Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 91.2%

Time: 28.8s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-281} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-281) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-281) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-281)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    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 t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-281) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-281) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-281) || !(t_1 <= 0.0))
		tmp = t_1;
	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)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-281) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-281], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, 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 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.0000000000000001e-281 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.4%

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

   if -4.0000000000000001e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 76.3%

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

      4. mul-1-neg 76.3%

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

      5. unsub-neg 76.3%

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

      6. distribute-rgt-out-- 76.5%

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

      7. associate-/l* 95.9%

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

   5. Simplified 95.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-281} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.0105:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.4e+84)
     t
     (if (<= z -2.3e+60)
       t_1
       (if (<= z -0.0105)
         t
         (if (<= z -1.15e-33)
           (* y (/ (- t x) a))
           (if (<= z 4.5e-76)
             t_2
             (if (<= z 6.4e-44)
               (* t (/ (- y z) a))
               (if (<= z 9.5e-6)
                 t_2
                 (if (<= z 1.5e+112)
                   (+ x (/ t (/ a y)))
                   (if (<= z 2.65e+147) t_1 t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.4e+84) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -0.0105) {
		tmp = t;
	} else if (z <= -1.15e-33) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e-76) {
		tmp = t_2;
	} else if (z <= 6.4e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.5e-6) {
		tmp = t_2;
	} else if (z <= 1.5e+112) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.65e+147) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-6.4d+84)) then
        tmp = t
    else if (z <= (-2.3d+60)) then
        tmp = t_1
    else if (z <= (-0.0105d0)) then
        tmp = t
    else if (z <= (-1.15d-33)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.5d-76) then
        tmp = t_2
    else if (z <= 6.4d-44) then
        tmp = t * ((y - z) / a)
    else if (z <= 9.5d-6) then
        tmp = t_2
    else if (z <= 1.5d+112) then
        tmp = x + (t / (a / y))
    else if (z <= 2.65d+147) 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 * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.4e+84) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -0.0105) {
		tmp = t;
	} else if (z <= -1.15e-33) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e-76) {
		tmp = t_2;
	} else if (z <= 6.4e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.5e-6) {
		tmp = t_2;
	} else if (z <= 1.5e+112) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.65e+147) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.4e+84:
		tmp = t
	elif z <= -2.3e+60:
		tmp = t_1
	elif z <= -0.0105:
		tmp = t
	elif z <= -1.15e-33:
		tmp = y * ((t - x) / a)
	elif z <= 4.5e-76:
		tmp = t_2
	elif z <= 6.4e-44:
		tmp = t * ((y - z) / a)
	elif z <= 9.5e-6:
		tmp = t_2
	elif z <= 1.5e+112:
		tmp = x + (t / (a / y))
	elif z <= 2.65e+147:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.4e+84)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -0.0105)
		tmp = t;
	elseif (z <= -1.15e-33)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.5e-76)
		tmp = t_2;
	elseif (z <= 6.4e-44)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 9.5e-6)
		tmp = t_2;
	elseif (z <= 1.5e+112)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 2.65e+147)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.4e+84)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -0.0105)
		tmp = t;
	elseif (z <= -1.15e-33)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.5e-76)
		tmp = t_2;
	elseif (z <= 6.4e-44)
		tmp = t * ((y - z) / a);
	elseif (z <= 9.5e-6)
		tmp = t_2;
	elseif (z <= 1.5e+112)
		tmp = x + (t / (a / y));
	elseif (z <= 2.65e+147)
		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[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+84], t, If[LessEqual[z, -2.3e+60], t$95$1, If[LessEqual[z, -0.0105], t, If[LessEqual[z, -1.15e-33], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-76], t$95$2, If[LessEqual[z, 6.4e-44], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-6], t$95$2, If[LessEqual[z, 1.5e+112], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+147], t$95$1, t]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.4000000000000002e84 or -2.30000000000000017e60 < z < -0.0105000000000000007 or 2.6500000000000001e147 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in z around inf 49.5%

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

   if -6.4000000000000002e84 < z < -2.30000000000000017e60 or 1.4999999999999999e112 < z < 2.6500000000000001e147

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. distribute-lft-out-- 49.9%

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

      3. div-sub 50.0%

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

      4. mul-1-neg 50.0%

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

      5. unsub-neg 50.0%

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

      6. distribute-rgt-out-- 50.0%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   if -0.0105000000000000007 < z < -1.14999999999999993e-33

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 61.2%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 65.0%

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

      1. div-sub 65.0%

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

   8. Simplified 65.0%

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

   if -1.14999999999999993e-33 < z < 4.5000000000000001e-76 or 6.3999999999999999e-44 < z < 9.5000000000000005e-6

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 79.4%

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

      1. associate-/l* 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in x around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. unsub-neg 73.2%

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

   8. Simplified 73.2%

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

   if 4.5000000000000001e-76 < z < 6.3999999999999999e-44

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 9.5000000000000005e-6 < z < 1.4999999999999999e112

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0105:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.8e-27)
     t
     (if (<= z -5.2e-138)
       x
       (if (<= z -2.6e-244)
         (* (/ x a) (- y))
         (if (<= z 7.5e-240)
           x
           (if (<= z 3.2e-210)
             t_1
             (if (<= z 1.25e-86)
               x
               (if (<= z 5e-31)
                 t_1
                 (if (<= z 1.75e+112)
                   x
                   (if (<= z 7.8e+147) (/ x (/ z y)) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= -5.2e-138) {
		tmp = x;
	} else if (z <= -2.6e-244) {
		tmp = (x / a) * -y;
	} else if (z <= 7.5e-240) {
		tmp = x;
	} else if (z <= 3.2e-210) {
		tmp = t_1;
	} else if (z <= 1.25e-86) {
		tmp = x;
	} else if (z <= 5e-31) {
		tmp = t_1;
	} else if (z <= 1.75e+112) {
		tmp = x;
	} else if (z <= 7.8e+147) {
		tmp = x / (z / y);
	} 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 = t * (y / a)
    if (z <= (-1.8d-27)) then
        tmp = t
    else if (z <= (-5.2d-138)) then
        tmp = x
    else if (z <= (-2.6d-244)) then
        tmp = (x / a) * -y
    else if (z <= 7.5d-240) then
        tmp = x
    else if (z <= 3.2d-210) then
        tmp = t_1
    else if (z <= 1.25d-86) then
        tmp = x
    else if (z <= 5d-31) then
        tmp = t_1
    else if (z <= 1.75d+112) then
        tmp = x
    else if (z <= 7.8d+147) then
        tmp = x / (z / y)
    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 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= -5.2e-138) {
		tmp = x;
	} else if (z <= -2.6e-244) {
		tmp = (x / a) * -y;
	} else if (z <= 7.5e-240) {
		tmp = x;
	} else if (z <= 3.2e-210) {
		tmp = t_1;
	} else if (z <= 1.25e-86) {
		tmp = x;
	} else if (z <= 5e-31) {
		tmp = t_1;
	} else if (z <= 1.75e+112) {
		tmp = x;
	} else if (z <= 7.8e+147) {
		tmp = x / (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.8e-27:
		tmp = t
	elif z <= -5.2e-138:
		tmp = x
	elif z <= -2.6e-244:
		tmp = (x / a) * -y
	elif z <= 7.5e-240:
		tmp = x
	elif z <= 3.2e-210:
		tmp = t_1
	elif z <= 1.25e-86:
		tmp = x
	elif z <= 5e-31:
		tmp = t_1
	elif z <= 1.75e+112:
		tmp = x
	elif z <= 7.8e+147:
		tmp = x / (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= -5.2e-138)
		tmp = x;
	elseif (z <= -2.6e-244)
		tmp = Float64(Float64(x / a) * Float64(-y));
	elseif (z <= 7.5e-240)
		tmp = x;
	elseif (z <= 3.2e-210)
		tmp = t_1;
	elseif (z <= 1.25e-86)
		tmp = x;
	elseif (z <= 5e-31)
		tmp = t_1;
	elseif (z <= 1.75e+112)
		tmp = x;
	elseif (z <= 7.8e+147)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= -5.2e-138)
		tmp = x;
	elseif (z <= -2.6e-244)
		tmp = (x / a) * -y;
	elseif (z <= 7.5e-240)
		tmp = x;
	elseif (z <= 3.2e-210)
		tmp = t_1;
	elseif (z <= 1.25e-86)
		tmp = x;
	elseif (z <= 5e-31)
		tmp = t_1;
	elseif (z <= 1.75e+112)
		tmp = x;
	elseif (z <= 7.8e+147)
		tmp = x / (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-27], t, If[LessEqual[z, -5.2e-138], x, If[LessEqual[z, -2.6e-244], N[(N[(x / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 7.5e-240], x, If[LessEqual[z, 3.2e-210], t$95$1, If[LessEqual[z, 1.25e-86], x, If[LessEqual[z, 5e-31], t$95$1, If[LessEqual[z, 1.75e+112], x, If[LessEqual[z, 7.8e+147], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7999999999999999e-27 or 7.80000000000000033e147 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in z around inf 43.8%

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

   if -1.7999999999999999e-27 < z < -5.2e-138 or -2.6000000000000001e-244 < z < 7.4999999999999995e-240 or 3.20000000000000028e-210 < z < 1.25e-86 or 5e-31 < z < 1.74999999999999998e112

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf 48.7%

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

   if -5.2e-138 < z < -2.6000000000000001e-244

   1. Initial program 89.9%

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

   3. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in t around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

      3. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in a around 0 38.5%

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

       1. mul-1-neg 38.5%

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

       2. associate-*l/ 43.3%

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

       3. distribute-rgt-neg-out 43.3%

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

   11. Simplified 43.3%

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

   if 7.4999999999999995e-240 < z < 3.20000000000000028e-210 or 1.25e-86 < z < 5e-31

   1. Initial program 82.8%

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

      1. associate-*r/ 94.2%

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

      2. clear-num 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in t around inf 71.0%

