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

Percentage Accurate: 96.7% → 99.5%

Time: 16.7s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% 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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{a \cdot \left(-y\right)}{1 - z}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ -1.0 (/ 1.0 z))))))
   (if (<= t -3.5e-5)
     (- x (* y (/ a t)))
     (if (<= t -1.2e-301)
       t_1
       (if (<= t 5.7e-263)
         (- x (* y a))
         (if (<= t 3.9e-212)
           t_1
           (if (<= t 1.15e-185)
             (/ (* a (- y)) (- 1.0 z))
             (if (<= t 0.00013)
               t_1
               (if (<= t 2e+110)
                 (- x (/ (* y a) t))
                 (if (<= t 4e+156) t_1 (+ x (/ a (/ t z)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (-1.0 + (1.0 / z)));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (y * (a / t));
	} else if (t <= -1.2e-301) {
		tmp = t_1;
	} else if (t <= 5.7e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (a * -y) / (1.0 - z);
	} else if (t <= 0.00013) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x - ((y * a) / t);
	} else if (t <= 4e+156) {
		tmp = t_1;
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a / ((-1.0d0) + (1.0d0 / z)))
    if (t <= (-3.5d-5)) then
        tmp = x - (y * (a / t))
    else if (t <= (-1.2d-301)) then
        tmp = t_1
    else if (t <= 5.7d-263) then
        tmp = x - (y * a)
    else if (t <= 3.9d-212) then
        tmp = t_1
    else if (t <= 1.15d-185) then
        tmp = (a * -y) / (1.0d0 - z)
    else if (t <= 0.00013d0) then
        tmp = t_1
    else if (t <= 2d+110) then
        tmp = x - ((y * a) / t)
    else if (t <= 4d+156) then
        tmp = t_1
    else
        tmp = x + (a / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (-1.0 + (1.0 / z)));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (y * (a / t));
	} else if (t <= -1.2e-301) {
		tmp = t_1;
	} else if (t <= 5.7e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (a * -y) / (1.0 - z);
	} else if (t <= 0.00013) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x - ((y * a) / t);
	} else if (t <= 4e+156) {
		tmp = t_1;
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (-1.0 + (1.0 / z)))
	tmp = 0
	if t <= -3.5e-5:
		tmp = x - (y * (a / t))
	elif t <= -1.2e-301:
		tmp = t_1
	elif t <= 5.7e-263:
		tmp = x - (y * a)
	elif t <= 3.9e-212:
		tmp = t_1
	elif t <= 1.15e-185:
		tmp = (a * -y) / (1.0 - z)
	elif t <= 0.00013:
		tmp = t_1
	elif t <= 2e+110:
		tmp = x - ((y * a) / t)
	elif t <= 4e+156:
		tmp = t_1
	else:
		tmp = x + (a / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(-1.0 + Float64(1.0 / z))))
	tmp = 0.0
	if (t <= -3.5e-5)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (t <= -1.2e-301)
		tmp = t_1;
	elseif (t <= 5.7e-263)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = Float64(Float64(a * Float64(-y)) / Float64(1.0 - z));
	elseif (t <= 0.00013)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (t <= 4e+156)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (-1.0 + (1.0 / z)));
	tmp = 0.0;
	if (t <= -3.5e-5)
		tmp = x - (y * (a / t));
	elseif (t <= -1.2e-301)
		tmp = t_1;
	elseif (t <= 5.7e-263)
		tmp = x - (y * a);
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = (a * -y) / (1.0 - z);
	elseif (t <= 0.00013)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = x - ((y * a) / t);
	elseif (t <= 4e+156)
		tmp = t_1;
	else
		tmp = x + (a / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(-1.0 + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-5], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-301], t$95$1, If[LessEqual[t, 5.7e-263], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-212], t$95$1, If[LessEqual[t, 1.15e-185], N[(N[(a * (-y)), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00013], t$95$1, If[LessEqual[t, 2e+110], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+156], t$95$1, N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.4999999999999997e-5

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 70.6%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in t around inf 70.1%

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

   9. Taylor expanded in x around 0 70.1%

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

       1. mul-1-neg 70.1%

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

       2. sub-neg 70.1%

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

       3. *-commutative 70.1%

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

       4. associate-*r/ 83.4%

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

   11. Simplified 83.4%

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

   if -3.4999999999999997e-5 < t < -1.19999999999999996e-301 or 5.6999999999999997e-263 < t < 3.9e-212 or 1.15e-185 < t < 1.29999999999999989e-4 or 2e110 < t < 3.9999999999999999e156

   1. Initial program 98.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 97.2%

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

   6. Taylor expanded in y around 0 68.5%

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

      1. sub-neg 68.5%

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

      2. mul-1-neg 68.5%

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

      3. remove-double-neg 68.5%

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

      4. associate-/l* 81.4%

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

      5. div-sub 81.4%

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

      6. *-inverses 81.4%

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

   8. Simplified 81.4%

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

   if -1.19999999999999996e-301 < t < 5.6999999999999997e-263

   1. Initial program 99.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in z around 0 92.8%

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

   if 3.9e-212 < t < 1.15e-185

   1. Initial program 99.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if 1.29999999999999989e-4 < t < 2e110

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 89.1%

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

      1. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in t around inf 88.1%

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

   if 3.9999999999999999e156 < t

   1. Initial program 96.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 92.9%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. cancel-sign-sub-inv 79.1%

