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

Percentage Accurate: 96.7% → 99.5%

Time: 14.5s

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: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-262}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(-a\right)}{1 - z}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+103}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ (/ 1.0 z) -1.0)))))
   (if (<= t -3.5e-5)
     (- x (/ a (/ t y)))
     (if (<= t -2.55e-296)
       t_1
       (if (<= t 5.5e-262)
         (- x (* y a))
         (if (<= t 3.9e-212)
           t_1
           (if (<= t 1.15e-185)
             (/ (* y (- a)) (- 1.0 z))
             (if (<= t 0.00013)
               t_1
               (if (<= t 1.6e+103)
                 (- x (/ (* y a) t))
                 (if (<= t 3.7e+158) 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 / z) + -1.0));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (a / (t / y));
	} else if (t <= -2.55e-296) {
		tmp = t_1;
	} else if (t <= 5.5e-262) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (y * -a) / (1.0 - z);
	} else if (t <= 0.00013) {
		tmp = t_1;
	} else if (t <= 1.6e+103) {
		tmp = x - ((y * a) / t);
	} else if (t <= 3.7e+158) {
		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 / z) + (-1.0d0)))
    if (t <= (-3.5d-5)) then
        tmp = x - (a / (t / y))
    else if (t <= (-2.55d-296)) then
        tmp = t_1
    else if (t <= 5.5d-262) then
        tmp = x - (y * a)
    else if (t <= 3.9d-212) then
        tmp = t_1
    else if (t <= 1.15d-185) then
        tmp = (y * -a) / (1.0d0 - z)
    else if (t <= 0.00013d0) then
        tmp = t_1
    else if (t <= 1.6d+103) then
        tmp = x - ((y * a) / t)
    else if (t <= 3.7d+158) 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 / z) + -1.0));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = x - (a / (t / y));
	} else if (t <= -2.55e-296) {
		tmp = t_1;
	} else if (t <= 5.5e-262) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = (y * -a) / (1.0 - z);
	} else if (t <= 0.00013) {
		tmp = t_1;
	} else if (t <= 1.6e+103) {
		tmp = x - ((y * a) / t);
	} else if (t <= 3.7e+158) {
		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 / z) + -1.0))
	tmp = 0
	if t <= -3.5e-5:
		tmp = x - (a / (t / y))
	elif t <= -2.55e-296:
		tmp = t_1
	elif t <= 5.5e-262:
		tmp = x - (y * a)
	elif t <= 3.9e-212:
		tmp = t_1
	elif t <= 1.15e-185:
		tmp = (y * -a) / (1.0 - z)
	elif t <= 0.00013:
		tmp = t_1
	elif t <= 1.6e+103:
		tmp = x - ((y * a) / t)
	elif t <= 3.7e+158:
		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(Float64(1.0 / z) + -1.0)))
	tmp = 0.0
	if (t <= -3.5e-5)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (t <= -2.55e-296)
		tmp = t_1;
	elseif (t <= 5.5e-262)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = Float64(Float64(y * Float64(-a)) / Float64(1.0 - z));
	elseif (t <= 0.00013)
		tmp = t_1;
	elseif (t <= 1.6e+103)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (t <= 3.7e+158)
		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 / z) + -1.0));
	tmp = 0.0;
	if (t <= -3.5e-5)
		tmp = x - (a / (t / y));
	elseif (t <= -2.55e-296)
		tmp = t_1;
	elseif (t <= 5.5e-262)
		tmp = x - (y * a);
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = (y * -a) / (1.0 - z);
	elseif (t <= 0.00013)
		tmp = t_1;
	elseif (t <= 1.6e+103)
		tmp = x - ((y * a) / t);
	elseif (t <= 3.7e+158)
		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[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-5], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.55e-296], t$95$1, If[LessEqual[t, 5.5e-262], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-212], t$95$1, If[LessEqual[t, 1.15e-185], N[(N[(y * (-a)), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00013], t$95$1, If[LessEqual[t, 1.6e+103], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+158], 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. Step-by-step derivation

      1. associate-/l* 83.3%

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

   10. Simplified 83.3%

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

   if -3.4999999999999997e-5 < t < -2.54999999999999984e-296 or 5.5000000000000004e-262 < t < 3.9e-212 or 1.15e-185 < t < 1.29999999999999989e-4 or 1.59999999999999996e103 < t < 3.70000000000000011e158

   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 -2.54999999999999984e-296 < t < 5.5000000000000004e-262

   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 < 1.59999999999999996e103

   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 3.70000000000000011e158 < 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. sub-neg 79.1%