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

      1. div-sub 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in z around 0 60.7%

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

   if 1.74999999999999998e112 < z < 7.80000000000000033e147

   1. Initial program 51.8%

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

   3. Taylor expanded in a around 0 17.1%

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

      1. associate-*r/ 17.1%

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

      2. *-commutative 17.1%

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

      3. neg-mul-1 17.1%

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

      4. distribute-rgt-neg-in 17.1%

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

      5. associate-/l* 39.5%

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

   5. Simplified 39.5%

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

   6. Taylor expanded in x around inf 42.0%

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

      1. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := x \cdot \frac{y - a}{z}\\ t_3 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -175000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a)))
        (t_2 (* x (/ (- y a) z)))
        (t_3 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.5e+88)
     t
     (if (<= z -2.5e+60)
       t_2
       (if (<= z -175000000.0)
         t
         (if (<= z -3e-26)
           t_1
           (if (<= z 3e-75)
             t_3
             (if (<= z 7e-44)
               t_1
               (if (<= z 2.35e+111) t_3 (if (<= z 5.8e+147) t_2 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double t_2 = x * ((y - a) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.5e+88) {
		tmp = t;
	} else if (z <= -2.5e+60) {
		tmp = t_2;
	} else if (z <= -175000000.0) {
		tmp = t;
	} else if (z <= -3e-26) {
		tmp = t_1;
	} else if (z <= 3e-75) {
		tmp = t_3;
	} else if (z <= 7e-44) {
		tmp = t_1;
	} else if (z <= 2.35e+111) {
		tmp = t_3;
	} else if (z <= 5.8e+147) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    t_2 = x * ((y - a) / z)
    t_3 = x * (1.0d0 - (y / a))
    if (z <= (-3.5d+88)) then
        tmp = t
    else if (z <= (-2.5d+60)) then
        tmp = t_2
    else if (z <= (-175000000.0d0)) then
        tmp = t
    else if (z <= (-3d-26)) then
        tmp = t_1
    else if (z <= 3d-75) then
        tmp = t_3
    else if (z <= 7d-44) then
        tmp = t_1
    else if (z <= 2.35d+111) then
        tmp = t_3
    else if (z <= 5.8d+147) then
        tmp = t_2
    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 = t * ((y - z) / a);
	double t_2 = x * ((y - a) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.5e+88) {
		tmp = t;
	} else if (z <= -2.5e+60) {
		tmp = t_2;
	} else if (z <= -175000000.0) {
		tmp = t;
	} else if (z <= -3e-26) {
		tmp = t_1;
	} else if (z <= 3e-75) {
		tmp = t_3;
	} else if (z <= 7e-44) {
		tmp = t_1;
	} else if (z <= 2.35e+111) {
		tmp = t_3;
	} else if (z <= 5.8e+147) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	t_2 = x * ((y - a) / z)
	t_3 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.5e+88:
		tmp = t
	elif z <= -2.5e+60:
		tmp = t_2
	elif z <= -175000000.0:
		tmp = t
	elif z <= -3e-26:
		tmp = t_1
	elif z <= 3e-75:
		tmp = t_3
	elif z <= 7e-44:
		tmp = t_1
	elif z <= 2.35e+111:
		tmp = t_3
	elif z <= 5.8e+147:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	t_2 = Float64(x * Float64(Float64(y - a) / z))
	t_3 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.5e+88)
		tmp = t;
	elseif (z <= -2.5e+60)
		tmp = t_2;
	elseif (z <= -175000000.0)
		tmp = t;
	elseif (z <= -3e-26)
		tmp = t_1;
	elseif (z <= 3e-75)
		tmp = t_3;
	elseif (z <= 7e-44)
		tmp = t_1;
	elseif (z <= 2.35e+111)
		tmp = t_3;
	elseif (z <= 5.8e+147)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	t_2 = x * ((y - a) / z);
	t_3 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.5e+88)
		tmp = t;
	elseif (z <= -2.5e+60)
		tmp = t_2;
	elseif (z <= -175000000.0)
		tmp = t;
	elseif (z <= -3e-26)
		tmp = t_1;
	elseif (z <= 3e-75)
		tmp = t_3;
	elseif (z <= 7e-44)
		tmp = t_1;
	elseif (z <= 2.35e+111)
		tmp = t_3;
	elseif (z <= 5.8e+147)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+88], t, If[LessEqual[z, -2.5e+60], t$95$2, If[LessEqual[z, -175000000.0], t, If[LessEqual[z, -3e-26], t$95$1, If[LessEqual[z, 3e-75], t$95$3, If[LessEqual[z, 7e-44], t$95$1, If[LessEqual[z, 2.35e+111], t$95$3, If[LessEqual[z, 5.8e+147], t$95$2, t]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e88 or -2.49999999999999987e60 < z < -1.75e8 or 5.7999999999999997e147 < z

   1. Initial program 53.3%

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

   3. Taylor expanded in z around inf 51.1%

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

   if -3.4999999999999998e88 < z < -2.49999999999999987e60 or 2.35000000000000004e111 < z < 5.7999999999999997e147

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. distribute-lft-out-- 49.9%

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

      3. div-sub 50.0%

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

      4. mul-1-neg 50.0%

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

      5. unsub-neg 50.0%

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

      6. distribute-rgt-out-- 50.0%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   if -1.75e8 < z < -3.00000000000000012e-26 or 2.9999999999999999e-75 < z < 6.9999999999999995e-44

   1. Initial program 89.2%

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

      1. associate-*r/ 89.2%

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

      2. clear-num 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in a around inf 67.2%

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

   if -3.00000000000000012e-26 < z < 2.9999999999999999e-75 or 6.9999999999999995e-44 < z < 2.35000000000000004e111

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 76.1%

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

      1. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -175000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.001:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.02e+89)
     t
     (if (<= z -2.35e+60)
       t_1
       (if (<= z -0.001)
         t
         (if (<= z -1.12e-35)
           (* y (/ (- t x) a))
           (if (<= z 3.2e-75)
             t_2
             (if (<= z 5.5e-42)
               (* t (/ (- y z) a))
               (if (<= z 3.4e+111) t_2 (if (<= z 4.7e+147) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.02e+89) {
		tmp = t;
	} else if (z <= -2.35e+60) {
		tmp = t_1;
	} else if (z <= -0.001) {
		tmp = t;
	} else if (z <= -1.12e-35) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 5.5e-42) {
		tmp = t * ((y - z) / a);
	} else if (z <= 3.4e+111) {
		tmp = t_2;
	} else if (z <= 4.7e+147) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.02d+89)) then
        tmp = t
    else if (z <= (-2.35d+60)) then
        tmp = t_1
    else if (z <= (-0.001d0)) then
        tmp = t
    else if (z <= (-1.12d-35)) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.2d-75) then
        tmp = t_2
    else if (z <= 5.5d-42) then
        tmp = t * ((y - z) / a)
    else if (z <= 3.4d+111) then
        tmp = t_2
    else if (z <= 4.7d+147) 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 * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.02e+89) {
		tmp = t;
	} else if (z <= -2.35e+60) {
		tmp = t_1;
	} else if (z <= -0.001) {
		tmp = t;
	} else if (z <= -1.12e-35) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 5.5e-42) {
		tmp = t * ((y - z) / a);
	} else if (z <= 3.4e+111) {
		tmp = t_2;
	} else if (z <= 4.7e+147) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.02e+89:
		tmp = t
	elif z <= -2.35e+60:
		tmp = t_1
	elif z <= -0.001:
		tmp = t
	elif z <= -1.12e-35:
		tmp = y * ((t - x) / a)
	elif z <= 3.2e-75:
		tmp = t_2
	elif z <= 5.5e-42:
		tmp = t * ((y - z) / a)
	elif z <= 3.4e+111:
		tmp = t_2
	elif z <= 4.7e+147:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.02e+89)
		tmp = t;
	elseif (z <= -2.35e+60)
		tmp = t_1;
	elseif (z <= -0.001)
		tmp = t;
	elseif (z <= -1.12e-35)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 5.5e-42)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 3.4e+111)
		tmp = t_2;
	elseif (z <= 4.7e+147)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.02e+89)
		tmp = t;
	elseif (z <= -2.35e+60)
		tmp = t_1;
	elseif (z <= -0.001)
		tmp = t;
	elseif (z <= -1.12e-35)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 5.5e-42)
		tmp = t * ((y - z) / a);
	elseif (z <= 3.4e+111)
		tmp = t_2;
	elseif (z <= 4.7e+147)
		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[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+89], t, If[LessEqual[z, -2.35e+60], t$95$1, If[LessEqual[z, -0.001], t, If[LessEqual[z, -1.12e-35], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-75], t$95$2, If[LessEqual[z, 5.5e-42], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+111], t$95$2, If[LessEqual[z, 4.7e+147], t$95$1, t]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.0199999999999999e89 or -2.3499999999999999e60 < z < -1e-3 or 4.7000000000000003e147 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in z around inf 49.5%

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

   if -1.0199999999999999e89 < z < -2.3499999999999999e60 or 3.4000000000000001e111 < z < 4.7000000000000003e147

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. distribute-lft-out-- 49.9%

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

      3. div-sub 50.0%

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

      4. mul-1-neg 50.0%

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

      5. unsub-neg 50.0%

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

      6. distribute-rgt-out-- 50.0%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   if -1e-3 < z < -1.12e-35

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 61.2%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 65.0%

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

      1. div-sub 65.0%

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

   8. Simplified 65.0%

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

   if -1.12e-35 < z < 3.19999999999999977e-75 or 5.5e-42 < z < 3.4000000000000001e111

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 76.8%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   8. Simplified 68.7%