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

      2. metadata-eval 79.1%

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

      3. *-lft-identity 79.1%

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

      4. +-commutative 79.1%

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

      5. associate-/l* 89.5%

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

   8. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{a}{\frac{t}{z}} + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{a \cdot \left(-y\right)}{1 - z}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+156}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{a \cdot \left(-y\right)}{1 - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ -1.0 (/ 1.0 z))))))
   (if (<= t -3.5e-5)
     (- x (* y (/ a t)))
     (if (<= t -1.7e-302)
       t_1
       (if (<= t 5.8e-263)
         (- x (* y a))
         (if (<= t 3.9e-212)
           t_1
           (if (<= t 1.15e-185)
             (/ (* a (- y)) (- 1.0 z))
             (if (<= t 2.3e-5)
               t_1
               (if (<= t 3.5e+121)
                 (- x (/ (* y a) t))
                 (+ x (/ a (+ (/ t z) -1.0))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (-1.0 + (1.0 / z)));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (y * (a / t));
	} else if (t <= -1.7e-302) {
		tmp = t_1;
	} else if (t <= 5.8e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (a * -y) / (1.0 - z);
	} else if (t <= 2.3e-5) {
		tmp = t_1;
	} else if (t <= 3.5e+121) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a / ((-1.0d0) + (1.0d0 / z)))
    if (t <= (-3.5d-5)) then
        tmp = x - (y * (a / t))
    else if (t <= (-1.7d-302)) then
        tmp = t_1
    else if (t <= 5.8d-263) then
        tmp = x - (y * a)
    else if (t <= 3.9d-212) then
        tmp = t_1
    else if (t <= 1.15d-185) then
        tmp = (a * -y) / (1.0d0 - z)
    else if (t <= 2.3d-5) then
        tmp = t_1
    else if (t <= 3.5d+121) then
        tmp = x - ((y * a) / t)
    else
        tmp = x + (a / ((t / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (-1.0 + (1.0 / z)));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (y * (a / t));
	} else if (t <= -1.7e-302) {
		tmp = t_1;
	} else if (t <= 5.8e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (a * -y) / (1.0 - z);
	} else if (t <= 2.3e-5) {
		tmp = t_1;
	} else if (t <= 3.5e+121) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (-1.0 + (1.0 / z)))
	tmp = 0
	if t <= -3.5e-5:
		tmp = x - (y * (a / t))
	elif t <= -1.7e-302:
		tmp = t_1
	elif t <= 5.8e-263:
		tmp = x - (y * a)
	elif t <= 3.9e-212:
		tmp = t_1
	elif t <= 1.15e-185:
		tmp = (a * -y) / (1.0 - z)
	elif t <= 2.3e-5:
		tmp = t_1
	elif t <= 3.5e+121:
		tmp = x - ((y * a) / t)
	else:
		tmp = x + (a / ((t / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(-1.0 + Float64(1.0 / z))))
	tmp = 0.0
	if (t <= -3.5e-5)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (t <= -1.7e-302)
		tmp = t_1;
	elseif (t <= 5.8e-263)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = Float64(Float64(a * Float64(-y)) / Float64(1.0 - z));
	elseif (t <= 2.3e-5)
		tmp = t_1;
	elseif (t <= 3.5e+121)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (-1.0 + (1.0 / z)));
	tmp = 0.0;
	if (t <= -3.5e-5)
		tmp = x - (y * (a / t));
	elseif (t <= -1.7e-302)
		tmp = t_1;
	elseif (t <= 5.8e-263)
		tmp = x - (y * a);
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = (a * -y) / (1.0 - z);
	elseif (t <= 2.3e-5)
		tmp = t_1;
	elseif (t <= 3.5e+121)
		tmp = x - ((y * a) / t);
	else
		tmp = x + (a / ((t / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(-1.0 + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-5], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-302], t$95$1, If[LessEqual[t, 5.8e-263], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-212], t$95$1, If[LessEqual[t, 1.15e-185], N[(N[(a * (-y)), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-5], t$95$1, If[LessEqual[t, 3.5e+121], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.4999999999999997e-5

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 70.6%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in t around inf 70.1%

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

   9. Taylor expanded in x around 0 70.1%

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

       1. mul-1-neg 70.1%

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

       2. sub-neg 70.1%

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

       3. *-commutative 70.1%

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

       4. associate-*r/ 83.4%

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

   11. Simplified 83.4%

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

   if -3.4999999999999997e-5 < t < -1.7e-302 or 5.80000000000000007e-263 < t < 3.9e-212 or 1.15e-185 < t < 2.3e-5

