \neg \left(z \leq 4 \cdot 10^{-32}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+26) (not (<= z 4e-32))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+26) || !(z <= 4e-32)) {
		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 <= (-1.45d+26)) .or. (.not. (z <= 4d-32))) 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 <= -1.45e+26) || !(z <= 4e-32)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+26) or not (z <= 4e-32):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+26) || !(z <= 4e-32))
		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 <= -1.45e+26) || ~((z <= 4e-32)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+26], N[Not[LessEqual[z, 4e-32]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e26 or 4.00000000000000022e-32 < z

   1. Initial program 94.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.1%

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

   if -1.45e26 < z < 4.00000000000000022e-32

   1. Initial program 99.1%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 87.0%

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

   6. Taylor expanded in t around 0 67.8%

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

      1. *-commutative 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+26} \lor \neg \left(z \leq 4 \cdot 10^{-32}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 54\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -48000000000000.0) (not (<= z 54.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 54.0)) {
		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 <= (-48000000000000.0d0)) .or. (.not. (z <= 54.0d0))) 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 <= -48000000000000.0) || !(z <= 54.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -48000000000000.0) or not (z <= 54.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -48000000000000.0) || !(z <= 54.0))
		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 <= -48000000000000.0) || ~((z <= 54.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -48000000000000.0], N[Not[LessEqual[z, 54.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e13 or 54 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.0%

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

   if -4.8e13 < z < 54

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 88.3%

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

   6. Taylor expanded in x around inf 60.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 54\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.9% 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 96.9%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around 0 69.1%

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

6. Taylor expanded in x around inf 55.9%

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

7. Final simplification 55.9%

   \[\leadsto x \]
8. 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 2024059 
(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))))