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

   if 3.19999999999999977e-75 < z < 5.5e-42

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.001:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t - \frac{t}{\frac{z}{y}}\\ t_3 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 165000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z)))
        (t_2 (- t (/ t (/ z y))))
        (t_3 (* x (- 1.0 (/ y a)))))
   (if (<= z -2e+85)
     t_2
     (if (<= z -2.6e+60)
       t_1
       (if (<= z -4.4e-27)
         t_2
         (if (<= z 2.8e-75)
           t_3
           (if (<= z 5.3e-39)
             (* t (/ (- y z) a))
             (if (<= z 165000000000.0)
               t_3
               (if (<= z 2.35e+111)
                 (+ x (/ t (/ a y)))
                 (if (<= z 2.25e+148) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t - (t / (z / y));
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2e+85) {
		tmp = t_2;
	} else if (z <= -2.6e+60) {
		tmp = t_1;
	} else if (z <= -4.4e-27) {
		tmp = t_2;
	} else if (z <= 2.8e-75) {
		tmp = t_3;
	} else if (z <= 5.3e-39) {
		tmp = t * ((y - z) / a);
	} else if (z <= 165000000000.0) {
		tmp = t_3;
	} else if (z <= 2.35e+111) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.25e+148) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t - (t / (z / y))
    t_3 = x * (1.0d0 - (y / a))
    if (z <= (-2d+85)) then
        tmp = t_2
    else if (z <= (-2.6d+60)) then
        tmp = t_1
    else if (z <= (-4.4d-27)) then
        tmp = t_2
    else if (z <= 2.8d-75) then
        tmp = t_3
    else if (z <= 5.3d-39) then
        tmp = t * ((y - z) / a)
    else if (z <= 165000000000.0d0) then
        tmp = t_3
    else if (z <= 2.35d+111) then
        tmp = x + (t / (a / y))
    else if (z <= 2.25d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t - (t / (z / y));
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2e+85) {
		tmp = t_2;
	} else if (z <= -2.6e+60) {
		tmp = t_1;
	} else if (z <= -4.4e-27) {
		tmp = t_2;
	} else if (z <= 2.8e-75) {
		tmp = t_3;
	} else if (z <= 5.3e-39) {
		tmp = t * ((y - z) / a);
	} else if (z <= 165000000000.0) {
		tmp = t_3;
	} else if (z <= 2.35e+111) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.25e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t - (t / (z / y))
	t_3 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2e+85:
		tmp = t_2
	elif z <= -2.6e+60:
		tmp = t_1
	elif z <= -4.4e-27:
		tmp = t_2
	elif z <= 2.8e-75:
		tmp = t_3
	elif z <= 5.3e-39:
		tmp = t * ((y - z) / a)
	elif z <= 165000000000.0:
		tmp = t_3
	elif z <= 2.35e+111:
		tmp = x + (t / (a / y))
	elif z <= 2.25e+148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t - Float64(t / Float64(z / y)))
	t_3 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2e+85)
		tmp = t_2;
	elseif (z <= -2.6e+60)
		tmp = t_1;
	elseif (z <= -4.4e-27)
		tmp = t_2;
	elseif (z <= 2.8e-75)
		tmp = t_3;
	elseif (z <= 5.3e-39)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 165000000000.0)
		tmp = t_3;
	elseif (z <= 2.35e+111)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 2.25e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t - (t / (z / y));
	t_3 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2e+85)
		tmp = t_2;
	elseif (z <= -2.6e+60)
		tmp = t_1;
	elseif (z <= -4.4e-27)
		tmp = t_2;
	elseif (z <= 2.8e-75)
		tmp = t_3;
	elseif (z <= 5.3e-39)
		tmp = t * ((y - z) / a);
	elseif (z <= 165000000000.0)
		tmp = t_3;
	elseif (z <= 2.35e+111)
		tmp = x + (t / (a / y));
	elseif (z <= 2.25e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+85], t$95$2, If[LessEqual[z, -2.6e+60], t$95$1, If[LessEqual[z, -4.4e-27], t$95$2, If[LessEqual[z, 2.8e-75], t$95$3, If[LessEqual[z, 5.3e-39], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 165000000000.0], t$95$3, If[LessEqual[z, 2.35e+111], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+148], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2e85 or -2.60000000000000008e60 < z < -4.39999999999999974e-27 or 2.24999999999999997e148 < z

   1. Initial program 57.3%

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

      1. associate-*r/ 43.7%

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

      2. clear-num 43.6%

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

   4. Applied egg-rr 43.6%

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

   5. Taylor expanded in t around inf 63.6%

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

      1. div-sub 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in a around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   10. Simplified 56.8%

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

   11. Taylor expanded in y around 0 51.9%

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

       1. mul-1-neg 51.9%

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

       2. unsub-neg 51.9%

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

       3. associate-/l* 56.8%

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

   13. Simplified 56.8%

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

   if -2e85 < z < -2.60000000000000008e60 or 2.35000000000000004e111 < z < 2.24999999999999997e148

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. distribute-lft-out-- 49.9%

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

      3. div-sub 50.0%

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

      4. mul-1-neg 50.0%

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

      5. unsub-neg 50.0%

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

      6. distribute-rgt-out-- 50.0%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   if -4.39999999999999974e-27 < z < 2.79999999999999998e-75 or 5.30000000000000003e-39 < z < 1.65e11

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 79.1%

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

      1. associate-/l* 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 2.79999999999999998e-75 < z < 5.30000000000000003e-39

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 1.65e11 < z < 2.35000000000000004e111

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 165000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 20000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (- t (/ t (/ z y)))))
   (if (<= z -3.8e+85)
     t_2
     (if (<= z -3.8e+60)
       t_1
       (if (<= z -4.4e-27)
         t_2
         (if (<= z 3.2e-75)
           (- x (/ x (/ a y)))
           (if (<= z 5.5e-42)
             (* t (/ (- y z) a))
             (if (<= z 20000000.0)
               (* x (- 1.0 (/ y a)))
               (if (<= z 8.4e+111)
                 (+ x (/ t (/ a y)))
                 (if (<= z 8.4e+146) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t - (t / (z / y));
	double tmp;
	if (z <= -3.8e+85) {
		tmp = t_2;
	} else if (z <= -3.8e+60) {
		tmp = t_1;
	} else if (z <= -4.4e-27) {
		tmp = t_2;
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 5.5e-42) {
		tmp = t * ((y - z) / a);
	} else if (z <= 20000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+111) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.4e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t - (t / (z / y))
    if (z <= (-3.8d+85)) then
        tmp = t_2
    else if (z <= (-3.8d+60)) then
        tmp = t_1
    else if (z <= (-4.4d-27)) then
        tmp = t_2
    else if (z <= 3.2d-75) then
        tmp = x - (x / (a / y))
    else if (z <= 5.5d-42) then
        tmp = t * ((y - z) / a)
    else if (z <= 20000000.0d0) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8.4d+111) then
        tmp = x + (t / (a / y))
    else if (z <= 8.4d+146) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t - (t / (z / y));
	double tmp;
	if (z <= -3.8e+85) {
		tmp = t_2;
	} else if (z <= -3.8e+60) {
		tmp = t_1;
	} else if (z <= -4.4e-27) {
		tmp = t_2;
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 5.5e-42) {
		tmp = t * ((y - z) / a);
	} else if (z <= 20000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+111) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.4e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t - (t / (z / y))
	tmp = 0
	if z <= -3.8e+85:
		tmp = t_2
	elif z <= -3.8e+60:
		tmp = t_1
	elif z <= -4.4e-27:
		tmp = t_2
	elif z <= 3.2e-75:
		tmp = x - (x / (a / y))
	elif z <= 5.5e-42:
		tmp = t * ((y - z) / a)
	elif z <= 20000000.0:
		tmp = x * (1.0 - (y / a))
	elif z <= 8.4e+111:
		tmp = x + (t / (a / y))
	elif z <= 8.4e+146:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -3.8e+85)
		tmp = t_2;
	elseif (z <= -3.8e+60)
		tmp = t_1;
	elseif (z <= -4.4e-27)
		tmp = t_2;
	elseif (z <= 3.2e-75)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 5.5e-42)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 20000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8.4e+111)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 8.4e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t - (t / (z / y));
	tmp = 0.0;
	if (z <= -3.8e+85)
		tmp = t_2;
	elseif (z <= -3.8e+60)
		tmp = t_1;
	elseif (z <= -4.4e-27)
		tmp = t_2;
	elseif (z <= 3.2e-75)
		tmp = x - (x / (a / y));
	elseif (z <= 5.5e-42)
		tmp = t * ((y - z) / a);
	elseif (z <= 20000000.0)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8.4e+111)
		tmp = x + (t / (a / y));
	elseif (z <= 8.4e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+85], t$95$2, If[LessEqual[z, -3.8e+60], t$95$1, If[LessEqual[z, -4.4e-27], t$95$2, If[LessEqual[z, 3.2e-75], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-42], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 20000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+111], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+146], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.79999999999999992e85 or -3.80000000000000009e60 < z < -4.39999999999999974e-27 or 8.4000000000000002e146 < z

   1. Initial program 57.3%

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

      1. associate-*r/ 43.7%

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

      2. clear-num 43.6%

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

   4. Applied egg-rr 43.6%

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

   5. Taylor expanded in t around inf 63.6%

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

      1. div-sub 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in a around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   10. Simplified 56.8%

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

   11. Taylor expanded in y around 0 51.9%

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

       1. mul-1-neg 51.9%

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

       2. unsub-neg 51.9%

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

       3. associate-/l* 56.8%

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

   13. Simplified 56.8%

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

   if -3.79999999999999992e85 < z < -3.80000000000000009e60 or 8.3999999999999998e111 < z < 8.4000000000000002e146

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. distribute-lft-out-- 49.9%

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

      3. div-sub 50.0%

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

      4. mul-1-neg 50.0%

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

      5. unsub-neg 50.0%

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

      6. distribute-rgt-out-- 50.0%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   if -4.39999999999999974e-27 < z < 3.19999999999999977e-75