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

      2. mul-1-neg 79.1%

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

      3. remove-double-neg 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-296}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-262}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(-a\right)}{1 - z}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+103}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-277}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-74}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (/ a (/ t y)))))
   (if (<= t -2.6e-14)
     t_2
     (if (<= t -2.85e-277)
       (- x a)
       (if (<= t 2e-129)
         t_1
         (if (<= t 9e-74)
           (- x a)
           (if (<= t 1.05e-58)
             t_1
             (if (<= t 1.8e-5)
               (- x (+ a (/ a z)))
               (if (<= t 5.2e+162) t_2 (+ x (/ a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -2.6e-14) {
		tmp = t_2;
	} else if (t <= -2.85e-277) {
		tmp = x - a;
	} else if (t <= 2e-129) {
		tmp = t_1;
	} else if (t <= 9e-74) {
		tmp = x - a;
	} else if (t <= 1.05e-58) {
		tmp = t_1;
	} else if (t <= 1.8e-5) {
		tmp = x - (a + (a / z));
	} else if (t <= 5.2e+162) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - (y * a)
    t_2 = x - (a / (t / y))
    if (t <= (-2.6d-14)) then
        tmp = t_2
    else if (t <= (-2.85d-277)) then
        tmp = x - a
    else if (t <= 2d-129) then
        tmp = t_1
    else if (t <= 9d-74) then
        tmp = x - a
    else if (t <= 1.05d-58) then
        tmp = t_1
    else if (t <= 1.8d-5) then
        tmp = x - (a + (a / z))
    else if (t <= 5.2d+162) then
        tmp = t_2
    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);
	double t_2 = x - (a / (t / y));
	double tmp;
	if (t <= -2.6e-14) {
		tmp = t_2;
	} else if (t <= -2.85e-277) {
		tmp = x - a;
	} else if (t <= 2e-129) {
		tmp = t_1;
	} else if (t <= 9e-74) {
		tmp = x - a;
	} else if (t <= 1.05e-58) {
		tmp = t_1;
	} else if (t <= 1.8e-5) {
		tmp = x - (a + (a / z));
	} else if (t <= 5.2e+162) {
		tmp = t_2;
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (a / (t / y))
	tmp = 0
	if t <= -2.6e-14:
		tmp = t_2
	elif t <= -2.85e-277:
		tmp = x - a
	elif t <= 2e-129:
		tmp = t_1
	elif t <= 9e-74:
		tmp = x - a
	elif t <= 1.05e-58:
		tmp = t_1
	elif t <= 1.8e-5:
		tmp = x - (a + (a / z))
	elif t <= 5.2e+162:
		tmp = t_2
	else:
		tmp = x + (a / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -2.6e-14)
		tmp = t_2;
	elseif (t <= -2.85e-277)
		tmp = Float64(x - a);
	elseif (t <= 2e-129)
		tmp = t_1;
	elseif (t <= 9e-74)
		tmp = Float64(x - a);
	elseif (t <= 1.05e-58)
		tmp = t_1;
	elseif (t <= 1.8e-5)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (t <= 5.2e+162)
		tmp = t_2;
	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_2 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -2.6e-14)
		tmp = t_2;
	elseif (t <= -2.85e-277)
		tmp = x - a;
	elseif (t <= 2e-129)
		tmp = t_1;
	elseif (t <= 9e-74)
		tmp = x - a;
	elseif (t <= 1.05e-58)
		tmp = t_1;
	elseif (t <= 1.8e-5)
		tmp = x - (a + (a / z));
	elseif (t <= 5.2e+162)
		tmp = t_2;
	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 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-14], t$95$2, If[LessEqual[t, -2.85e-277], N[(x - a), $MachinePrecision], If[LessEqual[t, 2e-129], t$95$1, If[LessEqual[t, 9e-74], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.05e-58], t$95$1, If[LessEqual[t, 1.8e-5], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+162], t$95$2, N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.59999999999999997e-14 or 1.80000000000000005e-5 < t < 5.2e162

   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. Step-by-step derivation

      1. associate-/l* 82.8%

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

   10. Simplified 82.8%

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

   if -2.59999999999999997e-14 < t < -2.84999999999999977e-277 or 1.9999999999999999e-129 < t < 8.9999999999999998e-74

   1. Initial program 97.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.3%

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

   if -2.84999999999999977e-277 < t < 1.9999999999999999e-129 or 8.9999999999999998e-74 < t < 1.04999999999999994e-58

   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 78.8%

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

   if 1.04999999999999994e-58 < t < 1.80000000000000005e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. frac-2neg 99.8%

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

      2. div-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. metadata-eval 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 78.7%

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

      1. associate-/l* 100.0%

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

      2. associate--r+ 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around 0 100.0%