   1. Initial program 98.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

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

   6. Taylor expanded in y around 0 68.2%

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

      1. sub-neg 68.2%

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

      2. mul-1-neg 68.2%

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

      3. remove-double-neg 68.2%

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

      4. associate-/l* 80.9%

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

      5. div-sub 80.9%

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

      6. *-inverses 80.9%

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

   8. Simplified 80.9%

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

   if -1.7e-302 < t < 5.80000000000000007e-263

   1. Initial program 99.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in z around 0 92.8%

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

   if 3.9e-212 < t < 1.15e-185

   1. Initial program 99.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if 2.3e-5 < t < 3.5e121

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 87.1%

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

      1. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around inf 86.3%

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

   if 3.5e121 < t

   1. Initial program 97.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 79.1%

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

      1. sub-neg 79.1%

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

      2. mul-1-neg 79.1%

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

      3. remove-double-neg 79.1%

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

      4. associate-/l* 94.3%

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

      5. div-sub 94.3%

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

      6. *-inverses 94.3%

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

   9. Simplified 94.3%

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

   10. Taylor expanded in t around inf 94.3%

       \[\leadsto x + \frac{a}{\color{blue}{\frac{t}{z}} - 1} \]
3. Recombined 6 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-302}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{a \cdot \left(-y\right)}{1 - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-277}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 0.000106:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))))
   (if (<= t -2.6e-14)
     t_1
     (if (<= t -4e-277)
       (- x a)
       (if (<= t 1.8e-134)
         (- x (* y a))
         (if (<= t 0.000106)
           (- x a)
           (if (<= t 3.8e+162) t_1 (+ x (/ a (/ t z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -2.6e-14) {
		tmp = t_1;
	} else if (t <= -4e-277) {
		tmp = x - a;
	} else if (t <= 1.8e-134) {
		tmp = x - (y * a);
	} else if (t <= 0.000106) {
		tmp = x - a;
	} else if (t <= 3.8e+162) {
		tmp = t_1;
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (a / t))
    if (t <= (-2.6d-14)) then
        tmp = t_1
    else if (t <= (-4d-277)) then
        tmp = x - a
    else if (t <= 1.8d-134) then
        tmp = x - (y * a)
    else if (t <= 0.000106d0) then
        tmp = x - a
    else if (t <= 3.8d+162) then
        tmp = t_1
    else
        tmp = x + (a / (t / z))
    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 / t));
	double tmp;
	if (t <= -2.6e-14) {
		tmp = t_1;
	} else if (t <= -4e-277) {
		tmp = x - a;
	} else if (t <= 1.8e-134) {
		tmp = x - (y * a);
	} else if (t <= 0.000106) {
		tmp = x - a;
	} else if (t <= 3.8e+162) {
		tmp = t_1;
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	tmp = 0
	if t <= -2.6e-14:
		tmp = t_1
	elif t <= -4e-277:
		tmp = x - a
	elif t <= 1.8e-134:
		tmp = x - (y * a)
	elif t <= 0.000106:
		tmp = x - a
	elif t <= 3.8e+162:
		tmp = t_1
	else:
		tmp = x + (a / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (t <= -2.6e-14)
		tmp = t_1;
	elseif (t <= -4e-277)
		tmp = Float64(x - a);
	elseif (t <= 1.8e-134)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 0.000106)
		tmp = Float64(x - a);
	elseif (t <= 3.8e+162)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	tmp = 0.0;
	if (t <= -2.6e-14)
		tmp = t_1;
	elseif (t <= -4e-277)
		tmp = x - a;
	elseif (t <= 1.8e-134)
		tmp = x - (y * a);
	elseif (t <= 0.000106)
		tmp = x - a;
	elseif (t <= 3.8e+162)
		tmp = t_1;
	else
		tmp = x + (a / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-14], t$95$1, If[LessEqual[t, -4e-277], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.8e-134], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.000106], N[(x - a), $MachinePrecision], If[LessEqual[t, 3.8e+162], t$95$1, N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.59999999999999997e-14 or 1.06e-4 < t < 3.80000000000000024e162

   1. Initial program 98.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 75.8%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in t around inf 74.9%

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

   9. Taylor expanded in x around 0 74.9%

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

       1. mul-1-neg 74.9%

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

       2. sub-neg 74.9%

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

       3. *-commutative 74.9%

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

       4. associate-*r/ 82.9%

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

   11. Simplified 82.9%

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

   if -2.59999999999999997e-14 < t < -3.99999999999999988e-277 or 1.79999999999999995e-134 < t < 1.06e-4