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

      3. associate-/l* 72.0%

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

   8. Simplified 72.0%

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

   if 3.19999999999999977e-75 < z < 5.5e-42

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 5.5e-42 < z < 2e7

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 2e7 < z < 8.3999999999999998e111

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 20000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.7:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ z y)))))
   (if (<= z -1.25e+88)
     t_1
     (if (<= z -4.5e+60)
       (* x (/ (- y a) z))
       (if (<= z -4.4e-27)
         t_1
         (if (<= z 3.2e-75)
           (- x (/ x (/ a y)))
           (if (<= z 6.4e-44)
             (* t (/ (- y z) a))
             (if (<= z 4.7)
               (* x (- 1.0 (/ y a)))
               (if (<= z 9.6e+100)
                 (+ x (/ t (/ a y)))
                 (if (<= z 1.52e+149) (/ y (/ z (- x t))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (z <= -1.25e+88) {
		tmp = t_1;
	} else if (z <= -4.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.4e-27) {
		tmp = t_1;
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 6.4e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.7) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.6e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.52e+149) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t / (z / y))
    if (z <= (-1.25d+88)) then
        tmp = t_1
    else if (z <= (-4.5d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-4.4d-27)) then
        tmp = t_1
    else if (z <= 3.2d-75) then
        tmp = x - (x / (a / y))
    else if (z <= 6.4d-44) then
        tmp = t * ((y - z) / a)
    else if (z <= 4.7d0) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9.6d+100) then
        tmp = x + (t / (a / y))
    else if (z <= 1.52d+149) then
        tmp = y / (z / (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (z <= -1.25e+88) {
		tmp = t_1;
	} else if (z <= -4.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.4e-27) {
		tmp = t_1;
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 6.4e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.7) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.6e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.52e+149) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t / (z / y))
	tmp = 0
	if z <= -1.25e+88:
		tmp = t_1
	elif z <= -4.5e+60:
		tmp = x * ((y - a) / z)
	elif z <= -4.4e-27:
		tmp = t_1
	elif z <= 3.2e-75:
		tmp = x - (x / (a / y))
	elif z <= 6.4e-44:
		tmp = t * ((y - z) / a)
	elif z <= 4.7:
		tmp = x * (1.0 - (y / a))
	elif z <= 9.6e+100:
		tmp = x + (t / (a / y))
	elif z <= 1.52e+149:
		tmp = y / (z / (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -1.25e+88)
		tmp = t_1;
	elseif (z <= -4.5e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -4.4e-27)
		tmp = t_1;
	elseif (z <= 3.2e-75)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 6.4e-44)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 4.7)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9.6e+100)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.52e+149)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t / (z / y));
	tmp = 0.0;
	if (z <= -1.25e+88)
		tmp = t_1;
	elseif (z <= -4.5e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -4.4e-27)
		tmp = t_1;
	elseif (z <= 3.2e-75)
		tmp = x - (x / (a / y));
	elseif (z <= 6.4e-44)
		tmp = t * ((y - z) / a);
	elseif (z <= 4.7)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9.6e+100)
		tmp = x + (t / (a / y));
	elseif (z <= 1.52e+149)
		tmp = y / (z / (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+88], t$95$1, If[LessEqual[z, -4.5e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-27], t$95$1, If[LessEqual[z, 3.2e-75], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-44], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+100], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e+149], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.24999999999999999e88 or -4.50000000000000013e60 < z < -4.39999999999999974e-27 or 1.5199999999999999e149 < z

   1. Initial program 57.3%

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

      1. associate-*r/ 43.7%

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

      2. clear-num 43.6%

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

   4. Applied egg-rr 43.6%

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

   5. Taylor expanded in t around inf 63.6%

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

      1. div-sub 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in a around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   10. Simplified 56.8%

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

   11. Taylor expanded in y around 0 51.9%

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

       1. mul-1-neg 51.9%

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

       2. unsub-neg 51.9%

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

       3. associate-/l* 56.8%

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

   13. Simplified 56.8%

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

   if -1.24999999999999999e88 < z < -4.50000000000000013e60

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. distribute-lft-out-- 46.2%

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

      3. div-sub 46.2%

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

      4. mul-1-neg 46.2%

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

      5. unsub-neg 46.2%

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

      6. distribute-rgt-out-- 46.2%

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

      7. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   8. Simplified 73.5%

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

   if -4.39999999999999974e-27 < z < 3.19999999999999977e-75

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

      3. associate-/l* 72.0%

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

   8. Simplified 72.0%

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

   if 3.19999999999999977e-75 < z < 6.3999999999999999e-44

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 6.3999999999999999e-44 < z < 4.70000000000000018

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 4.70000000000000018 < z < 9.60000000000000046e100

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if 9.60000000000000046e100 < z < 1.5199999999999999e149

   1. Initial program 57.1%

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

   3. Taylor expanded in a around 0 15.4%

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

      1. associate-*r/ 15.4%

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

      2. *-commutative 15.4%

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

      3. neg-mul-1 15.4%

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

      4. distribute-rgt-neg-in 15.4%

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

      5. associate-/l* 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in y around -inf 38.3%

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

      1. associate-/l* 68.5%

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

   8. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x - t}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.7:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.1:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ z y)))))
   (if (<= z -1.26e+84)
     t_1
     (if (<= z -2.5e+60)
       (* x (/ (- y a) z))
       (if (<= z -0.1)
         (* (- t) (/ z (- a z)))
         (if (<= z 3.2e-75)
           (- x (/ x (/ a y)))
           (if (<= z 8e-43)
             (* t (/ (- y z) a))
             (if (<= z 0.112)
               (* x (- 1.0 (/ y a)))
               (if (<= z 3.1e+106)
                 (+ x (/ t (/ a y)))
                 (if (<= z 5.5e+147) (/ y (/ z (- x t))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (z <= -1.26e+84) {
		tmp = t_1;
	} else if (z <= -2.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.1) {
		tmp = -t * (z / (a - z));
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 8e-43) {
		tmp = t * ((y - z) / a);
	} else if (z <= 0.112) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.1e+106) {
		tmp = x + (t / (a / y));
	} else if (z <= 5.5e+147) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t / (z / y))
    if (z <= (-1.26d+84)) then
        tmp = t_1
    else if (z <= (-2.5d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.1d0)) then
        tmp = -t * (z / (a - z))
    else if (z <= 3.2d-75) then
        tmp = x - (x / (a / y))
    else if (z <= 8d-43) then
        tmp = t * ((y - z) / a)
    else if (z <= 0.112d0) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.1d+106) then
        tmp = x + (t / (a / y))
    else if (z <= 5.5d+147) then
        tmp = y / (z / (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (z <= -1.26e+84) {
		tmp = t_1;
	} else if (z <= -2.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.1) {
		tmp = -t * (z / (a - z));
	} else if (z <= 3.2e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 8e-43) {
		tmp = t * ((y - z) / a);
	} else if (z <= 0.112) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.1e+106) {
		tmp = x + (t / (a / y));
	} else if (z <= 5.5e+147) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t / (z / y))
	tmp = 0
	if z <= -1.26e+84:
		tmp = t_1
	elif z <= -2.5e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.1:
		tmp = -t * (z / (a - z))
	elif z <= 3.2e-75:
		tmp = x - (x / (a / y))
	elif z <= 8e-43:
		tmp = t * ((y - z) / a)
	elif z <= 0.112:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.1e+106:
		tmp = x + (t / (a / y))
	elif z <= 5.5e+147:
		tmp = y / (z / (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -1.26e+84)
		tmp = t_1;
	elseif (z <= -2.5e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.1)
		tmp = Float64(Float64(-t) * Float64(z / Float64(a - z)));
	elseif (z <= 3.2e-75)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 8e-43)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 0.112)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.1e+106)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 5.5e+147)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t / (z / y));
	tmp = 0.0;
	if (z <= -1.26e+84)
		tmp = t_1;
	elseif (z <= -2.5e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.1)
		tmp = -t * (z / (a - z));
	elseif (z <= 3.2e-75)
		tmp = x - (x / (a / y));
	elseif (z <= 8e-43)
		tmp = t * ((y - z) / a);
	elseif (z <= 0.112)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.1e+106)
		tmp = x + (t / (a / y));
	elseif (z <= 5.5e+147)
		tmp = y / (z / (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+84], t$95$1, If[LessEqual[z, -2.5e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.1], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-75], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-43], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.112], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+106], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+147], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -1.26000000000000007e84 or 5.4999999999999997e147 < z

   1. Initial program 49.7%

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

      1. associate-*r/ 33.0%

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

      2. clear-num 32.9%

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

   4. Applied egg-rr 32.9%

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

   5. Taylor expanded in t around inf 60.9%

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

      1. div-sub 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in y around 0 51.8%

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

       1. mul-1-neg 51.8%

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

       2. unsub-neg 51.8%

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

       3. associate-/l* 57.9%

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

   13. Simplified 57.9%

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

   if -1.26000000000000007e84 < z < -2.49999999999999987e60

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. distribute-lft-out-- 46.2%

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

      3. div-sub 46.2%

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

      4. mul-1-neg 46.2%

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

      5. unsub-neg 46.2%

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

      6. distribute-rgt-out-- 46.2%

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

      7. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   8. Simplified 73.5%

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

   if -2.49999999999999987e60 < z < -0.10000000000000001

   1. Initial program 82.5%

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

      1. associate-*r/ 91.0%

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

      2. clear-num 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. div-sub 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

      2. distribute-neg-frac 68.8%

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

   10. Simplified 68.8%

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

   if -0.10000000000000001 < z < 3.19999999999999977e-75

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 69.6%

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

   8. Simplified 69.6%

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

   if 3.19999999999999977e-75 < z < 8.00000000000000062e-43

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 8.00000000000000062e-43 < z < 0.112000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 0.112000000000000002 < z < 3.0999999999999999e106

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if 3.0999999999999999e106 < z < 5.4999999999999997e147

