Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.6% → 88.6%

Time: 27.0s

Alternatives: 22

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

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 - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+197} \lor \neg \left(z \leq 8.2 \cdot 10^{+215}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+197) (not (<= z 8.2e+215)))
   (+ t (/ (- x t) (/ z (- y a))))
   (- x (* (- t x) (/ (- z y) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+197) || !(z <= 8.2e+215)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.2d+197)) .or. (.not. (z <= 8.2d+215))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x - ((t - x) * ((z - y) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+197) || !(z <= 8.2e+215)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+197) or not (z <= 8.2e+215):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x - ((t - x) * ((z - y) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+197) || !(z <= 8.2e+215))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+197) || ~((z <= 8.2e+215)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+197], N[Not[LessEqual[z, 8.2e+215]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999975e197 or 8.2000000000000007e215 < z

   1. Initial program 18.2%

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

      1. associate-*l/ 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in z around inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. associate-*r/ 61.7%

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

      3. associate-*r/ 61.7%

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

      4. div-sub 61.7%

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

      5. distribute-lft-out-- 61.7%

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

      6. associate-*r/ 61.7%

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

      7. distribute-rgt-out-- 62.1%

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

      8. mul-1-neg 62.1%

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

      9. unsub-neg 62.1%

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

      10. associate-/l* 92.5%

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

   6. Simplified 92.5%

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

   if -5.19999999999999975e197 < z < 8.2000000000000007e215

   1. Initial program 76.8%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+197} \lor \neg \left(z \leq 8.2 \cdot 10^{+215}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \]

Alternative 2: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* t (- z y)) (- a z)))))
   (if (<= y -6.6e+68)
     (* y (/ (- t x) (- a z)))
     (if (<= y -4.1e-31)
       t_1
       (if (<= y -3e-229)
         (/ t (/ (- a z) (- y z)))
         (if (<= y 7.8e-130)
           t_1
           (if (<= y 5.2e+62)
             (+ x (/ (- t x) (/ a (- y z))))
             (/ (- t x) (/ (- a z) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t * (z - y)) / (a - z));
	double tmp;
	if (y <= -6.6e+68) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -4.1e-31) {
		tmp = t_1;
	} else if (y <= -3e-229) {
		tmp = t / ((a - z) / (y - z));
	} else if (y <= 7.8e-130) {
		tmp = t_1;
	} else if (y <= 5.2e+62) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = (t - x) / ((a - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t * (z - y)) / (a - z))
    if (y <= (-6.6d+68)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= (-4.1d-31)) then
        tmp = t_1
    else if (y <= (-3d-229)) then
        tmp = t / ((a - z) / (y - z))
    else if (y <= 7.8d-130) then
        tmp = t_1
    else if (y <= 5.2d+62) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = (t - x) / ((a - z) / y)
    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 - ((t * (z - y)) / (a - z));
	double tmp;
	if (y <= -6.6e+68) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -4.1e-31) {
		tmp = t_1;
	} else if (y <= -3e-229) {
		tmp = t / ((a - z) / (y - z));
	} else if (y <= 7.8e-130) {
		tmp = t_1;
	} else if (y <= 5.2e+62) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = (t - x) / ((a - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t * (z - y)) / (a - z))
	tmp = 0
	if y <= -6.6e+68:
		tmp = y * ((t - x) / (a - z))
	elif y <= -4.1e-31:
		tmp = t_1
	elif y <= -3e-229:
		tmp = t / ((a - z) / (y - z))
	elif y <= 7.8e-130:
		tmp = t_1
	elif y <= 5.2e+62:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = (t - x) / ((a - z) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t * Float64(z - y)) / Float64(a - z)))
	tmp = 0.0
	if (y <= -6.6e+68)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= -4.1e-31)
		tmp = t_1;
	elseif (y <= -3e-229)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (y <= 7.8e-130)
		tmp = t_1;
	elseif (y <= 5.2e+62)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(Float64(t - x) / Float64(Float64(a - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t * (z - y)) / (a - z));
	tmp = 0.0;
	if (y <= -6.6e+68)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= -4.1e-31)
		tmp = t_1;
	elseif (y <= -3e-229)
		tmp = t / ((a - z) / (y - z));
	elseif (y <= 7.8e-130)
		tmp = t_1;
	elseif (y <= 5.2e+62)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = (t - x) / ((a - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+68], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-31], t$95$1, If[LessEqual[y, -3e-229], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-130], t$95$1, If[LessEqual[y, 5.2e+62], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.6000000000000001e68

   1. Initial program 49.9%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in y around inf 63.3%

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

      1. div-sub 63.3%

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

   6. Simplified 63.3%

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

   if -6.6000000000000001e68 < y < -4.0999999999999996e-31 or -3.00000000000000002e-229 < y < 7.8000000000000002e-130

   1. Initial program 68.3%

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

   2. Taylor expanded in t around inf 74.9%

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

   if -4.0999999999999996e-31 < y < -3.00000000000000002e-229

   1. Initial program 53.5%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 52.1%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   if 7.8000000000000002e-130 < y < 5.19999999999999968e62