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

   11. Taylor expanded in z around inf 87.2%

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

   if 5.2e162 < 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. sub-neg 81.2%

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

      2. mul-1-neg 81.2%

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

      3. remove-double-neg 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 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-277}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-129}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-74}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+162}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-278}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+162}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= t -2.6e-14)
     (- x (/ a (/ t y)))
     (if (<= t -8.6e-278)
       (- x a)
       (if (<= t 8.8e-136)
         t_1
         (if (<= t 7.4e-75)
           (- x a)
           (if (<= t 8.2e-57)
             t_1
             (if (<= t 1.2e-5)
               (- x (+ a (/ a z)))
               (if (<= t 3.5e+162)
                 (- x (/ (* y a) t))
                 (+ x (/ a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (t <= -2.6e-14) {
		tmp = x - (a / (t / y));
	} else if (t <= -8.6e-278) {
		tmp = x - a;
	} else if (t <= 8.8e-136) {
		tmp = t_1;
	} else if (t <= 7.4e-75) {
		tmp = x - a;
	} else if (t <= 8.2e-57) {
		tmp = t_1;
	} else if (t <= 1.2e-5) {
		tmp = x - (a + (a / z));
	} else if (t <= 3.5e+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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (t <= (-2.6d-14)) then
        tmp = x - (a / (t / y))
    else if (t <= (-8.6d-278)) then
        tmp = x - a
    else if (t <= 8.8d-136) then
        tmp = t_1
    else if (t <= 7.4d-75) then
        tmp = x - a
    else if (t <= 8.2d-57) then
        tmp = t_1
    else if (t <= 1.2d-5) then
        tmp = x - (a + (a / z))
    else if (t <= 3.5d+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 t_1 = x - (y * a);
	double tmp;
	if (t <= -2.6e-14) {
		tmp = x - (a / (t / y));
	} else if (t <= -8.6e-278) {
		tmp = x - a;
	} else if (t <= 8.8e-136) {
		tmp = t_1;
	} else if (t <= 7.4e-75) {
		tmp = x - a;
	} else if (t <= 8.2e-57) {
		tmp = t_1;
	} else if (t <= 1.2e-5) {
		tmp = x - (a + (a / z));
	} else if (t <= 3.5e+162) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + (a / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if t <= -2.6e-14:
		tmp = x - (a / (t / y))
	elif t <= -8.6e-278:
		tmp = x - a
	elif t <= 8.8e-136:
		tmp = t_1
	elif t <= 7.4e-75:
		tmp = x - a
	elif t <= 8.2e-57:
		tmp = t_1
	elif t <= 1.2e-5:
		tmp = x - (a + (a / z))
	elif t <= 3.5e+162:
		tmp = x - ((y * a) / t)
	else:
		tmp = x + (a / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (t <= -2.6e-14)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (t <= -8.6e-278)
		tmp = Float64(x - a);
	elseif (t <= 8.8e-136)
		tmp = t_1;
	elseif (t <= 7.4e-75)
		tmp = Float64(x - a);
	elseif (t <= 8.2e-57)
		tmp = t_1;
	elseif (t <= 1.2e-5)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (t <= 3.5e+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)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (t <= -2.6e-14)
		tmp = x - (a / (t / y));
	elseif (t <= -8.6e-278)
		tmp = x - a;
	elseif (t <= 8.8e-136)
		tmp = t_1;
	elseif (t <= 7.4e-75)
		tmp = x - a;
	elseif (t <= 8.2e-57)
		tmp = t_1;
	elseif (t <= 1.2e-5)
		tmp = x - (a + (a / z));
	elseif (t <= 3.5e+162)
		tmp = x - ((y * a) / t);
	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 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-14], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.6e-278], N[(x - a), $MachinePrecision], If[LessEqual[t, 8.8e-136], t$95$1, If[LessEqual[t, 7.4e-75], N[(x - a), $MachinePrecision], If[LessEqual[t, 8.2e-57], t$95$1, If[LessEqual[t, 1.2e-5], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+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 6 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. Step-by-step derivation

      1. associate-/l* 83.2%

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

   10. Simplified 83.2%

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

   if -2.59999999999999997e-14 < t < -8.5999999999999998e-278 or 8.8000000000000005e-136 < t < 7.40000000000000047e-75

   1. Initial program 97.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.3%

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

   if -8.5999999999999998e-278 < t < 8.8000000000000005e-136 or 7.40000000000000047e-75 < t < 8.2000000000000003e-57

   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 78.8%

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

   if 8.2000000000000003e-57 < t < 1.2e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. frac-2neg 99.8%

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

      2. div-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. metadata-eval 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 78.7%