   1. Initial program 57.1%

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

   3. Taylor expanded in a around 0 15.4%

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

      1. associate-*r/ 15.4%

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

      2. *-commutative 15.4%

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

      3. neg-mul-1 15.4%

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

      4. distribute-rgt-neg-in 15.4%

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

      5. associate-/l* 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in y around -inf 38.3%

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

      1. associate-/l* 68.5%

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

   8. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x - t}}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+84}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.1:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.009:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 0.0013:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+85)
   (* t (/ (- z y) z))
   (if (<= z -2.35e+60)
     (* x (/ (- y a) z))
     (if (<= z -0.009)
       (* (- t) (/ z (- a z)))
       (if (<= z 9.6e-79)
         (- x (/ x (/ a y)))
         (if (<= z 1.25e-43)
           (* t (/ (- y z) a))
           (if (<= z 0.0013)
             (* x (- 1.0 (/ y a)))
             (if (<= z 8.6e+100)
               (+ x (/ t (/ a y)))
               (if (<= z 2.35e+147)
                 (/ y (/ z (- x t)))
                 (- t (/ t (/ z y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+85) {
		tmp = t * ((z - y) / z);
	} else if (z <= -2.35e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.009) {
		tmp = -t * (z / (a - z));
	} else if (z <= 9.6e-79) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.25e-43) {
		tmp = t * ((y - z) / a);
	} else if (z <= 0.0013) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.6e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.35e+147) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t - (t / (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) :: tmp
    if (z <= (-4.8d+85)) then
        tmp = t * ((z - y) / z)
    else if (z <= (-2.35d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.009d0)) then
        tmp = -t * (z / (a - z))
    else if (z <= 9.6d-79) then
        tmp = x - (x / (a / y))
    else if (z <= 1.25d-43) then
        tmp = t * ((y - z) / a)
    else if (z <= 0.0013d0) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8.6d+100) then
        tmp = x + (t / (a / y))
    else if (z <= 2.35d+147) then
        tmp = y / (z / (x - t))
    else
        tmp = t - (t / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+85) {
		tmp = t * ((z - y) / z);
	} else if (z <= -2.35e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.009) {
		tmp = -t * (z / (a - z));
	} else if (z <= 9.6e-79) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.25e-43) {
		tmp = t * ((y - z) / a);
	} else if (z <= 0.0013) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.6e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.35e+147) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t - (t / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+85:
		tmp = t * ((z - y) / z)
	elif z <= -2.35e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.009:
		tmp = -t * (z / (a - z))
	elif z <= 9.6e-79:
		tmp = x - (x / (a / y))
	elif z <= 1.25e-43:
		tmp = t * ((y - z) / a)
	elif z <= 0.0013:
		tmp = x * (1.0 - (y / a))
	elif z <= 8.6e+100:
		tmp = x + (t / (a / y))
	elif z <= 2.35e+147:
		tmp = y / (z / (x - t))
	else:
		tmp = t - (t / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+85)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= -2.35e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.009)
		tmp = Float64(Float64(-t) * Float64(z / Float64(a - z)));
	elseif (z <= 9.6e-79)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 1.25e-43)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 0.0013)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8.6e+100)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 2.35e+147)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	else
		tmp = Float64(t - Float64(t / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+85)
		tmp = t * ((z - y) / z);
	elseif (z <= -2.35e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.009)
		tmp = -t * (z / (a - z));
	elseif (z <= 9.6e-79)
		tmp = x - (x / (a / y));
	elseif (z <= 1.25e-43)
		tmp = t * ((y - z) / a);
	elseif (z <= 0.0013)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8.6e+100)
		tmp = x + (t / (a / y));
	elseif (z <= 2.35e+147)
		tmp = y / (z / (x - t));
	else
		tmp = t - (t / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+85], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.009], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-79], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-43], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0013], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+100], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+147], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -4.79999999999999993e85

   1. Initial program 57.6%

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

      1. associate-*r/ 32.7%

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

      2. clear-num 32.6%

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

   4. Applied egg-rr 32.6%

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

   5. Taylor expanded in t around inf 61.2%

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

      1. div-sub 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in a around 0 57.3%

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

      1. associate-*r/ 57.3%

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

      2. neg-mul-1 57.3%

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

   10. Simplified 57.3%

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

   if -4.79999999999999993e85 < z < -2.3499999999999999e60

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. distribute-lft-out-- 46.2%

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

      3. div-sub 46.2%

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

      4. mul-1-neg 46.2%

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

      5. unsub-neg 46.2%

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

      6. distribute-rgt-out-- 46.2%

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

      7. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   8. Simplified 73.5%

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

   if -2.3499999999999999e60 < z < -0.00899999999999999932

   1. Initial program 82.5%

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

      1. associate-*r/ 91.0%

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

      2. clear-num 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. div-sub 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

      2. distribute-neg-frac 68.8%

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

   10. Simplified 68.8%

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

   if -0.00899999999999999932 < z < 9.60000000000000023e-79

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 69.6%

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

   8. Simplified 69.6%

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

   if 9.60000000000000023e-79 < z < 1.25000000000000005e-43

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 1.25000000000000005e-43 < z < 0.0012999999999999999

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 0.0012999999999999999 < z < 8.59999999999999986e100

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if 8.59999999999999986e100 < z < 2.3500000000000001e147

   1. Initial program 57.1%

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

   3. Taylor expanded in a around 0 15.4%

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

      1. associate-*r/ 15.4%

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

      2. *-commutative 15.4%

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

      3. neg-mul-1 15.4%

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

      4. distribute-rgt-neg-in 15.4%

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

      5. associate-/l* 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in y around -inf 38.3%

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

      1. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   if 2.3500000000000001e147 < z

   1. Initial program 42.2%

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

      1. associate-*r/ 33.2%

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

      2. clear-num 33.2%

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

   4. Applied egg-rr 33.2%

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

   5. Taylor expanded in t around inf 60.7%

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

      1. div-sub 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in a around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

   10. Simplified 58.4%

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

   11. Taylor expanded in y around 0 54.0%

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

       1. mul-1-neg 54.0%

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

       2. unsub-neg 54.0%

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

       3. associate-/l* 58.4%

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

   13. Simplified 58.4%

       \[\leadsto \color{blue}{t - \frac{t}{\frac{z}{y}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.009:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 0.0013:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.029:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+87)
   (* t (/ (- z y) z))
   (if (<= z -2.5e+60)
     (* x (/ (- y a) z))
     (if (<= z -0.029)
       (* (- t) (/ z (- a z)))
       (if (<= z 3.1e-75)
         (- x (/ x (/ a y)))
         (if (<= z 6e-44)
           (* t (/ (- y z) a))
           (if (<= z 8.2e-6)
             (* x (- 1.0 (/ y a)))
             (if (<= z 9.5e+100)
               (+ x (/ t (/ a y)))
               (if (<= z 5e+146)
                 (* (/ y z) (- x t))
                 (- t (/ t (/ z y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+87) {
		tmp = t * ((z - y) / z);
	} else if (z <= -2.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.029) {
		tmp = -t * (z / (a - z));
	} else if (z <= 3.1e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 6e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.2e-6) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.5e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 5e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t - (t / (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) :: tmp
    if (z <= (-5.1d+87)) then
        tmp = t * ((z - y) / z)
    else if (z <= (-2.5d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.029d0)) then
        tmp = -t * (z / (a - z))
    else if (z <= 3.1d-75) then
        tmp = x - (x / (a / y))
    else if (z <= 6d-44) then
        tmp = t * ((y - z) / a)
    else if (z <= 8.2d-6) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9.5d+100) then
        tmp = x + (t / (a / y))
    else if (z <= 5d+146) then
        tmp = (y / z) * (x - t)
    else
        tmp = t - (t / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+87) {
		tmp = t * ((z - y) / z);
	} else if (z <= -2.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.029) {
		tmp = -t * (z / (a - z));
	} else if (z <= 3.1e-75) {
		tmp = x - (x / (a / y));
	} else if (z <= 6e-44) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.2e-6) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.5e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 5e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t - (t / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+87:
		tmp = t * ((z - y) / z)
	elif z <= -2.5e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.029:
		tmp = -t * (z / (a - z))
	elif z <= 3.1e-75:
		tmp = x - (x / (a / y))
	elif z <= 6e-44:
		tmp = t * ((y - z) / a)
	elif z <= 8.2e-6:
		tmp = x * (1.0 - (y / a))
	elif z <= 9.5e+100:
		tmp = x + (t / (a / y))
	elif z <= 5e+146:
		tmp = (y / z) * (x - t)
	else:
		tmp = t - (t / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+87)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= -2.5e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.029)
		tmp = Float64(Float64(-t) * Float64(z / Float64(a - z)));
	elseif (z <= 3.1e-75)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 6e-44)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 8.2e-6)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9.5e+100)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 5e+146)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = Float64(t - Float64(t / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e+87)
		tmp = t * ((z - y) / z);
	elseif (z <= -2.5e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.029)
		tmp = -t * (z / (a - z));
	elseif (z <= 3.1e-75)
		tmp = x - (x / (a / y));
	elseif (z <= 6e-44)
		tmp = t * ((y - z) / a);
	elseif (z <= 8.2e-6)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9.5e+100)
		tmp = x + (t / (a / y));
	elseif (z <= 5e+146)
		tmp = (y / z) * (x - t);
	else
		tmp = t - (t / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+87], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.029], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-75], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-44], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-6], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+100], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+146], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -5.09999999999999988e87

   1. Initial program 57.6%

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

      1. associate-*r/ 32.7%

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

      2. clear-num 32.6%

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

   4. Applied egg-rr 32.6%

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

   5. Taylor expanded in t around inf 61.2%

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

      1. div-sub 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in a around 0 57.3%