   1. Initial program 97.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.8%

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

   if -3.99999999999999988e-277 < t < 1.79999999999999995e-134

   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 t around 0 100.0%

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

   6. Taylor expanded in z around 0 77.8%

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

   if 3.80000000000000024e162 < t

   1. Initial program 96.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 92.4%

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

   6. Taylor expanded in y around 0 81.2%

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

      1. cancel-sign-sub-inv 81.2%

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

      2. metadata-eval 81.2%

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

      3. *-lft-identity 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 92.4%

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

   8. Simplified 92.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-277}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 0.000106:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-278}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 0.000106:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+162}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e-14)
   (- x (* y (/ a t)))
   (if (<= t -7.8e-278)
     (- x a)
     (if (<= t 2.1e-134)
       (- x (* y a))
       (if (<= t 0.000106)
         (- x a)
         (if (<= t 4.2e+162) (- x (/ (* y a) t)) (+ x (/ a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-14) {
		tmp = x - (y * (a / t));
	} else if (t <= -7.8e-278) {
		tmp = x - a;
	} else if (t <= 2.1e-134) {
		tmp = x - (y * a);
	} else if (t <= 0.000106) {
		tmp = x - a;
	} else if (t <= 4.2e+162) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.6d-14)) then
        tmp = x - (y * (a / t))
    else if (t <= (-7.8d-278)) then
        tmp = x - a
    else if (t <= 2.1d-134) then
        tmp = x - (y * a)
    else if (t <= 0.000106d0) then
        tmp = x - a
    else if (t <= 4.2d+162) then
        tmp = x - ((y * a) / t)
    else
        tmp = x + (a / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-14) {
		tmp = x - (y * (a / t));
	} else if (t <= -7.8e-278) {
		tmp = x - a;
	} else if (t <= 2.1e-134) {
		tmp = x - (y * a);
	} else if (t <= 0.000106) {
		tmp = x - a;
	} else if (t <= 4.2e+162) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e-14:
		tmp = x - (y * (a / t))
	elif t <= -7.8e-278:
		tmp = x - a
	elif t <= 2.1e-134:
		tmp = x - (y * a)
	elif t <= 0.000106:
		tmp = x - a
	elif t <= 4.2e+162:
		tmp = x - ((y * a) / t)
	else:
		tmp = x + (a / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e-14)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (t <= -7.8e-278)
		tmp = Float64(x - a);
	elseif (t <= 2.1e-134)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 0.000106)
		tmp = Float64(x - a);
	elseif (t <= 4.2e+162)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	else
		tmp = Float64(x + Float64(a / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e-14)
		tmp = x - (y * (a / t));
	elseif (t <= -7.8e-278)
		tmp = x - a;
	elseif (t <= 2.1e-134)
		tmp = x - (y * a);
	elseif (t <= 0.000106)
		tmp = x - a;
	elseif (t <= 4.2e+162)
		tmp = x - ((y * a) / t);
	else
		tmp = x + (a / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e-14], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e-278], N[(x - a), $MachinePrecision], If[LessEqual[t, 2.1e-134], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.000106], N[(x - a), $MachinePrecision], If[LessEqual[t, 4.2e+162], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.59999999999999997e-14

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 71.6%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in t around inf 70.4%

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

   9. Taylor expanded in x around 0 70.4%

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

       1. mul-1-neg 70.4%

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

       2. sub-neg 70.4%

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

       3. *-commutative 70.4%

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

       4. associate-*r/ 83.3%

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

   11. Simplified 83.3%

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

   if -2.59999999999999997e-14 < t < -7.8000000000000002e-278 or 2.0999999999999999e-134 < t < 1.06e-4

   1. Initial program 97.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.8%

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

   if -7.8000000000000002e-278 < t < 2.0999999999999999e-134

   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 t around 0 100.0%

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

   6. Taylor expanded in z around 0 77.8%

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

   if 1.06e-4 < t < 4.2000000000000001e162

   1. Initial program 99.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.9%

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

      1. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in t around inf 82.3%

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

   if 4.2000000000000001e162 < t

   1. Initial program 96.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 92.4%

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

   6. Taylor expanded in y around 0 81.2%

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

      1. cancel-sign-sub-inv 81.2%

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

      2. metadata-eval 81.2%

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

      3. *-lft-identity 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 92.4%

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

   8. Simplified 92.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-278}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 0.000106:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+162}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(\left(y - z\right) \cdot \frac{-1}{z}\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+167}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2700:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t + 1}{z}}\\ \mathbf{elif}\;z \leq 105:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (* (- y z) (/ -1.0 z))))))
   (if (<= z -1.12e+167)
     (+ x (/ a (+ (/ t z) -1.0)))
     (if (<= z -7.5e+64)
       t_1
       (if (<= z -2700.0)
         (+ x (/ a (+ -1.0 (/ (+ t 1.0) z))))
         (if (<= z 105.0) (- x (* a (/ y (+ t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) * (-1.0 / z)));
	double tmp;
	if (z <= -1.12e+167) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= -7.5e+64) {
		tmp = t_1;
	} else if (z <= -2700.0) {
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	} else if (z <= 105.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * ((y - z) * ((-1.0d0) / z)))
    if (z <= (-1.12d+167)) then
        tmp = x + (a / ((t / z) + (-1.0d0)))
    else if (z <= (-7.5d+64)) then
        tmp = t_1
    else if (z <= (-2700.0d0)) then
        tmp = x + (a / ((-1.0d0) + ((t + 1.0d0) / z)))
    else if (z <= 105.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) * (-1.0 / z)));
	double tmp;
	if (z <= -1.12e+167) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= -7.5e+64) {
		tmp = t_1;
	} else if (z <= -2700.0) {
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	} else if (z <= 105.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * ((y - z) * (-1.0 / z)))
	tmp = 0
	if z <= -1.12e+167:
		tmp = x + (a / ((t / z) + -1.0))
	elif z <= -7.5e+64:
		tmp = t_1
	elif z <= -2700.0:
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)))
	elif z <= 105.0:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(Float64(y - z) * Float64(-1.0 / z))))
	tmp = 0.0
	if (z <= -1.12e+167)
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	elseif (z <= -7.5e+64)
		tmp = t_1;
	elseif (z <= -2700.0)
		tmp = Float64(x + Float64(a / Float64(-1.0 + Float64(Float64(t + 1.0) / z))));
	elseif (z <= 105.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * ((y - z) * (-1.0 / z)));
	tmp = 0.0;
	if (z <= -1.12e+167)
		tmp = x + (a / ((t / z) + -1.0));
	elseif (z <= -7.5e+64)
		tmp = t_1;
	elseif (z <= -2700.0)
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	elseif (z <= 105.0)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(N[(y - z), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+167], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e+64], t$95$1, If[LessEqual[z, -2700.0], N[(x + N[(a / N[(-1.0 + N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.11999999999999999e167