   1. Initial program 78.0%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 74.0%

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

      1. associate-/l* 74.2%

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

   6. Simplified 74.2%

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

   if 5.19999999999999968e62 < y

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*l/ 90.9%

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

      3. fma-def 91.0%

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

   3. Simplified 91.0%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 91.0%

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

   5. Applied egg-rr 91.0%

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

   6. Taylor expanded in y around inf 79.7%

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

      1. div-sub 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-/r/ 82.5%

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

   8. Simplified 82.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-31}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-130}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 3: 47.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -5e+71)
     t
     (if (<= z -8.5e-246)
       t_1
       (if (<= z -2.5e-307)
         (* y (/ (- t x) a))
         (if (<= z 4.5e+28)
           t_1
           (if (<= z 9.4e+61)
             (* t (/ (- y z) a))
             (if (<= z 1.75e+85) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+71) {
		tmp = t;
	} else if (z <= -8.5e-246) {
		tmp = t_1;
	} else if (z <= -2.5e-307) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e+28) {
		tmp = t_1;
	} else if (z <= 9.4e+61) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.75e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-5d+71)) then
        tmp = t
    else if (z <= (-8.5d-246)) then
        tmp = t_1
    else if (z <= (-2.5d-307)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.5d+28) then
        tmp = t_1
    else if (z <= 9.4d+61) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.75d+85) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+71) {
		tmp = t;
	} else if (z <= -8.5e-246) {
		tmp = t_1;
	} else if (z <= -2.5e-307) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e+28) {
		tmp = t_1;
	} else if (z <= 9.4e+61) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.75e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5e+71:
		tmp = t
	elif z <= -8.5e-246:
		tmp = t_1
	elif z <= -2.5e-307:
		tmp = y * ((t - x) / a)
	elif z <= 4.5e+28:
		tmp = t_1
	elif z <= 9.4e+61:
		tmp = t * ((y - z) / a)
	elif z <= 1.75e+85:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5e+71)
		tmp = t;
	elseif (z <= -8.5e-246)
		tmp = t_1;
	elseif (z <= -2.5e-307)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.5e+28)
		tmp = t_1;
	elseif (z <= 9.4e+61)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.75e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5e+71)
		tmp = t;
	elseif (z <= -8.5e-246)
		tmp = t_1;
	elseif (z <= -2.5e-307)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.5e+28)
		tmp = t_1;
	elseif (z <= 9.4e+61)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.75e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+71], t, If[LessEqual[z, -8.5e-246], t$95$1, If[LessEqual[z, -2.5e-307], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+28], t$95$1, If[LessEqual[z, 9.4e+61], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+85], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999972e71 or 1.75000000000000003e85 < z

   1. Initial program 33.5%

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

      1. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 50.4%

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

   if -4.99999999999999972e71 < z < -8.4999999999999998e-246 or -2.50000000000000007e-307 < z < 4.4999999999999997e28 or 9.3999999999999997e61 < z < 1.75000000000000003e85

   1. Initial program 86.5%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in x around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

   9. Simplified 55.0%

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

   if -8.4999999999999998e-246 < z < -2.50000000000000007e-307

   1. Initial program 74.0%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in y around inf 87.9%

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

      1. div-sub 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in a around inf 87.9%

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

   if 4.4999999999999997e28 < z < 9.3999999999999997e61

   1. Initial program 65.5%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 51.2%

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

   5. Taylor expanded in a around inf 42.0%

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

      1. associate-/l* 50.7%

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

   7. Simplified 50.7%

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

      1. clear-num 50.5%

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

      2. associate-/r/ 50.8%

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

      3. clear-num 50.8%

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

   9. Applied egg-rr 50.8%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-230}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-126}:\\ \;\;\;\;x - \frac{z \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= y -2.2e+82)
     (* y (/ (- t x) (- a z)))
     (if (<= y -8.5e-32)
       t_1
       (if (<= y -1.1e-230)
         (/ (- t) (+ (/ a z) -1.0))
         (if (<= y 6.5e-126)
           (- x (/ (* z t) (- a z)))
           (if (<= y 6.5e+56) t_1 (* (- t x) (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (y <= -2.2e+82) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -8.5e-32) {
		tmp = t_1;
	} else if (y <= -1.1e-230) {
		tmp = -t / ((a / z) + -1.0);
	} else if (y <= 6.5e-126) {
		tmp = x - ((z * t) / (a - z));
	} else if (y <= 6.5e+56) {
		tmp = t_1;
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (y <= (-2.2d+82)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= (-8.5d-32)) then
        tmp = t_1
    else if (y <= (-1.1d-230)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if (y <= 6.5d-126) then
        tmp = x - ((z * t) / (a - z))
    else if (y <= 6.5d+56) then
        tmp = t_1
    else
        tmp = (t - x) * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (y <= -2.2e+82) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -8.5e-32) {
		tmp = t_1;
	} else if (y <= -1.1e-230) {
		tmp = -t / ((a / z) + -1.0);
	} else if (y <= 6.5e-126) {
		tmp = x - ((z * t) / (a - z));
	} else if (y <= 6.5e+56) {
		tmp = t_1;
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if y <= -2.2e+82:
		tmp = y * ((t - x) / (a - z))
	elif y <= -8.5e-32:
		tmp = t_1
	elif y <= -1.1e-230:
		tmp = -t / ((a / z) + -1.0)
	elif y <= 6.5e-126:
		tmp = x - ((z * t) / (a - z))
	elif y <= 6.5e+56:
		tmp = t_1
	else:
		tmp = (t - x) * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (y <= -2.2e+82)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= -8.5e-32)
		tmp = t_1;
	elseif (y <= -1.1e-230)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif (y <= 6.5e-126)
		tmp = Float64(x - Float64(Float64(z * t) / Float64(a - z)));
	elseif (y <= 6.5e+56)
		tmp = t_1;
	else
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (y <= -2.2e+82)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= -8.5e-32)
		tmp = t_1;
	elseif (y <= -1.1e-230)
		tmp = -t / ((a / z) + -1.0);
	elseif (y <= 6.5e-126)
		tmp = x - ((z * t) / (a - z));
	elseif (y <= 6.5e+56)
		tmp = t_1;
	else
		tmp = (t - x) * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+82], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-32], t$95$1, If[LessEqual[y, -1.1e-230], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-126], N[(x - N[(N[(z * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+56], t$95$1, N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.2000000000000001e82

   1. Initial program 49.9%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.2%

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

   6. Simplified 65.2%

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

   if -2.2000000000000001e82 < y < -8.5000000000000003e-32 or 6.50000000000000014e-126 < y < 6.5000000000000001e56

   1. Initial program 77.7%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 67.7%

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

   6. Simplified 67.7%

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

   if -8.5000000000000003e-32 < y < -1.0999999999999999e-230

   1. Initial program 53.5%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 52.1%

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

   5. Taylor expanded in y around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 64.4%

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

      3. div-sub 64.4%

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

      4. *-inverses 64.4%

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

   7. Simplified 64.4%

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

   if -1.0999999999999999e-230 < y < 6.50000000000000014e-126

   1. Initial program 62.5%

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

      1. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. associate-*r/ 70.1%

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

      3. unsub-neg 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in t around inf 66.8%