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

      1. associate-*r/ 57.3%

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

      2. neg-mul-1 57.3%

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

   10. Simplified 57.3%

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

   if -5.09999999999999988e87 < z < -2.49999999999999987e60

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. distribute-lft-out-- 46.2%

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

      3. div-sub 46.2%

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

      4. mul-1-neg 46.2%

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

      5. unsub-neg 46.2%

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

      6. distribute-rgt-out-- 46.2%

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

      7. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   8. Simplified 73.5%

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

   if -2.49999999999999987e60 < z < -0.0290000000000000015

   1. Initial program 82.5%

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

      1. associate-*r/ 91.0%

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

      2. clear-num 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. div-sub 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

      2. distribute-neg-frac 68.8%

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

   10. Simplified 68.8%

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

   if -0.0290000000000000015 < z < 3.10000000000000007e-75

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 69.6%

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

   8. Simplified 69.6%

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

   if 3.10000000000000007e-75 < z < 6.0000000000000005e-44

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 6.0000000000000005e-44 < z < 8.1999999999999994e-6

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 8.1999999999999994e-6 < z < 9.4999999999999995e100

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if 9.4999999999999995e100 < z < 4.9999999999999999e146

   1. Initial program 57.1%

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

   3. Taylor expanded in y around -inf 38.3%

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

   4. Taylor expanded in a around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate-/l* 68.5%

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

      3. associate-/r/ 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

   6. Simplified 68.6%

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

   if 4.9999999999999999e146 < z

   1. Initial program 42.2%

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

      1. associate-*r/ 33.2%

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

      2. clear-num 33.2%

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

   4. Applied egg-rr 33.2%

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

   5. Taylor expanded in t around inf 60.7%

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

      1. div-sub 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in a around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

   10. Simplified 58.4%

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

   11. Taylor expanded in y around 0 54.0%

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

       1. mul-1-neg 54.0%

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

       2. unsub-neg 54.0%

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

       3. associate-/l* 58.4%

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

   13. Simplified 58.4%

       \[\leadsto \color{blue}{t - \frac{t}{\frac{z}{y}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.029:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq -0.00105:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+134)
   (* t (/ (- z y) z))
   (if (<= z -3.7e+61)
     (/ (- x) (/ (- a z) y))
     (if (<= z -0.00105)
       (* (- t) (/ z (- a z)))
       (if (<= z 2.5e-77)
         (- x (/ x (/ a y)))
         (if (<= z 5.6e-41)
           (* t (/ (- y z) a))
           (if (<= z 8.5e-7)
             (* x (- 1.0 (/ y a)))
             (if (<= z 9e+100)
               (+ x (/ t (/ a y)))
               (if (<= z 8.5e+146)
                 (* (/ y z) (- x t))
                 (- t (/ t (/ z y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+134) {
		tmp = t * ((z - y) / z);
	} else if (z <= -3.7e+61) {
		tmp = -x / ((a - z) / y);
	} else if (z <= -0.00105) {
		tmp = -t * (z / (a - z));
	} else if (z <= 2.5e-77) {
		tmp = x - (x / (a / y));
	} else if (z <= 5.6e-41) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.5e-7) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.5e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t - (t / (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) :: tmp
    if (z <= (-2d+134)) then
        tmp = t * ((z - y) / z)
    else if (z <= (-3.7d+61)) then
        tmp = -x / ((a - z) / y)
    else if (z <= (-0.00105d0)) then
        tmp = -t * (z / (a - z))
    else if (z <= 2.5d-77) then
        tmp = x - (x / (a / y))
    else if (z <= 5.6d-41) then
        tmp = t * ((y - z) / a)
    else if (z <= 8.5d-7) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9d+100) then
        tmp = x + (t / (a / y))
    else if (z <= 8.5d+146) then
        tmp = (y / z) * (x - t)
    else
        tmp = t - (t / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+134) {
		tmp = t * ((z - y) / z);
	} else if (z <= -3.7e+61) {
		tmp = -x / ((a - z) / y);
	} else if (z <= -0.00105) {
		tmp = -t * (z / (a - z));
	} else if (z <= 2.5e-77) {
		tmp = x - (x / (a / y));
	} else if (z <= 5.6e-41) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.5e-7) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9e+100) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.5e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t - (t / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+134:
		tmp = t * ((z - y) / z)
	elif z <= -3.7e+61:
		tmp = -x / ((a - z) / y)
	elif z <= -0.00105:
		tmp = -t * (z / (a - z))
	elif z <= 2.5e-77:
		tmp = x - (x / (a / y))
	elif z <= 5.6e-41:
		tmp = t * ((y - z) / a)
	elif z <= 8.5e-7:
		tmp = x * (1.0 - (y / a))
	elif z <= 9e+100:
		tmp = x + (t / (a / y))
	elif z <= 8.5e+146:
		tmp = (y / z) * (x - t)
	else:
		tmp = t - (t / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+134)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= -3.7e+61)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (z <= -0.00105)
		tmp = Float64(Float64(-t) * Float64(z / Float64(a - z)));
	elseif (z <= 2.5e-77)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 5.6e-41)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 8.5e-7)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9e+100)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 8.5e+146)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = Float64(t - Float64(t / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+134)
		tmp = t * ((z - y) / z);
	elseif (z <= -3.7e+61)
		tmp = -x / ((a - z) / y);
	elseif (z <= -0.00105)
		tmp = -t * (z / (a - z));
	elseif (z <= 2.5e-77)
		tmp = x - (x / (a / y));
	elseif (z <= 5.6e-41)
		tmp = t * ((y - z) / a);
	elseif (z <= 8.5e-7)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9e+100)
		tmp = x + (t / (a / y));
	elseif (z <= 8.5e+146)
		tmp = (y / z) * (x - t);
	else
		tmp = t - (t / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+134], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e+61], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00105], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-77], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-41], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-7], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+100], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+146], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -1.99999999999999984e134

   1. Initial program 60.1%

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

      1. associate-*r/ 28.3%

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

      2. clear-num 28.2%

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

   4. Applied egg-rr 28.2%

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

   5. Taylor expanded in t around inf 65.3%

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

      1. div-sub 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   10. Simplified 61.0%

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

   if -1.99999999999999984e134 < z < -3.70000000000000003e61

   1. Initial program 55.7%

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

   3. Taylor expanded in y around -inf 56.7%

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

   4. Taylor expanded in t around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-/l* 65.0%

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

      3. distribute-neg-frac 65.0%

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

   6. Simplified 65.0%

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

   if -3.70000000000000003e61 < z < -0.00104999999999999994

   1. Initial program 84.0%

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

      1. associate-*r/ 83.5%

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

      2. clear-num 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in t around inf 75.6%

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

      1. div-sub 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 63.3%

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

      1. neg-mul-1 63.3%

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

      2. distribute-neg-frac 63.3%

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

   10. Simplified 63.3%

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

   if -0.00104999999999999994 < z < 2.49999999999999982e-77

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 69.6%

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

   8. Simplified 69.6%

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

   if 2.49999999999999982e-77 < z < 5.6000000000000003e-41

   1. Initial program 89.0%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. div-sub 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in a around inf 78.4%

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

   if 5.6000000000000003e-41 < z < 8.50000000000000014e-7

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-/l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if 8.50000000000000014e-7 < z < 9.00000000000000073e100

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if 9.00000000000000073e100 < z < 8.5e146

   1. Initial program 57.1%

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

   3. Taylor expanded in y around -inf 38.3%

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

   4. Taylor expanded in a around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate-/l* 68.5%

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

      3. associate-/r/ 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

   6. Simplified 68.6%

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

   if 8.5e146 < z

   1. Initial program 42.2%

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

      1. associate-*r/ 33.2%

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

      2. clear-num 33.2%

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

   4. Applied egg-rr 33.2%

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

   5. Taylor expanded in t around inf 60.7%

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

      1. div-sub 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in a around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

   10. Simplified 58.4%

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

   11. Taylor expanded in y around 0 54.0%

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

       1. mul-1-neg 54.0%

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

       2. unsub-neg 54.0%

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

       3. associate-/l* 58.4%

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

   13. Simplified 58.4%

       \[\leadsto \color{blue}{t - \frac{t}{\frac{z}{y}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq -0.00105:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -215000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -4.8e+159)
     t
     (if (<= z -2.3e+60)
       t_2
       (if (<= z -215000000.0)
         t
         (if (<= z -2.6e-26)
           t_1
           (if (<= z 1.35e-78)
             t_2
             (if (<= z 7e-44)
               t_1
               (if (<= z 4.8e+112)
                 t_2
                 (if (<= z 1e+151) (/ x (/ z y)) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.8e+159) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= -215000000.0) {
		tmp = t;
	} else if (z <= -2.6e-26) {
		tmp = t_1;
	} else if (z <= 1.35e-78) {
		tmp = t_2;
	} else if (z <= 7e-44) {
		tmp = t_1;
	} else if (z <= 4.8e+112) {
		tmp = t_2;
	} else if (z <= 1e+151) {
		tmp = x / (z / y);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-4.8d+159)) then
        tmp = t
    else if (z <= (-2.3d+60)) then
        tmp = t_2
    else if (z <= (-215000000.0d0)) then
        tmp = t
    else if (z <= (-2.6d-26)) then
        tmp = t_1
    else if (z <= 1.35d-78) then
        tmp = t_2
    else if (z <= 7d-44) then
        tmp = t_1
    else if (z <= 4.8d+112) then
        tmp = t_2
    else if (z <= 1d+151) then
        tmp = x / (z / y)
    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 = t * ((y - z) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.8e+159) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= -215000000.0) {
		tmp = t;
	} else if (z <= -2.6e-26) {
		tmp = t_1;
	} else if (z <= 1.35e-78) {
		tmp = t_2;
	} else if (z <= 7e-44) {
		tmp = t_1;
	} else if (z <= 4.8e+112) {
		tmp = t_2;
	} else if (z <= 1e+151) {
		tmp = x / (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -4.8e+159:
		tmp = t
	elif z <= -2.3e+60:
		tmp = t_2
	elif z <= -215000000.0:
		tmp = t
	elif z <= -2.6e-26:
		tmp = t_1
	elif z <= 1.35e-78:
		tmp = t_2
	elif z <= 7e-44:
		tmp = t_1
	elif z <= 4.8e+112:
		tmp = t_2
	elif z <= 1e+151:
		tmp = x / (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -4.8e+159)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= -215000000.0)
		tmp = t;
	elseif (z <= -2.6e-26)
		tmp = t_1;
	elseif (z <= 1.35e-78)
		tmp = t_2;
	elseif (z <= 7e-44)
		tmp = t_1;
	elseif (z <= 4.8e+112)
		tmp = t_2;
	elseif (z <= 1e+151)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -4.8e+159)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= -215000000.0)
		tmp = t;
	elseif (z <= -2.6e-26)
		tmp = t_1;
	elseif (z <= 1.35e-78)
		tmp = t_2;
	elseif (z <= 7e-44)
		tmp = t_1;
	elseif (z <= 4.8e+112)
		tmp = t_2;
	elseif (z <= 1e+151)
		tmp = x / (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+159], t, If[LessEqual[z, -2.3e+60], t$95$2, If[LessEqual[z, -215000000.0], t, If[LessEqual[z, -2.6e-26], t$95$1, If[LessEqual[z, 1.35e-78], t$95$2, If[LessEqual[z, 7e-44], t$95$1, If[LessEqual[z, 4.8e+112], t$95$2, If[LessEqual[z, 1e+151], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e159 or -2.30000000000000017e60 < z < -2.15e8 or 1.00000000000000002e151 < z