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

      1. associate-/l* 100.0%

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

      2. associate--r+ 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around 0 100.0%

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

   11. Taylor expanded in z around inf 87.2%

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

   if 1.2e-5 < t < 3.50000000000000018e162

   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 3.50000000000000018e162 < 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. sub-neg 81.2%

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

      2. mul-1-neg 81.2%

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

      3. remove-double-neg 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 6 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-278}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-136}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-57}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+162}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{1}{z} + -1}\\ t_2 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(-a\right)}{1 - z}\\ \mathbf{elif}\;t \leq 6600000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ (/ 1.0 z) -1.0)))) (t_2 (+ x (* (/ a t) (- z y)))))
   (if (<= t -3.5e-5)
     t_2
     (if (<= t -1.9e-301)
       t_1
       (if (<= t 6.2e-263)
         (- x (* y a))
         (if (<= t 3.9e-212)
           t_1
           (if (<= t 3e-185)
             (/ (* y (- a)) (- 1.0 z))
             (if (<= t 6600000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((1.0 / z) + -1.0));
	double t_2 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = t_2;
	} else if (t <= -1.9e-301) {
		tmp = t_1;
	} else if (t <= 6.2e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 3e-185) {
		tmp = (y * -a) / (1.0 - z);
	} else if (t <= 6600000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a / ((1.0d0 / z) + (-1.0d0)))
    t_2 = x + ((a / t) * (z - y))
    if (t <= (-3.5d-5)) then
        tmp = t_2
    else if (t <= (-1.9d-301)) then
        tmp = t_1
    else if (t <= 6.2d-263) then
        tmp = x - (y * a)
    else if (t <= 3.9d-212) then
        tmp = t_1
    else if (t <= 3d-185) then
        tmp = (y * -a) / (1.0d0 - z)
    else if (t <= 6600000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((1.0 / z) + -1.0));
	double t_2 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -3.5e-5) {
		tmp = t_2;
	} else if (t <= -1.9e-301) {
		tmp = t_1;
	} else if (t <= 6.2e-263) {
		tmp = x - (y * a);
	} else if (t <= 3.9e-212) {
		tmp = t_1;
	} else if (t <= 3e-185) {
		tmp = (y * -a) / (1.0 - z);
	} else if (t <= 6600000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((1.0 / z) + -1.0))
	t_2 = x + ((a / t) * (z - y))
	tmp = 0
	if t <= -3.5e-5:
		tmp = t_2
	elif t <= -1.9e-301:
		tmp = t_1
	elif t <= 6.2e-263:
		tmp = x - (y * a)
	elif t <= 3.9e-212:
		tmp = t_1
	elif t <= 3e-185:
		tmp = (y * -a) / (1.0 - z)
	elif t <= 6600000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(1.0 / z) + -1.0)))
	t_2 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -3.5e-5)
		tmp = t_2;
	elseif (t <= -1.9e-301)
		tmp = t_1;
	elseif (t <= 6.2e-263)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 3e-185)
		tmp = Float64(Float64(y * Float64(-a)) / Float64(1.0 - z));
	elseif (t <= 6600000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / ((1.0 / z) + -1.0));
	t_2 = x + ((a / t) * (z - y));
	tmp = 0.0;
	if (t <= -3.5e-5)
		tmp = t_2;
	elseif (t <= -1.9e-301)
		tmp = t_1;
	elseif (t <= 6.2e-263)
		tmp = x - (y * a);
	elseif (t <= 3.9e-212)
		tmp = t_1;
	elseif (t <= 3e-185)
		tmp = (y * -a) / (1.0 - z);
	elseif (t <= 6600000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-5], t$95$2, If[LessEqual[t, -1.9e-301], t$95$1, If[LessEqual[t, 6.2e-263], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-212], t$95$1, If[LessEqual[t, 3e-185], N[(N[(y * (-a)), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6600000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.4999999999999997e-5 or 6.6e6 < t

   1. Initial program 98.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 86.9%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. associate-*l/ 87.1%

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

   8. Simplified 87.1%

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

   if -3.4999999999999997e-5 < t < -1.89999999999999998e-301 or 6.20000000000000008e-263 < t < 3.9e-212 or 3.0000000000000003e-185 < t < 6.6e6