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

   if 6.5000000000000001e56 < y

   1. Initial program 76.3%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around -inf 69.6%

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

      1. associate-*l/ 81.3%

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

   6. Simplified 81.3%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-230}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-126}:\\ \;\;\;\;x - \frac{z \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 5: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* t (- z y)) (- a z)))))
   (if (<= y -3.7e+64)
     (* y (/ (- t x) (- a z)))
     (if (<= y -9e-32)
       t_1
       (if (<= y -2.8e-230)
         (/ t (/ (- a z) (- y z)))
         (if (<= y 3.5e-124)
           t_1
           (if (<= y 1.6e+57)
             (+ x (/ y (/ a (- t x))))
             (/ (- t x) (/ (- a z) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t * (z - y)) / (a - z));
	double tmp;
	if (y <= -3.7e+64) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -9e-32) {
		tmp = t_1;
	} else if (y <= -2.8e-230) {
		tmp = t / ((a - z) / (y - z));
	} else if (y <= 3.5e-124) {
		tmp = t_1;
	} else if (y <= 1.6e+57) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = (t - x) / ((a - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t * (z - y)) / (a - z))
    if (y <= (-3.7d+64)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= (-9d-32)) then
        tmp = t_1
    else if (y <= (-2.8d-230)) then
        tmp = t / ((a - z) / (y - z))
    else if (y <= 3.5d-124) then
        tmp = t_1
    else if (y <= 1.6d+57) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = (t - x) / ((a - z) / y)
    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 - ((t * (z - y)) / (a - z));
	double tmp;
	if (y <= -3.7e+64) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -9e-32) {
		tmp = t_1;
	} else if (y <= -2.8e-230) {
		tmp = t / ((a - z) / (y - z));
	} else if (y <= 3.5e-124) {
		tmp = t_1;
	} else if (y <= 1.6e+57) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = (t - x) / ((a - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t * (z - y)) / (a - z))
	tmp = 0
	if y <= -3.7e+64:
		tmp = y * ((t - x) / (a - z))
	elif y <= -9e-32:
		tmp = t_1
	elif y <= -2.8e-230:
		tmp = t / ((a - z) / (y - z))
	elif y <= 3.5e-124:
		tmp = t_1
	elif y <= 1.6e+57:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = (t - x) / ((a - z) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t * Float64(z - y)) / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.7e+64)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= -9e-32)
		tmp = t_1;
	elseif (y <= -2.8e-230)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (y <= 3.5e-124)
		tmp = t_1;
	elseif (y <= 1.6e+57)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(Float64(t - x) / Float64(Float64(a - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t * (z - y)) / (a - z));
	tmp = 0.0;
	if (y <= -3.7e+64)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= -9e-32)
		tmp = t_1;
	elseif (y <= -2.8e-230)
		tmp = t / ((a - z) / (y - z));
	elseif (y <= 3.5e-124)
		tmp = t_1;
	elseif (y <= 1.6e+57)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = (t - x) / ((a - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+64], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-32], t$95$1, If[LessEqual[y, -2.8e-230], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-124], t$95$1, If[LessEqual[y, 1.6e+57], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.69999999999999983e64

   1. Initial program 49.9%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in y around inf 63.3%

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

      1. div-sub 63.3%

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

   6. Simplified 63.3%

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

   if -3.69999999999999983e64 < y < -9.00000000000000009e-32 or -2.8000000000000001e-230 < y < 3.4999999999999999e-124

   1. Initial program 66.6%

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

   2. Taylor expanded in t around inf 72.9%

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

   if -9.00000000000000009e-32 < y < -2.8000000000000001e-230

   1. Initial program 53.5%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 52.1%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   if 3.4999999999999999e-124 < y < 1.60000000000000015e57

   1. Initial program 80.4%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 74.2%

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

   6. Simplified 74.2%

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

   if 1.60000000000000015e57 < y

   1. Initial program 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-*l/ 91.3%

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

      3. fma-def 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.2%

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

      2. associate-/r/ 91.3%

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

   5. Applied egg-rr 91.3%

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

   6. Taylor expanded in y around inf 78.7%

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

      1. div-sub 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-/r/ 81.4%

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

   8. Simplified 81.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-32}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 6: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-98}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ 1.0 (/ (- z y) (- a z))))))
   (if (<= x -3e+44)
     t_1
     (if (<= x 7e-98)
       (/ t (/ (- a z) (- y z)))
       (if (<= x 4e-13)
         (+ x (* (- t x) (/ y a)))
         (if (<= x 4.5e+134) (* y (/ (- t x) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 + ((z - y) / (a - z)));
	double tmp;
	if (x <= -3e+44) {
		tmp = t_1;
	} else if (x <= 7e-98) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 4e-13) {
		tmp = x + ((t - x) * (y / a));
	} else if (x <= 4.5e+134) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 + ((z - y) / (a - z)))
    if (x <= (-3d+44)) then
        tmp = t_1
    else if (x <= 7d-98) then
        tmp = t / ((a - z) / (y - z))
    else if (x <= 4d-13) then
        tmp = x + ((t - x) * (y / a))
    else if (x <= 4.5d+134) then
        tmp = y * ((t - x) / (a - z))
    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 * (1.0 + ((z - y) / (a - z)));
	double tmp;
	if (x <= -3e+44) {
		tmp = t_1;
	} else if (x <= 7e-98) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 4e-13) {
		tmp = x + ((t - x) * (y / a));
	} else if (x <= 4.5e+134) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 + ((z - y) / (a - z)))
	tmp = 0
	if x <= -3e+44:
		tmp = t_1
	elif x <= 7e-98:
		tmp = t / ((a - z) / (y - z))
	elif x <= 4e-13:
		tmp = x + ((t - x) * (y / a))
	elif x <= 4.5e+134:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 + Float64(Float64(z - y) / Float64(a - z))))
	tmp = 0.0
	if (x <= -3e+44)
		tmp = t_1;
	elseif (x <= 7e-98)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (x <= 4e-13)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (x <= 4.5e+134)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 + ((z - y) / (a - z)));
	tmp = 0.0;
	if (x <= -3e+44)
		tmp = t_1;
	elseif (x <= 7e-98)
		tmp = t / ((a - z) / (y - z));
	elseif (x <= 4e-13)
		tmp = x + ((t - x) * (y / a));
	elseif (x <= 4.5e+134)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 + N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+44], t$95$1, If[LessEqual[x, 7e-98], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-13], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+134], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.99999999999999987e44 or 4.4999999999999997e134 < x