   1. Initial program 51.0%

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

   3. Taylor expanded in z around inf 54.0%

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

   if -4.8e159 < z < -2.30000000000000017e60 or -2.6000000000000001e-26 < z < 1.34999999999999997e-78 or 6.9999999999999995e-44 < z < 4.8e112

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in x around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   8. Simplified 65.0%

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

   if -2.15e8 < z < -2.6000000000000001e-26 or 1.34999999999999997e-78 < z < 6.9999999999999995e-44

   1. Initial program 89.2%

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

      1. associate-*r/ 89.2%

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

      2. clear-num 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in a around inf 67.2%

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

   if 4.8e112 < z < 1.00000000000000002e151

   1. Initial program 51.8%

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

   3. Taylor expanded in a around 0 17.1%

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

      1. associate-*r/ 17.1%

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

      2. *-commutative 17.1%

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

      3. neg-mul-1 17.1%

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

      4. distribute-rgt-neg-in 17.1%

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

      5. associate-/l* 39.5%

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

   5. Simplified 39.5%

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

   6. Taylor expanded in x around inf 42.0%

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

      1. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -215000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.8e-27)
     t
     (if (<= z 6.4e-240)
       x
       (if (<= z 4.5e-207)
         t_1
         (if (<= z 4.8e-82)
           x
           (if (<= z 8.5e-31)
             t_1
             (if (<= z 8.4e+111) x (if (<= z 5.8e+147) (/ x (/ z y)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= 6.4e-240) {
		tmp = x;
	} else if (z <= 4.5e-207) {
		tmp = t_1;
	} else if (z <= 4.8e-82) {
		tmp = x;
	} else if (z <= 8.5e-31) {
		tmp = t_1;
	} else if (z <= 8.4e+111) {
		tmp = x;
	} else if (z <= 5.8e+147) {
		tmp = x / (z / y);
	} 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 = t * (y / a)
    if (z <= (-1.8d-27)) then
        tmp = t
    else if (z <= 6.4d-240) then
        tmp = x
    else if (z <= 4.5d-207) then
        tmp = t_1
    else if (z <= 4.8d-82) then
        tmp = x
    else if (z <= 8.5d-31) then
        tmp = t_1
    else if (z <= 8.4d+111) then
        tmp = x
    else if (z <= 5.8d+147) then
        tmp = x / (z / y)
    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 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= 6.4e-240) {
		tmp = x;
	} else if (z <= 4.5e-207) {
		tmp = t_1;
	} else if (z <= 4.8e-82) {
		tmp = x;
	} else if (z <= 8.5e-31) {
		tmp = t_1;
	} else if (z <= 8.4e+111) {
		tmp = x;
	} else if (z <= 5.8e+147) {
		tmp = x / (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.8e-27:
		tmp = t
	elif z <= 6.4e-240:
		tmp = x
	elif z <= 4.5e-207:
		tmp = t_1
	elif z <= 4.8e-82:
		tmp = x
	elif z <= 8.5e-31:
		tmp = t_1
	elif z <= 8.4e+111:
		tmp = x
	elif z <= 5.8e+147:
		tmp = x / (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 6.4e-240)
		tmp = x;
	elseif (z <= 4.5e-207)
		tmp = t_1;
	elseif (z <= 4.8e-82)
		tmp = x;
	elseif (z <= 8.5e-31)
		tmp = t_1;
	elseif (z <= 8.4e+111)
		tmp = x;
	elseif (z <= 5.8e+147)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 6.4e-240)
		tmp = x;
	elseif (z <= 4.5e-207)
		tmp = t_1;
	elseif (z <= 4.8e-82)
		tmp = x;
	elseif (z <= 8.5e-31)
		tmp = t_1;
	elseif (z <= 8.4e+111)
		tmp = x;
	elseif (z <= 5.8e+147)
		tmp = x / (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-27], t, If[LessEqual[z, 6.4e-240], x, If[LessEqual[z, 4.5e-207], t$95$1, If[LessEqual[z, 4.8e-82], x, If[LessEqual[z, 8.5e-31], t$95$1, If[LessEqual[z, 8.4e+111], x, If[LessEqual[z, 5.8e+147], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7999999999999999e-27 or 5.7999999999999997e147 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in z around inf 43.8%

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

   if -1.7999999999999999e-27 < z < 6.3999999999999998e-240 or 4.49999999999999992e-207 < z < 4.80000000000000017e-82 or 8.5000000000000007e-31 < z < 8.3999999999999998e111

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 44.2%

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

   if 6.3999999999999998e-240 < z < 4.49999999999999992e-207 or 4.80000000000000017e-82 < z < 8.5000000000000007e-31

   1. Initial program 82.8%

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

      1. associate-*r/ 94.2%

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

      2. clear-num 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in t around inf 71.0%

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

      1. div-sub 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in z around 0 60.7%

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

   if 8.3999999999999998e111 < z < 5.7999999999999997e147

   1. Initial program 51.8%

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

   3. Taylor expanded in a around 0 17.1%

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

      1. associate-*r/ 17.1%

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

      2. *-commutative 17.1%

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

      3. neg-mul-1 17.1%

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

      4. distribute-rgt-neg-in 17.1%

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

      5. associate-/l* 39.5%

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

   5. Simplified 39.5%

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

   6. Taylor expanded in x around inf 42.0%

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

      1. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.028:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.45e+82)
     t_1
     (if (<= z -4.1e+60)
       (* x (/ (- y a) z))
       (if (<= z -0.028)
         t_1
         (if (<= z 2.5e+103)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 6.5e+140)
             (* (/ y z) (- x t))
             (+ t (/ a (/ z (- t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.45e+82) {
		tmp = t_1;
	} else if (z <= -4.1e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.028) {
		tmp = t_1;
	} else if (z <= 2.5e+103) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 6.5e+140) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.45d+82)) then
        tmp = t_1
    else if (z <= (-4.1d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.028d0)) then
        tmp = t_1
    else if (z <= 2.5d+103) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 6.5d+140) then
        tmp = (y / z) * (x - t)
    else
        tmp = t + (a / (z / (t - x)))
    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) / (a - z));
	double tmp;
	if (z <= -1.45e+82) {
		tmp = t_1;
	} else if (z <= -4.1e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.028) {
		tmp = t_1;
	} else if (z <= 2.5e+103) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 6.5e+140) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.45e+82:
		tmp = t_1
	elif z <= -4.1e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.028:
		tmp = t_1
	elif z <= 2.5e+103:
		tmp = x + ((t - x) * (y / a))
	elif z <= 6.5e+140:
		tmp = (y / z) * (x - t)
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.45e+82)
		tmp = t_1;
	elseif (z <= -4.1e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.028)
		tmp = t_1;
	elseif (z <= 2.5e+103)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 6.5e+140)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.45e+82)
		tmp = t_1;
	elseif (z <= -4.1e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.028)
		tmp = t_1;
	elseif (z <= 2.5e+103)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 6.5e+140)
		tmp = (y / z) * (x - t);
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+82], t$95$1, If[LessEqual[z, -4.1e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.028], t$95$1, If[LessEqual[z, 2.5e+103], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+140], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.4500000000000001e82 or -4.1e60 < z < -0.0280000000000000006

   1. Initial program 64.1%

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

      1. associate-*r/ 45.2%

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

      2. clear-num 45.0%

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

   4. Applied egg-rr 45.0%

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

   5. Taylor expanded in t around inf 66.7%

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

      1. div-sub 66.7%

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

   7. Simplified 66.7%

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

   if -1.4500000000000001e82 < z < -4.1e60

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. distribute-lft-out-- 53.9%

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

      3. div-sub 53.9%

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

      4. mul-1-neg 53.9%

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

      5. unsub-neg 53.9%

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

      6. distribute-rgt-out-- 53.9%

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

      7. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. associate-*r/ 84.6%

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

   8. Simplified 84.6%

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

   if -0.0280000000000000006 < z < 2.5e103

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 75.7%

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

      1. associate-/l* 79.6%

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

      2. associate-/r/ 81.1%

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

   5. Simplified 81.1%

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

   if 2.5e103 < z < 6.4999999999999999e140

   1. Initial program 63.9%

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

   3. Taylor expanded in y around -inf 41.7%

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

   4. Taylor expanded in a around 0 41.8%

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

      1. mul-1-neg 41.8%

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

      2. associate-/l* 75.8%

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

      3. associate-/r/ 75.9%

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

      4. distribute-rgt-neg-in 75.9%

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

   6. Simplified 75.9%

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

   if 6.4999999999999999e140 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. distribute-lft-out-- 66.0%