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around 0 61.1%

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

      1. sub-neg 61.1%

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

      2. mul-1-neg 61.1%

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

      3. remove-double-neg 61.1%

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

      4. associate-/l* 100.0%

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

      5. div-sub 100.0%

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

      6. *-inverses 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around inf 100.0%

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

   if -1.11999999999999999e167 < z < -7.5000000000000005e64 or 105 < z

   1. Initial program 96.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 86.2%

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

   if -7.5000000000000005e64 < z < -2700

   1. Initial program 99.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 89.2%

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

      1. sub-neg 89.2%

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

      2. mul-1-neg 89.2%

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

      3. remove-double-neg 89.2%

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

      4. associate-/l* 99.8%

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

      5. div-sub 99.8%

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

      6. *-inverses 99.8%

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

   9. Simplified 99.8%

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

   if -2700 < z < 105

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+167}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x - a \cdot \left(\left(y - z\right) \cdot \frac{-1}{z}\right)\\ \mathbf{elif}\;z \leq -2700:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t + 1}{z}}\\ \mathbf{elif}\;z \leq 105:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(\left(y - z\right) \cdot \frac{-1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{\frac{-z}{a}}\\ t_2 := x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1820000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1550:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- y z) (/ (- z) a)))) (t_2 (+ x (/ a (+ (/ t z) -1.0)))))
   (if (<= z -4.1e+193)
     t_2
     (if (<= z -4.5e+64)
       t_1
       (if (<= z -1820000.0)
         t_2
         (if (<= z 1550.0) (- x (* a (/ y (+ t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (-z / a));
	double t_2 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -4.1e+193) {
		tmp = t_2;
	} else if (z <= -4.5e+64) {
		tmp = t_1;
	} else if (z <= -1820000.0) {
		tmp = t_2;
	} else if (z <= 1550.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - ((y - z) / (-z / a))
    t_2 = x + (a / ((t / z) + (-1.0d0)))
    if (z <= (-4.1d+193)) then
        tmp = t_2
    else if (z <= (-4.5d+64)) then
        tmp = t_1
    else if (z <= (-1820000.0d0)) then
        tmp = t_2
    else if (z <= 1550.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 t_2 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -4.1e+193) {
		tmp = t_2;
	} else if (z <= -4.5e+64) {
		tmp = t_1;
	} else if (z <= -1820000.0) {
		tmp = t_2;
	} else if (z <= 1550.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) / (-z / a))
	t_2 = x + (a / ((t / z) + -1.0))
	tmp = 0
	if z <= -4.1e+193:
		tmp = t_2
	elif z <= -4.5e+64:
		tmp = t_1
	elif z <= -1820000.0:
		tmp = t_2
	elif z <= 1550.0:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)))
	t_2 = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)))
	tmp = 0.0
	if (z <= -4.1e+193)
		tmp = t_2;
	elseif (z <= -4.5e+64)
		tmp = t_1;
	elseif (z <= -1820000.0)
		tmp = t_2;
	elseif (z <= 1550.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	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));
	t_2 = x + (a / ((t / z) + -1.0));
	tmp = 0.0;
	if (z <= -4.1e+193)
		tmp = t_2;
	elseif (z <= -4.5e+64)
		tmp = t_1;
	elseif (z <= -1820000.0)
		tmp = t_2;
	elseif (z <= 1550.0)
		tmp = x - (a * (y / (t + 1.0)));
	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]}, Block[{t$95$2 = N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+193], t$95$2, If[LessEqual[z, -4.5e+64], t$95$1, If[LessEqual[z, -1820000.0], t$95$2, If[LessEqual[z, 1550.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999997e193 or -4.49999999999999973e64 < z < -1.82e6

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 63.0%

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

      1. sub-neg 63.0%

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

      2. mul-1-neg 63.0%

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

      3. remove-double-neg 63.0%

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

      4. associate-/l* 99.9%

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

      5. div-sub 99.9%

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

      6. *-inverses 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in t around inf 98.1%

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

   if -4.0999999999999997e193 < z < -4.49999999999999973e64 or 1550 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. distribute-neg-frac 84.3%

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

   5. Simplified 84.3%

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

   if -1.82e6 < z < 1550

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+193}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -1820000:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 1550:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7500:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t + 1}{z}}\\ \mathbf{elif}\;z \leq 1450:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- y z) (/ (- z) a)))))
   (if (<= z -1e+194)
     (+ x (/ a (+ (/ t z) -1.0)))
     (if (<= z -1.95e+65)
       t_1
       (if (<= z -7500.0)
         (+ x (/ a (+ -1.0 (/ (+ t 1.0) z))))
         (if (<= z 1450.0) (- x (* a (/ y (+ t 1.0)))) 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 <= -1e+194) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= -1.95e+65) {
		tmp = t_1;
	} else if (z <= -7500.0) {
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	} else if (z <= 1450.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 <= (-1d+194)) then
        tmp = x + (a / ((t / z) + (-1.0d0)))
    else if (z <= (-1.95d+65)) then
        tmp = t_1
    else if (z <= (-7500.0d0)) then
        tmp = x + (a / ((-1.0d0) + ((t + 1.0d0) / z)))
    else if (z <= 1450.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 <= -1e+194) {
		tmp = x + (a / ((t / z) + -1.0));
	} else if (z <= -1.95e+65) {
		tmp = t_1;
	} else if (z <= -7500.0) {
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	} else if (z <= 1450.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 <= -1e+194:
		tmp = x + (a / ((t / z) + -1.0))
	elif z <= -1.95e+65:
		tmp = t_1
	elif z <= -7500.0:
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)))
	elif z <= 1450.0:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)))
	tmp = 0.0
	if (z <= -1e+194)
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	elseif (z <= -1.95e+65)
		tmp = t_1;
	elseif (z <= -7500.0)
		tmp = Float64(x + Float64(a / Float64(-1.0 + Float64(Float64(t + 1.0) / z))));
	elseif (z <= 1450.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	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 <= -1e+194)
		tmp = x + (a / ((t / z) + -1.0));
	elseif (z <= -1.95e+65)
		tmp = t_1;
	elseif (z <= -7500.0)
		tmp = x + (a / (-1.0 + ((t + 1.0) / z)));
	elseif (z <= 1450.0)
		tmp = x - (a * (y / (t + 1.0)));
	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, -1e+194], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e+65], t$95$1, If[LessEqual[z, -7500.0], N[(x + N[(a / N[(-1.0 + N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1450.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.99999999999999945e193