   1. Initial program 55.7%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

   6. Simplified 69.6%

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

   if -2.99999999999999987e44 < x < 7.0000000000000004e-98

   1. Initial program 70.8%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

   if 7.0000000000000004e-98 < x < 4.0000000000000001e-13

   1. Initial program 79.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 75.9%

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

   if 4.0000000000000001e-13 < x < 4.4999999999999997e134

   1. Initial program 71.6%

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

      1. associate-*l/ 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in y around inf 66.6%

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

      1. div-sub 66.6%

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

   6. Simplified 66.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-98}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \end{array} \]

Alternative 7: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-268}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- z y) (/ (- a z) t)))))
   (if (<= a -5.5e-82)
     t_1
     (if (<= a -1.05e-268)
       (/ (- t x) (/ (- a z) y))
       (if (<= a 1.15e-100)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 3.9e-31) (* (- t x) (/ y (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - y) / ((a - z) / t));
	double tmp;
	if (a <= -5.5e-82) {
		tmp = t_1;
	} else if (a <= -1.05e-268) {
		tmp = (t - x) / ((a - z) / y);
	} else if (a <= 1.15e-100) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 3.9e-31) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((z - y) / ((a - z) / t))
    if (a <= (-5.5d-82)) then
        tmp = t_1
    else if (a <= (-1.05d-268)) then
        tmp = (t - x) / ((a - z) / y)
    else if (a <= 1.15d-100) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 3.9d-31) then
        tmp = (t - x) * (y / (a - z))
    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) / ((a - z) / t));
	double tmp;
	if (a <= -5.5e-82) {
		tmp = t_1;
	} else if (a <= -1.05e-268) {
		tmp = (t - x) / ((a - z) / y);
	} else if (a <= 1.15e-100) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 3.9e-31) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - y) / ((a - z) / t))
	tmp = 0
	if a <= -5.5e-82:
		tmp = t_1
	elif a <= -1.05e-268:
		tmp = (t - x) / ((a - z) / y)
	elif a <= 1.15e-100:
		tmp = t / ((a - z) / (y - z))
	elif a <= 3.9e-31:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - y) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -5.5e-82)
		tmp = t_1;
	elseif (a <= -1.05e-268)
		tmp = Float64(Float64(t - x) / Float64(Float64(a - z) / y));
	elseif (a <= 1.15e-100)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 3.9e-31)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - y) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -5.5e-82)
		tmp = t_1;
	elseif (a <= -1.05e-268)
		tmp = (t - x) / ((a - z) / y);
	elseif (a <= 1.15e-100)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 3.9e-31)
		tmp = (t - x) * (y / (a - z));
	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[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e-82], t$95$1, If[LessEqual[a, -1.05e-268], N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-100], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-31], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.4999999999999998e-82 or 3.9000000000000001e-31 < a

   1. Initial program 65.0%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 79.0%

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

   if -5.4999999999999998e-82 < a < -1.04999999999999999e-268

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*l/ 67.7%

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

      3. fma-def 67.6%

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

   3. Simplified 67.6%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 67.8%

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

   5. Applied egg-rr 67.8%

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

   6. Taylor expanded in y around inf 68.6%

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

      1. div-sub 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-/r/ 72.8%

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

   8. Simplified 72.8%

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

   if -1.04999999999999999e-268 < a < 1.14999999999999997e-100

   1. Initial program 63.7%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 62.3%

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

      1. associate-/l* 71.1%

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

   6. Simplified 71.1%

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

   if 1.14999999999999997e-100 < a < 3.9000000000000001e-31

   1. Initial program 79.8%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around -inf 65.9%

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

      1. associate-*l/ 83.0%

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

   6. Simplified 83.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-268}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 8: 33.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+153)
   (/ y (/ a t))
   (if (<= y -3.9e+21)
     t
     (if (<= y -3.6e-32)
       x
       (if (<= y -1.5e-236) t (if (<= y 7.6e+16) x (* t (/ y (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+153) {
		tmp = y / (a / t);
	} else if (y <= -3.9e+21) {
		tmp = t;
	} else if (y <= -3.6e-32) {
		tmp = x;
	} else if (y <= -1.5e-236) {
		tmp = t;
	} else if (y <= 7.6e+16) {
		tmp = x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.05d+153)) then
        tmp = y / (a / t)
    else if (y <= (-3.9d+21)) then
        tmp = t
    else if (y <= (-3.6d-32)) then
        tmp = x
    else if (y <= (-1.5d-236)) then
        tmp = t
    else if (y <= 7.6d+16) then
        tmp = x
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+153) {
		tmp = y / (a / t);
	} else if (y <= -3.9e+21) {
		tmp = t;
	} else if (y <= -3.6e-32) {
		tmp = x;
	} else if (y <= -1.5e-236) {
		tmp = t;
	} else if (y <= 7.6e+16) {
		tmp = x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+153:
		tmp = y / (a / t)
	elif y <= -3.9e+21:
		tmp = t
	elif y <= -3.6e-32:
		tmp = x
	elif y <= -1.5e-236:
		tmp = t
	elif y <= 7.6e+16:
		tmp = x
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+153)
		tmp = Float64(y / Float64(a / t));
	elseif (y <= -3.9e+21)
		tmp = t;
	elseif (y <= -3.6e-32)
		tmp = x;
	elseif (y <= -1.5e-236)
		tmp = t;
	elseif (y <= 7.6e+16)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+153)
		tmp = y / (a / t);
	elseif (y <= -3.9e+21)
		tmp = t;
	elseif (y <= -3.6e-32)
		tmp = x;
	elseif (y <= -1.5e-236)
		tmp = t;
	elseif (y <= 7.6e+16)
		tmp = x;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+153], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e+21], t, If[LessEqual[y, -3.6e-32], x, If[LessEqual[y, -1.5e-236], t, If[LessEqual[y, 7.6e+16], x, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05000000000000008e153