   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 67.9%

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

      1. sub-neg 67.9%

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

      2. mul-1-neg 67.9%

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

      3. remove-double-neg 67.9%

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

      4. associate-/l* 81.2%

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

      5. div-sub 81.2%

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

      6. *-inverses 81.2%

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

   8. Simplified 81.2%

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

   if -1.89999999999999998e-301 < t < 6.20000000000000008e-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 < 3.0000000000000003e-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%

      \[\leadsto \color{blue}{\frac{\left(-a\right) \cdot y}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-212}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot \left(-a\right)}{1 - z}\\ \mathbf{elif}\;t \leq 6600000:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - y}{\frac{-z}{a}}\\ t_2 := x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -43:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 12.5:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z y) (/ (- z) a))))
        (t_2 (+ x (/ a (/ (+ (- t z) 1.0) z)))))
   (if (<= z -1.5e+194)
     t_2
     (if (<= z -3.8e+64)
       t_1
       (if (<= z -43.0)
         t_2
         (if (<= z 12.5) (- 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 + ((z - y) / (-z / a));
	double t_2 = x + (a / (((t - z) + 1.0) / z));
	double tmp;
	if (z <= -1.5e+194) {
		tmp = t_2;
	} else if (z <= -3.8e+64) {
		tmp = t_1;
	} else if (z <= -43.0) {
		tmp = t_2;
	} else if (z <= 12.5) {
		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 + ((z - y) / (-z / a))
    t_2 = x + (a / (((t - z) + 1.0d0) / z))
    if (z <= (-1.5d+194)) then
        tmp = t_2
    else if (z <= (-3.8d+64)) then
        tmp = t_1
    else if (z <= (-43.0d0)) then
        tmp = t_2
    else if (z <= 12.5d0) 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 + ((z - y) / (-z / a));
	double t_2 = x + (a / (((t - z) + 1.0) / z));
	double tmp;
	if (z <= -1.5e+194) {
		tmp = t_2;
	} else if (z <= -3.8e+64) {
		tmp = t_1;
	} else if (z <= -43.0) {
		tmp = t_2;
	} else if (z <= 12.5) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) / (-z / a))
	t_2 = x + (a / (((t - z) + 1.0) / z))
	tmp = 0
	if z <= -1.5e+194:
		tmp = t_2
	elif z <= -3.8e+64:
		tmp = t_1
	elif z <= -43.0:
		tmp = t_2
	elif z <= 12.5:
		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(z - y) / Float64(Float64(-z) / a)))
	t_2 = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)))
	tmp = 0.0
	if (z <= -1.5e+194)
		tmp = t_2;
	elseif (z <= -3.8e+64)
		tmp = t_1;
	elseif (z <= -43.0)
		tmp = t_2;
	elseif (z <= 12.5)
		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 + ((z - y) / (-z / a));
	t_2 = x + (a / (((t - z) + 1.0) / z));
	tmp = 0.0;
	if (z <= -1.5e+194)
		tmp = t_2;
	elseif (z <= -3.8e+64)
		tmp = t_1;
	elseif (z <= -43.0)
		tmp = t_2;
	elseif (z <= 12.5)
		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[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+194], t$95$2, If[LessEqual[z, -3.8e+64], t$95$1, If[LessEqual[z, -43.0], t$95$2, If[LessEqual[z, 12.5], 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 < -1.5000000000000002e194 or -3.8000000000000001e64 < z < -43

   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 y around 0 63.0%

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   6. 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. *-commutative 63.0%

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

      4. associate--l+ 63.0%

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

      5. +-commutative 63.0%

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

      6. associate-*r/ 97.3%

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

      7. remove-double-neg 97.3%

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

      8. associate-*r/ 63.0%

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

      9. *-commutative 63.0%

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

      10. +-commutative 63.0%

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

      11. associate--l+ 63.0%

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

      12. associate-/l* 99.9%

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

      13. associate--l+ 99.9%

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

   7. Simplified 99.9%

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

   if -1.5000000000000002e194 < z < -3.8000000000000001e64 or 12.5 < 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 -43 < z < 12.5

   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 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+194}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -43:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 12.5:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -500000:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -500000.0)
   (+ x (/ a (+ (/ 1.0 z) -1.0)))
   (if (<= z 5.7e-12)
     (- x (* a (/ y (+ t 1.0))))
     (if (<= z 6.2e+216) (- x (* a (/ y (- 1.0 z)))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -500000.0) {
		tmp = x + (a / ((1.0 / z) + -1.0));
	} else if (z <= 5.7e-12) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 6.2e+216) {
		tmp = x - (a * (y / (1.0 - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-500000.0d0)) then
        tmp = x + (a / ((1.0d0 / z) + (-1.0d0)))
    else if (z <= 5.7d-12) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 6.2d+216) then
        tmp = x - (a * (y / (1.0d0 - z)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -500000.0) {
		tmp = x + (a / ((1.0 / z) + -1.0));
	} else if (z <= 5.7e-12) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 6.2e+216) {
		tmp = x - (a * (y / (1.0 - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -500000.0:
		tmp = x + (a / ((1.0 / z) + -1.0))
	elif z <= 5.7e-12:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 6.2e+216:
		tmp = x - (a * (y / (1.0 - z)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -500000.0)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 / z) + -1.0)));
	elseif (z <= 5.7e-12)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 6.2e+216)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -500000.0)
		tmp = x + (a / ((1.0 / z) + -1.0));
	elseif (z <= 5.7e-12)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 6.2e+216)
		tmp = x - (a * (y / (1.0 - z)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -500000.0], N[(x + N[(a / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-12], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+216], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5e5