   1. Initial program 96.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 54.3%

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

      1. sub-neg 54.3%

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

      2. mul-1-neg 54.3%

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

      3. remove-double-neg 54.3%

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

      4. associate-/l* 99.9%

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

      5. div-sub 99.9%

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

      6. *-inverses 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in t around inf 99.9%

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

   if -9.99999999999999945e193 < z < -1.9499999999999999e65 or 1450 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. distribute-neg-frac 84.3%

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

   5. Simplified 84.3%

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

   if -1.9499999999999999e65 < z < -7500

   1. Initial program 99.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 89.2%

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

      1. sub-neg 89.2%

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

      2. mul-1-neg 89.2%

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

      3. remove-double-neg 89.2%

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

      4. associate-/l* 99.8%

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

      5. div-sub 99.8%

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

      6. *-inverses 99.8%

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

   9. Simplified 99.8%

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

   if -7500 < z < 1450

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -7500:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t + 1}{z}}\\ \mathbf{elif}\;z \leq 1450:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{if}\;z \leq -1550000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+67} \lor \neg \left(z \leq 2.8 \cdot 10^{+153}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ (/ t z) -1.0)))))
   (if (<= z -1550000.0)
     t_1
     (if (<= z 1.05)
       (- x (* a (/ y (+ t 1.0))))
       (if (or (<= z 7.8e+67) (not (<= z 2.8e+153)))
         t_1
         (+ x (* y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -1550000.0) {
		tmp = t_1;
	} else if (z <= 1.05) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if ((z <= 7.8e+67) || !(z <= 2.8e+153)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a / ((t / z) + (-1.0d0)))
    if (z <= (-1550000.0d0)) then
        tmp = t_1
    else if (z <= 1.05d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if ((z <= 7.8d+67) .or. (.not. (z <= 2.8d+153))) then
        tmp = t_1
    else
        tmp = x + (y * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -1550000.0) {
		tmp = t_1;
	} else if (z <= 1.05) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if ((z <= 7.8e+67) || !(z <= 2.8e+153)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((t / z) + -1.0))
	tmp = 0
	if z <= -1550000.0:
		tmp = t_1
	elif z <= 1.05:
		tmp = x - (a * (y / (t + 1.0)))
	elif (z <= 7.8e+67) or not (z <= 2.8e+153):
		tmp = t_1
	else:
		tmp = x + (y * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)))
	tmp = 0.0
	if (z <= -1550000.0)
		tmp = t_1;
	elseif (z <= 1.05)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif ((z <= 7.8e+67) || !(z <= 2.8e+153))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / ((t / z) + -1.0));
	tmp = 0.0;
	if (z <= -1550000.0)
		tmp = t_1;
	elseif (z <= 1.05)
		tmp = x - (a * (y / (t + 1.0)));
	elseif ((z <= 7.8e+67) || ~((z <= 2.8e+153)))
		tmp = t_1;
	else
		tmp = x + (y * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1550000.0], t$95$1, If[LessEqual[z, 1.05], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.8e+67], N[Not[LessEqual[z, 2.8e+153]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e6 or 1.05000000000000004 < z < 7.80000000000000013e67 or 2.79999999999999985e153 < z

   1. Initial program 96.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 66.1%

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

      1. sub-neg 66.1%

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

      2. mul-1-neg 66.1%

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

      3. remove-double-neg 66.1%

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

      4. associate-/l* 87.5%

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

      5. div-sub 87.5%

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

      6. *-inverses 87.5%

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

   9. Simplified 87.5%

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

   10. Taylor expanded in t around inf 86.9%

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

   if -1.55e6 < z < 1.05000000000000004

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.4%

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

   if 7.80000000000000013e67 < z < 2.79999999999999985e153

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-neg-frac 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*r* 68.7%

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

      3. neg-mul-1 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in a around 0 68.7%