   1. Initial program 49.4%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 21.6%

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

   5. Taylor expanded in z around 0 23.7%

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

      1. associate-/l* 31.3%

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

   7. Simplified 31.3%

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

      1. associate-/r/ 34.5%

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

   9. Applied egg-rr 34.5%

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

       1. *-commutative 34.5%

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

       2. clear-num 34.5%

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

       3. un-div-inv 34.5%

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

   11. Applied egg-rr 34.5%

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

   if -1.05000000000000008e153 < y < -3.9e21 or -3.59999999999999993e-32 < y < -1.50000000000000007e-236

   1. Initial program 55.4%

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

      1. associate-*l/ 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in z around inf 47.0%

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

   if -3.9e21 < y < -3.59999999999999993e-32 or -1.50000000000000007e-236 < y < 7.6e16

   1. Initial program 71.5%

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

      1. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in a around inf 44.7%

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

   if 7.6e16 < y

   1. Initial program 75.9%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around 0 45.0%

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

   5. Taylor expanded in y around inf 40.4%

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

      1. associate-*r/ 46.1%

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

   7. Simplified 46.1%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 9: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-14} \lor \neg \left(x \leq 9 \cdot 10^{+182}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9e+48)
   (+ x (/ y (/ a (- t x))))
   (if (<= x 7.5e-98)
     (/ t (/ (- a z) (- y z)))
     (if (or (<= x 3.8e-14) (not (<= x 9e+182)))
       (+ x (* (- t x) (/ y a)))
       (* y (/ (- t x) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e+48) {
		tmp = x + (y / (a / (t - x)));
	} else if (x <= 7.5e-98) {
		tmp = t / ((a - z) / (y - z));
	} else if ((x <= 3.8e-14) || !(x <= 9e+182)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-9d+48)) then
        tmp = x + (y / (a / (t - x)))
    else if (x <= 7.5d-98) then
        tmp = t / ((a - z) / (y - z))
    else if ((x <= 3.8d-14) .or. (.not. (x <= 9d+182))) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = y * ((t - x) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e+48) {
		tmp = x + (y / (a / (t - x)));
	} else if (x <= 7.5e-98) {
		tmp = t / ((a - z) / (y - z));
	} else if ((x <= 3.8e-14) || !(x <= 9e+182)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9e+48:
		tmp = x + (y / (a / (t - x)))
	elif x <= 7.5e-98:
		tmp = t / ((a - z) / (y - z))
	elif (x <= 3.8e-14) or not (x <= 9e+182):
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = y * ((t - x) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9e+48)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (x <= 7.5e-98)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif ((x <= 3.8e-14) || !(x <= 9e+182))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9e+48)
		tmp = x + (y / (a / (t - x)));
	elseif (x <= 7.5e-98)
		tmp = t / ((a - z) / (y - z));
	elseif ((x <= 3.8e-14) || ~((x <= 9e+182)))
		tmp = x + ((t - x) * (y / a));
	else
		tmp = y * ((t - x) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9e+48], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-98], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.8e-14], N[Not[LessEqual[x, 9e+182]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.99999999999999991e48

   1. Initial program 53.8%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in z around 0 55.5%

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

      1. associate-/l* 62.5%

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

   6. Simplified 62.5%

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

   if -8.99999999999999991e48 < x < 7.5000000000000006e-98

   1. Initial program 70.8%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

   if 7.5000000000000006e-98 < x < 3.8000000000000002e-14 or 9.00000000000000058e182 < x

   1. Initial program 65.3%

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

      1. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in z around 0 73.5%

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

   if 3.8000000000000002e-14 < x < 9.00000000000000058e182

   1. Initial program 69.3%

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

      1. associate-*l/ 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.3%

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

   6. Simplified 65.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-14} \lor \neg \left(x \leq 9 \cdot 10^{+182}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 10: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-170}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -1.4e+29)
     t_2
     (if (<= a -6.8e-273)
       t_1
       (if (<= a 6.4e-170) (- t (/ t (/ z y))) (if (<= a 3.8e+91) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -1.4e+29) {
		tmp = t_2;
	} else if (a <= -6.8e-273) {
		tmp = t_1;
	} else if (a <= 6.4e-170) {
		tmp = t - (t / (z / y));
	} else if (a <= 3.8e+91) {
		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 = y * ((t - x) / (a - z))
    t_2 = x + (y / (a / t))
    if (a <= (-1.4d+29)) then
        tmp = t_2
    else if (a <= (-6.8d-273)) then
        tmp = t_1
    else if (a <= 6.4d-170) then
        tmp = t - (t / (z / y))
    else if (a <= 3.8d+91) 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 = y * ((t - x) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -1.4e+29) {
		tmp = t_2;
	} else if (a <= -6.8e-273) {
		tmp = t_1;
	} else if (a <= 6.4e-170) {
		tmp = t - (t / (z / y));
	} else if (a <= 3.8e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -1.4e+29:
		tmp = t_2
	elif a <= -6.8e-273:
		tmp = t_1
	elif a <= 6.4e-170:
		tmp = t - (t / (z / y))
	elif a <= 3.8e+91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -1.4e+29)
		tmp = t_2;
	elseif (a <= -6.8e-273)
		tmp = t_1;
	elseif (a <= 6.4e-170)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 3.8e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -1.4e+29)
		tmp = t_2;
	elseif (a <= -6.8e-273)
		tmp = t_1;
	elseif (a <= 6.4e-170)
		tmp = t - (t / (z / y));
	elseif (a <= 3.8e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+29], t$95$2, If[LessEqual[a, -6.8e-273], t$95$1, If[LessEqual[a, 6.4e-170], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+91], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e29 or 3.7999999999999998e91 < a