   1. Initial program 96.6%

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

      1. associate-/r/ 99.9%

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

   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 89.4%

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

   6. Taylor expanded in y around 0 60.0%

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

      1. sub-neg 60.0%

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

      2. mul-1-neg 60.0%

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

      3. remove-double-neg 60.0%

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

      4. associate-/l* 80.8%

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

      5. div-sub 80.8%

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

      6. *-inverses 80.8%

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

   8. Simplified 80.8%

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

   if -5e5 < z < 5.7000000000000003e-12

   1. Initial program 99.8%

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

      1. associate-/r/ 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 93.9%

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

   if 5.7000000000000003e-12 < z < 6.20000000000000007e216

   1. Initial program 98.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 81.5%

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

   6. Taylor expanded in y around inf 70.4%

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

   if 6.20000000000000007e216 < z

   1. Initial program 93.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500000:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+46}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -75000000.0)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 5e+46)
     (- x (* a (/ (- y z) (- 1.0 z))))
     (+ x (/ a (/ (+ (- t z) 1.0) z))))))

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 <= 5e+46) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x + (a / (((t - z) + 1.0) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-75000000.0d0)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 5d+46) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -75000000.0) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 5e+46) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x + (a / (((t - z) + 1.0) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -75000000.0:
		tmp = x + ((z - y) / (t / a))
	elif t <= 5e+46:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	else:
		tmp = x + (a / (((t - z) + 1.0) / z))
	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 <= 5e+46)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	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 <= 5e+46)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	else
		tmp = x + (a / (((t - z) + 1.0) / z));
	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, 5e+46], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 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 < 5.0000000000000002e46

   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 5.0000000000000002e46 < 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. Taylor expanded in y around 0 74.2%

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   6. 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. *-commutative 74.2%

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

      4. associate--l+ 74.2%

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

      5. +-commutative 74.2%

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

      6. associate-*r/ 85.0%

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

      7. remove-double-neg 85.0%

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

      8. associate-*r/ 74.2%

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

      9. *-commutative 74.2%

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

      10. +-commutative 74.2%

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

      11. associate--l+ 74.2%

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

      12. associate-/l* 86.8%

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

      13. associate--l+ 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+46}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15 \lor \neg \left(z \leq 1200\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -15.0) (not (<= z 1200.0)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -15.0) || !(z <= 1200.0)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-15.0d0)) .or. (.not. (z <= 1200.0d0))) then
        tmp = x + ((z - y) / (-z / a))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -15.0) || !(z <= 1200.0)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -15.0) or not (z <= 1200.0):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -15.0) || !(z <= 1200.0))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -15.0) || ~((z <= 1200.0)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -15.0], N[Not[LessEqual[z, 1200.0]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -15 or 1200 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-neg-frac 83.3%

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

   5. Simplified 83.3%

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

   if -15 < z < 1200

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 94.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15 \lor \neg \left(z \leq 1200\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.14:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -3.05e-33)
     (- x a)
     (if (<= z 5.4e-169)
       t_1
       (if (<= z 8.2e-53) x (if (<= z 0.14) 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 <= -3.05e-33) {
		tmp = x - a;
	} else if (z <= 5.4e-169) {
		tmp = t_1;
	} else if (z <= 8.2e-53) {
		tmp = x;
	} else if (z <= 0.14) {
		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 <= (-3.05d-33)) then
        tmp = x - a
    else if (z <= 5.4d-169) then
        tmp = t_1
    else if (z <= 8.2d-53) then
        tmp = x
    else if (z <= 0.14d0) 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 <= -3.05e-33) {
		tmp = x - a;
	} else if (z <= 5.4e-169) {
		tmp = t_1;
	} else if (z <= 8.2e-53) {
		tmp = x;
	} else if (z <= 0.14) {
		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 <= -3.05e-33:
		tmp = x - a
	elif z <= 5.4e-169:
		tmp = t_1
	elif z <= 8.2e-53:
		tmp = x
	elif z <= 0.14:
		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 <= -3.05e-33)
		tmp = Float64(x - a);
	elseif (z <= 5.4e-169)
		tmp = t_1;
	elseif (z <= 8.2e-53)
		tmp = x;
	elseif (z <= 0.14)
		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 <= -3.05e-33)
		tmp = x - a;
	elseif (z <= 5.4e-169)
		tmp = t_1;
	elseif (z <= 8.2e-53)
		tmp = x;
	elseif (z <= 0.14)
		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, -3.05e-33], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.4e-169], t$95$1, If[LessEqual[z, 8.2e-53], x, If[LessEqual[z, 0.14], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0500000000000001e-33 or 0.14000000000000001 < 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 -3.0500000000000001e-33 < z < 5.4000000000000003e-169 or 8.2000000000000001e-53 < z < 0.14000000000000001