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

       1. mul-1-neg 68.7%

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

       2. *-commutative 68.7%

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

       3. associate-*r/ 82.0%

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

       4. distribute-rgt-neg-in 82.0%

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

   11. Simplified 82.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1550000:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+67} \lor \neg \left(z \leq 2.8 \cdot 10^{+153}\right):\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{if}\;z \leq -16500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 110:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 10^{+68} \lor \neg \left(z \leq 2.9 \cdot 10^{+153}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ (/ t z) -1.0)))))
   (if (<= z -16500.0)
     t_1
     (if (<= z 110.0)
       (- x (* a (/ y (+ t 1.0))))
       (if (or (<= z 1e+68) (not (<= z 2.9e+153)))
         t_1
         (- x (* a (/ y (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -16500.0) {
		tmp = t_1;
	} else if (z <= 110.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if ((z <= 1e+68) || !(z <= 2.9e+153)) {
		tmp = t_1;
	} else {
		tmp = x - (a * (y / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a / ((t / z) + (-1.0d0)))
    if (z <= (-16500.0d0)) then
        tmp = t_1
    else if (z <= 110.0d0) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if ((z <= 1d+68) .or. (.not. (z <= 2.9d+153))) then
        tmp = t_1
    else
        tmp = x - (a * (y / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((t / z) + -1.0));
	double tmp;
	if (z <= -16500.0) {
		tmp = t_1;
	} else if (z <= 110.0) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if ((z <= 1e+68) || !(z <= 2.9e+153)) {
		tmp = t_1;
	} else {
		tmp = x - (a * (y / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((t / z) + -1.0))
	tmp = 0
	if z <= -16500.0:
		tmp = t_1
	elif z <= 110.0:
		tmp = x - (a * (y / (t + 1.0)))
	elif (z <= 1e+68) or not (z <= 2.9e+153):
		tmp = t_1
	else:
		tmp = x - (a * (y / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)))
	tmp = 0.0
	if (z <= -16500.0)
		tmp = t_1;
	elseif (z <= 110.0)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif ((z <= 1e+68) || !(z <= 2.9e+153))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / ((t / z) + -1.0));
	tmp = 0.0;
	if (z <= -16500.0)
		tmp = t_1;
	elseif (z <= 110.0)
		tmp = x - (a * (y / (t + 1.0)));
	elseif ((z <= 1e+68) || ~((z <= 2.9e+153)))
		tmp = t_1;
	else
		tmp = x - (a * (y / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -16500.0], t$95$1, If[LessEqual[z, 110.0], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1e+68], N[Not[LessEqual[z, 2.9e+153]], $MachinePrecision]], t$95$1, N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -16500 or 110 < z < 9.99999999999999953e67 or 2.90000000000000002e153 < z

   1. Initial program 96.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 66.1%

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

      1. sub-neg 66.1%

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

      2. mul-1-neg 66.1%

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

      3. remove-double-neg 66.1%

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

      4. associate-/l* 87.5%

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

      5. div-sub 87.5%

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

      6. *-inverses 87.5%

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

   9. Simplified 87.5%

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

   10. Taylor expanded in t around inf 86.9%

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

   if -16500 < z < 110

   1. Initial program 99.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.4%

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

   if 9.99999999999999953e67 < z < 2.90000000000000002e153

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 86.4%

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

   6. Taylor expanded in y around inf 82.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16500:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 110:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 10^{+68} \lor \neg \left(z \leq 2.9 \cdot 10^{+153}\right):\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;x - \frac{a}{\frac{\left(t - z\right) + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -75000000.0)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 0.00013)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (if (<= t 2.8e+112)
       (- x (/ a (/ (+ (- t z) 1.0) y)))
       (+ x (/ a (+ (/ t z) -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -75000000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 0.00013) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else if (t <= 2.8e+112) {
		tmp = x - (a / (((t - z) + 1.0) / y));
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-75000000.0d0)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 0.00013d0) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else if (t <= 2.8d+112) then
        tmp = x - (a / (((t - z) + 1.0d0) / y))
    else
        tmp = x + (a / ((t / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -75000000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 0.00013) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else if (t <= 2.8e+112) {
		tmp = x - (a / (((t - z) + 1.0) / y));
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -75000000.0:
		tmp = x + ((z - y) / (t / a))
	elif t <= 0.00013:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	elif t <= 2.8e+112:
		tmp = x - (a / (((t - z) + 1.0) / y))
	else:
		tmp = x + (a / ((t / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -75000000.0)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (t <= 0.00013)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	elseif (t <= 2.8e+112)
		tmp = Float64(x - Float64(a / Float64(Float64(Float64(t - z) + 1.0) / y)));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -75000000.0)
		tmp = x + ((z - y) / (t / a));
	elseif (t <= 0.00013)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	elseif (t <= 2.8e+112)
		tmp = x - (a / (((t - z) + 1.0) / y));
	else
		tmp = x + (a / ((t / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -75000000.0], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00013], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+112], N[(x - N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.5e7

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 92.4%

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

   if -7.5e7 < t < 1.29999999999999989e-4

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.6%

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

   if 1.29999999999999989e-4 < t < 2.8000000000000001e112

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 95.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   7. Simplified 99.8%