   1. Initial program 61.8%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around 0 59.4%

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

      1. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in t around inf 63.6%

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

   if -1.4e29 < a < -6.79999999999999982e-273 or 6.3999999999999999e-170 < a < 3.7999999999999998e91

   1. Initial program 72.7%

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

      1. associate-*l/ 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in y around inf 59.5%

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

      1. div-sub 60.6%

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

   6. Simplified 60.6%

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

   if -6.79999999999999982e-273 < a < 6.3999999999999999e-170

   1. Initial program 58.0%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in x around 0 59.7%

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

   5. Taylor expanded in a around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. associate-/l* 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in z around 0 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

      4. associate-/l* 69.1%

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

   10. Simplified 69.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-170}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 11: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -1.35e+90)
     (- t (/ t (/ z y)))
     (if (<= z 1.8e-19)
       t_1
       (if (<= z 3.45e+49)
         (* y (/ (- x t) z))
         (if (<= z 8e+84) t_1 (/ (- t) (/ z (- y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -1.35e+90) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.8e-19) {
		tmp = t_1;
	} else if (z <= 3.45e+49) {
		tmp = y * ((x - t) / z);
	} else if (z <= 8e+84) {
		tmp = t_1;
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (z <= (-1.35d+90)) then
        tmp = t - (t / (z / y))
    else if (z <= 1.8d-19) then
        tmp = t_1
    else if (z <= 3.45d+49) then
        tmp = y * ((x - t) / z)
    else if (z <= 8d+84) then
        tmp = t_1
    else
        tmp = -t / (z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -1.35e+90) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.8e-19) {
		tmp = t_1;
	} else if (z <= 3.45e+49) {
		tmp = y * ((x - t) / z);
	} else if (z <= 8e+84) {
		tmp = t_1;
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -1.35e+90:
		tmp = t - (t / (z / y))
	elif z <= 1.8e-19:
		tmp = t_1
	elif z <= 3.45e+49:
		tmp = y * ((x - t) / z)
	elif z <= 8e+84:
		tmp = t_1
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -1.35e+90)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 1.8e-19)
		tmp = t_1;
	elseif (z <= 3.45e+49)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= 8e+84)
		tmp = t_1;
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -1.35e+90)
		tmp = t - (t / (z / y));
	elseif (z <= 1.8e-19)
		tmp = t_1;
	elseif (z <= 3.45e+49)
		tmp = y * ((x - t) / z);
	elseif (z <= 8e+84)
		tmp = t_1;
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+90], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-19], t$95$1, If[LessEqual[z, 3.45e+49], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+84], t$95$1, N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e90

   1. Initial program 25.0%

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

      1. associate-*l/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 28.0%

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

   5. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. associate-/l* 57.9%

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

   10. Simplified 57.9%

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

   if -1.35e90 < z < 1.8000000000000001e-19 or 3.4500000000000002e49 < z < 8.00000000000000046e84

   1. Initial program 84.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 64.4%

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

      1. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in t around inf 60.4%

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

   if 1.8000000000000001e-19 < z < 3.4500000000000002e49

   1. Initial program 74.3%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. div-sub 50.7%

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

   6. Simplified 50.7%

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

   7. Taylor expanded in a around 0 48.1%

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

      1. associate-*r/ 48.1%

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

      2. neg-mul-1 48.1%

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

   9. Simplified 48.1%

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

   if 8.00000000000000046e84 < z

   1. Initial program 37.4%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in x around 0 38.8%

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

   5. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 12: 47.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -9e+77)
     t
     (if (<= z -2.4e-246)
       t_1
       (if (<= z -8e-307) (/ y (/ a t)) (if (<= z 1.2e+85) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -9e+77) {
		tmp = t;
	} else if (z <= -2.4e-246) {
		tmp = t_1;
	} else if (z <= -8e-307) {
		tmp = y / (a / t);
	} else if (z <= 1.2e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-9d+77)) then
        tmp = t
    else if (z <= (-2.4d-246)) then
        tmp = t_1
    else if (z <= (-8d-307)) then
        tmp = y / (a / t)
    else if (z <= 1.2d+85) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -9e+77) {
		tmp = t;
	} else if (z <= -2.4e-246) {
		tmp = t_1;
	} else if (z <= -8e-307) {
		tmp = y / (a / t);
	} else if (z <= 1.2e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -9e+77:
		tmp = t
	elif z <= -2.4e-246:
		tmp = t_1
	elif z <= -8e-307:
		tmp = y / (a / t)
	elif z <= 1.2e+85:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -9e+77)
		tmp = t;
	elseif (z <= -2.4e-246)
		tmp = t_1;
	elseif (z <= -8e-307)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.2e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -9e+77)
		tmp = t;
	elseif (z <= -2.4e-246)
		tmp = t_1;
	elseif (z <= -8e-307)
		tmp = y / (a / t);
	elseif (z <= 1.2e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+77], t, If[LessEqual[z, -2.4e-246], t$95$1, If[LessEqual[z, -8e-307], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+85], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000049e77 or 1.19999999999999998e85 < z

   1. Initial program 33.5%

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

      1. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 50.4%

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

   if -9.00000000000000049e77 < z < -2.3999999999999998e-246 or -7.99999999999999927e-307 < z < 1.19999999999999998e85

   1. Initial program 85.0%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 60.4%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in x around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