   1. Initial program 99.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 75.9%

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

   6. Taylor expanded in z around 0 73.4%

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

   if 5.4000000000000003e-169 < z < 8.2000000000000001e-53

   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 x around inf 77.9%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.14:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -4 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-63}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 44:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -4e-33)
     (- x a)
     (if (<= z 8e-169)
       t_1
       (if (<= z 2.5e-63) (+ x (* z a)) (if (<= z 44.0) 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 <= -4e-33) {
		tmp = x - a;
	} else if (z <= 8e-169) {
		tmp = t_1;
	} else if (z <= 2.5e-63) {
		tmp = x + (z * a);
	} else if (z <= 44.0) {
		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 <= (-4d-33)) then
        tmp = x - a
    else if (z <= 8d-169) then
        tmp = t_1
    else if (z <= 2.5d-63) then
        tmp = x + (z * a)
    else if (z <= 44.0d0) 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 <= -4e-33) {
		tmp = x - a;
	} else if (z <= 8e-169) {
		tmp = t_1;
	} else if (z <= 2.5e-63) {
		tmp = x + (z * a);
	} else if (z <= 44.0) {
		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 <= -4e-33:
		tmp = x - a
	elif z <= 8e-169:
		tmp = t_1
	elif z <= 2.5e-63:
		tmp = x + (z * a)
	elif z <= 44.0:
		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 <= -4e-33)
		tmp = Float64(x - a);
	elseif (z <= 8e-169)
		tmp = t_1;
	elseif (z <= 2.5e-63)
		tmp = Float64(x + Float64(z * a));
	elseif (z <= 44.0)
		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 <= -4e-33)
		tmp = x - a;
	elseif (z <= 8e-169)
		tmp = t_1;
	elseif (z <= 2.5e-63)
		tmp = x + (z * a);
	elseif (z <= 44.0)
		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, -4e-33], N[(x - a), $MachinePrecision], If[LessEqual[z, 8e-169], t$95$1, If[LessEqual[z, 2.5e-63], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 44.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000002e-33 or 44 < 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 -4.0000000000000002e-33 < z < 8.00000000000000016e-169 or 2.5000000000000001e-63 < z < 44

   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 < 2.5000000000000001e-63

   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. frac-2neg 100.0%

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

      2. div-inv 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 89.2%

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

      1. associate-/l* 89.2%

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

      2. associate--r+ 89.2%

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

      3. sub-neg 89.2%

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

      4. metadata-eval 89.2%

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

   9. Simplified 89.2%

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

   10. Taylor expanded in t around 0 89.1%

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

   11. Taylor expanded in z around 0 89.2%

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

       1. mul-1-neg 89.2%

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

       2. distribute-rgt-neg-out 89.2%

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

   13. Simplified 89.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-33}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-63}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 44:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -2.5e-33)
     (- x (+ a (/ a z)))
     (if (<= z 2e-169)
       t_1
       (if (<= z 3.7e-65) (+ x (* z a)) (if (<= z 1.0) 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 <= -2.5e-33) {
		tmp = x - (a + (a / z));
	} else if (z <= 2e-169) {
		tmp = t_1;
	} else if (z <= 3.7e-65) {
		tmp = x + (z * a);
	} else if (z <= 1.0) {
		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 <= (-2.5d-33)) then
        tmp = x - (a + (a / z))
    else if (z <= 2d-169) then
        tmp = t_1
    else if (z <= 3.7d-65) then
        tmp = x + (z * a)
    else if (z <= 1.0d0) 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 <= -2.5e-33) {
		tmp = x - (a + (a / z));
	} else if (z <= 2e-169) {
		tmp = t_1;
	} else if (z <= 3.7e-65) {
		tmp = x + (z * a);
	} else if (z <= 1.0) {
		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 <= -2.5e-33:
		tmp = x - (a + (a / z))
	elif z <= 2e-169:
		tmp = t_1
	elif z <= 3.7e-65:
		tmp = x + (z * a)
	elif z <= 1.0:
		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 <= -2.5e-33)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (z <= 2e-169)
		tmp = t_1;
	elseif (z <= 3.7e-65)
		tmp = Float64(x + Float64(z * a));
	elseif (z <= 1.0)
		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 <= -2.5e-33)
		tmp = x - (a + (a / z));
	elseif (z <= 2e-169)
		tmp = t_1;
	elseif (z <= 3.7e-65)
		tmp = x + (z * a);
	elseif (z <= 1.0)
		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, -2.5e-33], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-169], t$95$1, If[LessEqual[z, 3.7e-65], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.50000000000000014e-33