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

   if 2.8000000000000001e112 < t

   1. Initial program 97.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 76.6%

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

      1. sub-neg 76.6%

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

      2. mul-1-neg 76.6%

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

      3. remove-double-neg 76.6%

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

      4. associate-/l* 92.6%

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

      5. div-sub 92.6%

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

      6. *-inverses 92.6%

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

   9. Simplified 92.6%

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

   10. Taylor expanded in t around inf 92.6%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;x - \frac{a}{\frac{\left(t - z\right) + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 13:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -3.5e-33)
     (- x a)
     (if (<= z 8e-169)
       t_1
       (if (<= z 6.2e-65) (+ x (* z a)) (if (<= z 13.0) 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 <= -3.5e-33) {
		tmp = x - a;
	} else if (z <= 8e-169) {
		tmp = t_1;
	} else if (z <= 6.2e-65) {
		tmp = x + (z * a);
	} else if (z <= 13.0) {
		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 <= (-3.5d-33)) then
        tmp = x - a
    else if (z <= 8d-169) then
        tmp = t_1
    else if (z <= 6.2d-65) then
        tmp = x + (z * a)
    else if (z <= 13.0d0) 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 <= -3.5e-33) {
		tmp = x - a;
	} else if (z <= 8e-169) {
		tmp = t_1;
	} else if (z <= 6.2e-65) {
		tmp = x + (z * a);
	} else if (z <= 13.0) {
		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 <= -3.5e-33:
		tmp = x - a
	elif z <= 8e-169:
		tmp = t_1
	elif z <= 6.2e-65:
		tmp = x + (z * a)
	elif z <= 13.0:
		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 <= -3.5e-33)
		tmp = Float64(x - a);
	elseif (z <= 8e-169)
		tmp = t_1;
	elseif (z <= 6.2e-65)
		tmp = Float64(x + Float64(z * a));
	elseif (z <= 13.0)
		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 <= -3.5e-33)
		tmp = x - a;
	elseif (z <= 8e-169)
		tmp = t_1;
	elseif (z <= 6.2e-65)
		tmp = x + (z * a);
	elseif (z <= 13.0)
		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, -3.5e-33], N[(x - a), $MachinePrecision], If[LessEqual[z, 8e-169], t$95$1, If[LessEqual[z, 6.2e-65], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e-33 or 13 < z

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -3.4999999999999999e-33 < z < 8.00000000000000016e-169 or 6.20000000000000032e-65 < z < 13

   1. Initial program 99.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 75.0%

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

   6. Taylor expanded in z around 0 73.5%

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

   if 8.00000000000000016e-169 < z < 6.20000000000000032e-65

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 89.2%

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

      1. sub-neg 89.2%

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

      2. mul-1-neg 89.2%

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

      3. remove-double-neg 89.2%

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

      4. associate-/l* 89.2%

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

      5. div-sub 89.2%

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

      6. *-inverses 89.2%

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

   9. Simplified 89.2%

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

   10. Taylor expanded in z around 0 89.2%

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

   11. Taylor expanded in t around 0 89.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 13:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -460000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -460000.0)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 1.5e+47)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (+ x (/ a (+ (/ t z) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -460000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 1.5e+47) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-460000.0d0)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 1.5d+47) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x + (a / ((t / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -460000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 1.5e+47) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a / ((t / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -460000.0:
		tmp = x + ((z - y) / (t / a))
	elif t <= 1.5e+47:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x + (a / ((t / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -460000.0)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (t <= 1.5e+47)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(t / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -460000.0)
		tmp = x + ((z - y) / (t / a));
	elseif (t <= 1.5e+47)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x + (a / ((t / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -460000.0], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+47], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6e5

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 92.4%

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

   if -4.6e5 < t < 1.5000000000000001e47

   1. Initial program 98.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.4%

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

   if 1.5000000000000001e47 < t

   1. Initial program 97.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 74.2%

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

      1. sub-neg 74.2%

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

      2. mul-1-neg 74.2%

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

      3. remove-double-neg 74.2%

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

      4. associate-/l* 86.8%

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

      5. div-sub 86.8%

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

      6. *-inverses 86.8%

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

   9. Simplified 86.8%

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

   10. Taylor expanded in t around inf 86.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -460000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.12 \cdot 10^{-33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.12e-33))) (- x a) (+ x (* z a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.12e-33)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 1.12d-33))) 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 <= -1.0) || !(z <= 1.12e-33)) {
		tmp = x - a;
	} else {
		tmp = x + (z * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.12e-33):
		tmp = x - a
	else:
		tmp = x + (z * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.12e-33))
		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 <= -1.0) || ~((z <= 1.12e-33)))
		tmp = x - a;
	else
		tmp = x + (z * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.12e-33]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.11999999999999999e-33 < z

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.5%

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

   if -1 < z < 1.11999999999999999e-33

   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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 70.1%

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

      1. sub-neg 70.1%

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

      2. mul-1-neg 70.1%

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

      3. remove-double-neg 70.1%

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

      4. associate-/l* 70.1%

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

      5. div-sub 70.1%

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

      6. *-inverses 70.1%

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

   9. Simplified 70.1%

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

   10. Taylor expanded in z around 0 70.1%

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

   11. Taylor expanded in t around 0 66.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.12 \cdot 10^{-33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -26000.0) (not (<= z 1.05e-33))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.05e-33)) {
		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 <= (-26000.0d0)) .or. (.not. (z <= 1.05d-33))) 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 <= -26000.0) || !(z <= 1.05e-33)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -26000.0) or not (z <= 1.05e-33):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -26000.0) || !(z <= 1.05e-33))
		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 <= -26000.0) || ~((z <= 1.05e-33)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -26000.0], N[Not[LessEqual[z, 1.05e-33]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -26000 or 1.05e-33 < z

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -26000 < z < 1.05e-33

   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 x around inf 63.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 x around inf 56.7%

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

6. Final simplification 56.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.5% 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 2024019 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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