   9. Simplified 51.8%

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

   if -2.3999999999999998e-246 < z < -7.99999999999999927e-307

   1. Initial program 74.0%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 62.0%

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

   5. Taylor expanded in z around 0 62.0%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

      1. associate-/r/ 79.3%

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

   9. Applied egg-rr 79.3%

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

       1. *-commutative 79.3%

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

       2. clear-num 79.3%

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

       3. un-div-inv 79.4%

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

   11. Applied egg-rr 79.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 48.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.4e+70)
     t
     (if (<= z -3.7e-246)
       t_1
       (if (<= z -1.2e-307) (* y (/ (- t x) a)) (if (<= z 1.05e+85) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.4e+70) {
		tmp = t;
	} else if (z <= -3.7e-246) {
		tmp = t_1;
	} else if (z <= -1.2e-307) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.05e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-3.4d+70)) then
        tmp = t
    else if (z <= (-3.7d-246)) then
        tmp = t_1
    else if (z <= (-1.2d-307)) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.05d+85) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.4e+70) {
		tmp = t;
	} else if (z <= -3.7e-246) {
		tmp = t_1;
	} else if (z <= -1.2e-307) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.05e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.4e+70:
		tmp = t
	elif z <= -3.7e-246:
		tmp = t_1
	elif z <= -1.2e-307:
		tmp = y * ((t - x) / a)
	elif z <= 1.05e+85:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.4e+70)
		tmp = t;
	elseif (z <= -3.7e-246)
		tmp = t_1;
	elseif (z <= -1.2e-307)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.05e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.4e+70)
		tmp = t;
	elseif (z <= -3.7e-246)
		tmp = t_1;
	elseif (z <= -1.2e-307)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.05e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+70], t, If[LessEqual[z, -3.7e-246], t$95$1, If[LessEqual[z, -1.2e-307], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+85], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e70 or 1.05000000000000005e85 < z

   1. Initial program 33.5%

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

      1. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 50.4%

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

   if -3.4000000000000001e70 < z < -3.7e-246 or -1.20000000000000009e-307 < z < 1.05000000000000005e85

   1. Initial program 85.0%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 60.4%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in x around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

   9. Simplified 51.8%

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

   if -3.7e-246 < z < -1.20000000000000009e-307

   1. Initial program 74.0%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in y around inf 87.9%

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

      1. div-sub 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in a around inf 87.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-94} \lor \neg \left(a \leq 2.8 \cdot 10^{-29}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e-94) (not (<= a 2.8e-29)))
   (- x (/ (- z y) (/ (- a z) t)))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-94) || !(a <= 2.8e-29)) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d-94)) .or. (.not. (a <= 2.8d-29))) then
        tmp = x - ((z - y) / ((a - z) / t))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-94) || !(a <= 2.8e-29)) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e-94) or not (a <= 2.8e-29):
		tmp = x - ((z - y) / ((a - z) / t))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e-94) || !(a <= 2.8e-29))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e-94) || ~((a <= 2.8e-29)))
		tmp = x - ((z - y) / ((a - z) / t));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e-94], N[Not[LessEqual[a, 2.8e-29]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999997e-94 or 2.8000000000000002e-29 < a

   1. Initial program 65.3%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 79.1%

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

   if -3.19999999999999997e-94 < a < 2.8000000000000002e-29

   1. Initial program 66.7%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. div-sub 71.7%

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

      5. distribute-lft-out-- 71.7%

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

      6. associate-*r/ 71.7%

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

      7. distribute-rgt-out-- 71.7%

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

      8. mul-1-neg 71.7%

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

      9. unsub-neg 71.7%

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

      10. associate-/l* 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-94} \lor \neg \left(a \leq 2.8 \cdot 10^{-29}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 15: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+85}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+85)
   (- t (/ t (/ z y)))
   (if (<= z 1.1e+85) (+ x (* (- t x) (/ y a))) (/ (- t) (/ z (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+85) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.1e+85) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+85)) then
        tmp = t - (t / (z / y))
    else if (z <= 1.1d+85) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = -t / (z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+85) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.1e+85) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+85:
		tmp = t - (t / (z / y))
	elif z <= 1.1e+85:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+85)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 1.1e+85)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+85)
		tmp = t - (t / (z / y));
	elseif (z <= 1.1e+85)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+85], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+85], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e85

   1. Initial program 25.0%

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

      1. associate-*l/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 28.0%

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

   5. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. associate-/l* 57.9%

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

   10. Simplified 57.9%

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

   if -1.1499999999999999e85 < z < 1.1000000000000001e85

   1. Initial program 84.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 66.9%

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

   if 1.1000000000000001e85 < z

   1. Initial program 37.4%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in x around 0 38.8%

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

   5. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+85}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 16: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+86}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+86)
   (- t (/ t (/ z y)))
   (if (<= z 2.1e+85) (+ x (/ y (/ a (- t x)))) (/ (- t) (/ z (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+86) {
		tmp = t - (t / (z / y));
	} else if (z <= 2.1e+85) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d+86)) then
        tmp = t - (t / (z / y))
    else if (z <= 2.1d+85) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = -t / (z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+86) {
		tmp = t - (t / (z / y));
	} else if (z <= 2.1e+85) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+86:
		tmp = t - (t / (z / y))
	elif z <= 2.1e+85:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+86)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 2.1e+85)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+86)
		tmp = t - (t / (z / y));
	elseif (z <= 2.1e+85)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+86], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+85], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999979e86

   1. Initial program 25.0%

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

      1. associate-*l/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 28.0%

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

   5. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. associate-/l* 57.9%

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

   10. Simplified 57.9%

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

   if -4.59999999999999979e86 < z < 2.1000000000000001e85

   1. Initial program 84.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 61.4%

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

      1. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   if 2.1000000000000001e85 < z

   1. Initial program 37.4%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in x around 0 38.8%

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

   5. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+86}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 17: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+84}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+84)
   (- t (/ t (/ z y)))
   (if (<= z 1.2e+85) (+ x (/ y (/ a t))) (/ (- t) (/ z (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+84) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.2e+85) {
		tmp = x + (y / (a / t));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+84)) then
        tmp = t - (t / (z / y))
    else if (z <= 1.2d+85) then
        tmp = x + (y / (a / t))
    else
        tmp = -t / (z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+84) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.2e+85) {
		tmp = x + (y / (a / t));
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+84:
		tmp = t - (t / (z / y))
	elif z <= 1.2e+85:
		tmp = x + (y / (a / t))
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+84)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 1.2e+85)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+84)
		tmp = t - (t / (z / y));
	elseif (z <= 1.2e+85)
		tmp = x + (y / (a / t));
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+84], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+85], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000008e84