   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. frac-2neg 99.9%

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

      2. div-inv 99.7%

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

      3. +-commutative 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. metadata-eval 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 61.5%

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

      1. associate-/l* 86.9%

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

      2. associate--r+ 86.9%

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

      3. sub-neg 86.9%

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

      4. metadata-eval 86.9%

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

   9. Simplified 86.9%

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

   10. Taylor expanded in t around 0 78.4%

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

   11. Taylor expanded in z around inf 78.4%

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

   if -2.50000000000000014e-33 < z < 2.00000000000000004e-169 or 3.7e-65 < z < 1

   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 2.00000000000000004e-169 < z < 3.7e-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. frac-2neg 100.0%

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

      2. div-inv 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 89.2%

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

      1. associate-/l* 89.2%

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

      2. associate--r+ 89.2%

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

      3. sub-neg 89.2%

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

      4. metadata-eval 89.2%

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

   9. Simplified 89.2%

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

   10. Taylor expanded in t around 0 89.1%

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

   11. Taylor expanded in z around 0 89.2%

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

       1. mul-1-neg 89.2%

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

       2. distribute-rgt-neg-out 89.2%

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

   13. Simplified 89.2%

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

   if 1 < z

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 68.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165 \lor \neg \left(z \leq 150\right):\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -165.0) (not (<= z 150.0)))
   (+ x (/ a (+ (/ 1.0 z) -1.0)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -165.0) || !(z <= 150.0)) {
		tmp = x + (a / ((1.0 / z) + -1.0));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-165.0d0)) .or. (.not. (z <= 150.0d0))) then
        tmp = x + (a / ((1.0d0 / z) + (-1.0d0)))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -165.0) || !(z <= 150.0)) {
		tmp = x + (a / ((1.0 / z) + -1.0));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -165.0) or not (z <= 150.0):
		tmp = x + (a / ((1.0 / z) + -1.0))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -165.0) || !(z <= 150.0))
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 / z) + -1.0)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -165.0) || ~((z <= 150.0)))
		tmp = x + (a / ((1.0 / z) + -1.0));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -165.0], N[Not[LessEqual[z, 150.0]], $MachinePrecision]], N[(x + N[(a / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -165 or 150 < z

   1. Initial program 96.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 86.7%

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

   6. Taylor expanded in y around 0 59.7%

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

      1. sub-neg 59.7%

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

      2. mul-1-neg 59.7%

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

      3. remove-double-neg 59.7%

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

      4. associate-/l* 74.2%

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

      5. div-sub 74.2%

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

      6. *-inverses 74.2%

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

   8. Simplified 74.2%

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

   if -165 < z < 150

   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 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165 \lor \neg \left(z \leq 150\right):\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10600 \lor \neg \left(z \leq 9.2 \cdot 10^{-34}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -10600.0) (not (<= z 9.2e-34))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -10600.0) || !(z <= 9.2e-34)) {
		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 <= (-10600.0d0)) .or. (.not. (z <= 9.2d-34))) 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 <= -10600.0) || !(z <= 9.2e-34)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -10600.0) or not (z <= 9.2e-34):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -10600.0) || !(z <= 9.2e-34))
		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 <= -10600.0) || ~((z <= 9.2e-34)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -10600.0], N[Not[LessEqual[z, 9.2e-34]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -10600 or 9.20000000000000045e-34 < 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 -10600 < z < 9.20000000000000045e-34

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10600 \lor \neg \left(z \leq 9.2 \cdot 10^{-34}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+244}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -6.2e+244) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+244) {
		tmp = -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 (a <= (-6.2d+244)) then
        tmp = -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 (a <= -6.2e+244) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+244:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+244)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+244)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+244], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -6.20000000000000001e244

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-neg-frac 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in x around 0 11.8%

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

   7. Taylor expanded in y around 0 58.3%

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

      1. neg-mul-1 58.3%

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

   9. Simplified 58.3%

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

   if -6.20000000000000001e244 < a

   1. Initial program 98.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 59.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+244}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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))))