   1. Initial program 25.0%

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

      1. associate-*l/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 28.0%

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

   5. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. associate-/l* 57.9%

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

   10. Simplified 57.9%

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

   if -8.5000000000000008e84 < z < 1.19999999999999998e85

   1. Initial program 84.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 61.4%

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

      1. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 56.6%

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

   if 1.19999999999999998e85 < z

   1. Initial program 37.4%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in x around 0 38.8%

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

   5. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+84}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 18: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+75)
   t
   (if (<= z -2e-166)
     x
     (if (<= z 6.9e-276) (* y (/ t a)) (if (<= z 1.22e+69) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+75) {
		tmp = t;
	} else if (z <= -2e-166) {
		tmp = x;
	} else if (z <= 6.9e-276) {
		tmp = y * (t / a);
	} else if (z <= 1.22e+69) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+75)) then
        tmp = t
    else if (z <= (-2d-166)) then
        tmp = x
    else if (z <= 6.9d-276) then
        tmp = y * (t / a)
    else if (z <= 1.22d+69) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+75) {
		tmp = t;
	} else if (z <= -2e-166) {
		tmp = x;
	} else if (z <= 6.9e-276) {
		tmp = y * (t / a);
	} else if (z <= 1.22e+69) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+75:
		tmp = t
	elif z <= -2e-166:
		tmp = x
	elif z <= 6.9e-276:
		tmp = y * (t / a)
	elif z <= 1.22e+69:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+75)
		tmp = t;
	elseif (z <= -2e-166)
		tmp = x;
	elseif (z <= 6.9e-276)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.22e+69)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+75)
		tmp = t;
	elseif (z <= -2e-166)
		tmp = x;
	elseif (z <= 6.9e-276)
		tmp = y * (t / a);
	elseif (z <= 1.22e+69)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+75], t, If[LessEqual[z, -2e-166], x, If[LessEqual[z, 6.9e-276], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+69], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e75 or 1.22e69 < z

   1. Initial program 33.9%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   if -1.5e75 < z < -2.00000000000000008e-166 or 6.89999999999999985e-276 < z < 1.22e69

   1. Initial program 82.7%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around inf 35.2%

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

   if -2.00000000000000008e-166 < z < 6.89999999999999985e-276

   1. Initial program 91.8%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 49.1%

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

   5. Taylor expanded in z around 0 44.0%

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

      1. associate-/l* 45.0%

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

   7. Simplified 45.0%

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

      1. associate-/r/ 51.8%

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

   9. Applied egg-rr 51.8%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 54.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+86} \lor \neg \left(z \leq 1.45 \cdot 10^{+85}\right):\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+86) (not (<= z 1.45e+85)))
   (- t (/ t (/ z y)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+86) || !(z <= 1.45e+85)) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d+86)) .or. (.not. (z <= 1.45d+85))) then
        tmp = t - (t / (z / y))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+86) || !(z <= 1.45e+85)) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+86) or not (z <= 1.45e+85):
		tmp = t - (t / (z / y))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+86) || !(z <= 1.45e+85))
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+86) || ~((z <= 1.45e+85)))
		tmp = t - (t / (z / y));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+86], N[Not[LessEqual[z, 1.45e+85]], $MachinePrecision]], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e86 or 1.44999999999999999e85 < z

   1. Initial program 32.3%

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

      1. associate-*l/ 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in x around 0 34.3%

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

   5. Taylor expanded in a around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. associate-/l* 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in z around 0 47.0%

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

      1. +-commutative 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

      4. associate-/l* 58.4%

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

   10. Simplified 58.4%

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

   if -3.2e86 < z < 1.44999999999999999e85

   1. Initial program 84.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 61.4%

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

      1. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 56.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+86} \lor \neg \left(z \leq 1.45 \cdot 10^{+85}\right):\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 20: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+86) t (if (<= z 1.7e+85) (+ x (/ y (/ a t))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+86) {
		tmp = t;
	} else if (z <= 1.7e+85) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+86)) then
        tmp = t
    else if (z <= 1.7d+85) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+86) {
		tmp = t;
	} else if (z <= 1.7e+85) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+86:
		tmp = t
	elif z <= 1.7e+85:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+86)
		tmp = t;
	elseif (z <= 1.7e+85)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+86)
		tmp = t;
	elseif (z <= 1.7e+85)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+86], t, If[LessEqual[z, 1.7e+85], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999995e86 or 1.7000000000000002e85 < z

   1. Initial program 32.3%

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

      1. associate-*l/ 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in z around inf 50.9%

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

   if -6.7999999999999995e86 < z < 1.7000000000000002e85

   1. Initial program 84.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 61.4%

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

      1. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 56.6%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+69) t (if (<= z 1.7e+66) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+69) {
		tmp = t;
	} else if (z <= 1.7e+66) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.7d+69)) then
        tmp = t
    else if (z <= 1.7d+66) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+69) {
		tmp = t;
	} else if (z <= 1.7e+66) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+69:
		tmp = t
	elif z <= 1.7e+66:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+69)
		tmp = t;
	elseif (z <= 1.7e+66)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+69)
		tmp = t;
	elseif (z <= 1.7e+66)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+69], t, If[LessEqual[z, 1.7e+66], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.69999999999999996e69 or 1.70000000000000015e66 < z

   1. Initial program 33.9%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   if -4.69999999999999996e69 < z < 1.70000000000000015e66

   1. Initial program 84.7%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 33.0%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.8%

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

   1. associate-*l/ 83.4%

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

3. Simplified 83.4%

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

4. Taylor expanded in z around inf 24.5%

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

5. Final simplification 24.5%

   \[\leadsto t \]

Developer target: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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