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

      3. div-sub 66.1%

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

      4. mul-1-neg 66.1%

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

      5. unsub-neg 66.1%

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

      6. distribute-rgt-out-- 66.2%

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

      7. associate-/l* 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around 0 54.5%

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

      1. sub-neg 54.5%

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

      2. mul-1-neg 54.5%

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

      3. remove-double-neg 54.5%

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

      4. associate-/l* 66.9%

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

   8. Simplified 66.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.028:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.8e-27)
     t
     (if (<= z 5.3e-241)
       x
       (if (<= z 5.8e-208)
         t_1
         (if (<= z 5.1e-82)
           x
           (if (<= z 4.2e-30) t_1 (if (<= z 2.35e+111) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= 5.3e-241) {
		tmp = x;
	} else if (z <= 5.8e-208) {
		tmp = t_1;
	} else if (z <= 5.1e-82) {
		tmp = x;
	} else if (z <= 4.2e-30) {
		tmp = t_1;
	} else if (z <= 2.35e+111) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.8d-27)) then
        tmp = t
    else if (z <= 5.3d-241) then
        tmp = x
    else if (z <= 5.8d-208) then
        tmp = t_1
    else if (z <= 5.1d-82) then
        tmp = x
    else if (z <= 4.2d-30) then
        tmp = t_1
    else if (z <= 2.35d+111) 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 t_1 = t * (y / a);
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= 5.3e-241) {
		tmp = x;
	} else if (z <= 5.8e-208) {
		tmp = t_1;
	} else if (z <= 5.1e-82) {
		tmp = x;
	} else if (z <= 4.2e-30) {
		tmp = t_1;
	} else if (z <= 2.35e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.8e-27:
		tmp = t
	elif z <= 5.3e-241:
		tmp = x
	elif z <= 5.8e-208:
		tmp = t_1
	elif z <= 5.1e-82:
		tmp = x
	elif z <= 4.2e-30:
		tmp = t_1
	elif z <= 2.35e+111:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 5.3e-241)
		tmp = x;
	elseif (z <= 5.8e-208)
		tmp = t_1;
	elseif (z <= 5.1e-82)
		tmp = x;
	elseif (z <= 4.2e-30)
		tmp = t_1;
	elseif (z <= 2.35e+111)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 5.3e-241)
		tmp = x;
	elseif (z <= 5.8e-208)
		tmp = t_1;
	elseif (z <= 5.1e-82)
		tmp = x;
	elseif (z <= 4.2e-30)
		tmp = t_1;
	elseif (z <= 2.35e+111)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-27], t, If[LessEqual[z, 5.3e-241], x, If[LessEqual[z, 5.8e-208], t$95$1, If[LessEqual[z, 5.1e-82], x, If[LessEqual[z, 4.2e-30], t$95$1, If[LessEqual[z, 2.35e+111], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-27 or 2.35000000000000004e111 < z

   1. Initial program 58.2%

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

   3. Taylor expanded in z around inf 40.9%

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

   if -1.7999999999999999e-27 < z < 5.2999999999999998e-241 or 5.7999999999999999e-208 < z < 5.09999999999999992e-82 or 4.2000000000000004e-30 < z < 2.35000000000000004e111

   1. Initial program 94.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.2%

      \[\leadsto \color{blue}{x} \]

   if 5.2999999999999998e-241 < z < 5.7999999999999999e-208 or 5.09999999999999992e-82 < z < 4.2000000000000004e-30

   1. Initial program 82.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 94.2%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 94.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in t around inf 71.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 71.0%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   8. Taylor expanded in z around 0 60.7%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-162}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5e+224)
   (/ x (/ z y))
   (if (<= x -2.6e+63)
     x
     (if (<= x -1.4e-162)
       t
       (if (<= x 5.2e-69)
         (* t (/ (- y z) a))
         (if (<= x 8e+144) (* (/ x a) (- y)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e+224) {
		tmp = x / (z / y);
	} else if (x <= -2.6e+63) {
		tmp = x;
	} else if (x <= -1.4e-162) {
		tmp = t;
	} else if (x <= 5.2e-69) {
		tmp = t * ((y - z) / a);
	} else if (x <= 8e+144) {
		tmp = (x / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5d+224)) then
        tmp = x / (z / y)
    else if (x <= (-2.6d+63)) then
        tmp = x
    else if (x <= (-1.4d-162)) then
        tmp = t
    else if (x <= 5.2d-69) then
        tmp = t * ((y - z) / a)
    else if (x <= 8d+144) then
        tmp = (x / a) * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e+224) {
		tmp = x / (z / y);
	} else if (x <= -2.6e+63) {
		tmp = x;
	} else if (x <= -1.4e-162) {
		tmp = t;
	} else if (x <= 5.2e-69) {
		tmp = t * ((y - z) / a);
	} else if (x <= 8e+144) {
		tmp = (x / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5e+224:
		tmp = x / (z / y)
	elif x <= -2.6e+63:
		tmp = x
	elif x <= -1.4e-162:
		tmp = t
	elif x <= 5.2e-69:
		tmp = t * ((y - z) / a)
	elif x <= 8e+144:
		tmp = (x / a) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5e+224)
		tmp = Float64(x / Float64(z / y));
	elseif (x <= -2.6e+63)
		tmp = x;
	elseif (x <= -1.4e-162)
		tmp = t;
	elseif (x <= 5.2e-69)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (x <= 8e+144)
		tmp = Float64(Float64(x / a) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5e+224)
		tmp = x / (z / y);
	elseif (x <= -2.6e+63)
		tmp = x;
	elseif (x <= -1.4e-162)
		tmp = t;
	elseif (x <= 5.2e-69)
		tmp = t * ((y - z) / a);
	elseif (x <= 8e+144)
		tmp = (x / a) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5e+224], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e+63], x, If[LessEqual[x, -1.4e-162], t, If[LessEqual[x, 5.2e-69], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+144], N[(N[(x / a), $MachinePrecision] * (-y)), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.99999999999999964e224

   1. Initial program 64.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 34.6%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 34.6%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(\left(t - x\right) \cdot \left(y - z\right)\right)}{z}} \]

      2. *-commutative 34.6%

         \[\leadsto x + \frac{-1 \cdot \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right)}}{z} \]

      3. neg-mul-1 34.6%

         \[\leadsto x + \frac{\color{blue}{-\left(y - z\right) \cdot \left(t - x\right)}}{z} \]

      4. distribute-rgt-neg-in 34.6%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-\left(t - x\right)\right)}}{z} \]

      5. associate-/l* 43.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{z}{-\left(t - x\right)}}} \]

   5. Simplified 43.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{z}{-\left(t - x\right)}}} \]

   6. Taylor expanded in x around inf 42.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 58.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   if -4.99999999999999964e224 < x < -2.6000000000000001e63 or 8.00000000000000019e144 < x

   1. Initial program 76.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.6%

      \[\leadsto \color{blue}{x} \]

   if -2.6000000000000001e63 < x < -1.40000000000000011e-162

   1. Initial program 74.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 32.8%

      \[\leadsto \color{blue}{t} \]

   if -1.40000000000000011e-162 < x < 5.2000000000000004e-69

   1. Initial program 83.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 83.4%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 83.2%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 83.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in t around inf 77.5%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 77.6%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   7. Simplified 77.6%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   8. Taylor expanded in a around inf 49.2%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]

   if 5.2000000000000004e-69 < x < 8.00000000000000019e144

   1. Initial program 85.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 48.2%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   5. Simplified 54.7%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 48.1%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 48.1%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 54.6%

         \[\leadsto x - \color{blue}{\frac{x}{\frac{a}{y}}} \]

   8. Simplified 54.6%

      \[\leadsto \color{blue}{x - \frac{x}{\frac{a}{y}}} \]

   9. Taylor expanded in a around 0 29.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   10. Step-by-step derivation

       1. mul-1-neg 29.6%

          \[\leadsto \color{blue}{-\frac{x \cdot y}{a}} \]

       2. associate-*l/ 36.2%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot y} \]

       3. distribute-rgt-neg-out 36.2%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-y\right)} \]

   11. Simplified 36.2%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-162}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-158}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.7e+224)
   (/ x (/ z y))
   (if (<= x -1.15e+67)
     x
     (if (<= x -2.3e-158) t (if (<= x 6e+18) (* t (/ y (- a z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+224) {
		tmp = x / (z / y);
	} else if (x <= -1.15e+67) {
		tmp = x;
	} else if (x <= -2.3e-158) {
		tmp = t;
	} else if (x <= 6e+18) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.7d+224)) then
        tmp = x / (z / y)
    else if (x <= (-1.15d+67)) then
        tmp = x
    else if (x <= (-2.3d-158)) then
        tmp = t
    else if (x <= 6d+18) then
        tmp = t * (y / (a - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+224) {
		tmp = x / (z / y);
	} else if (x <= -1.15e+67) {
		tmp = x;
	} else if (x <= -2.3e-158) {
		tmp = t;
	} else if (x <= 6e+18) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.7e+224:
		tmp = x / (z / y)
	elif x <= -1.15e+67:
		tmp = x
	elif x <= -2.3e-158:
		tmp = t
	elif x <= 6e+18:
		tmp = t * (y / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.7e+224)
		tmp = Float64(x / Float64(z / y));
	elseif (x <= -1.15e+67)
		tmp = x;
	elseif (x <= -2.3e-158)
		tmp = t;
	elseif (x <= 6e+18)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.7e+224)
		tmp = x / (z / y);
	elseif (x <= -1.15e+67)
		tmp = x;
	elseif (x <= -2.3e-158)
		tmp = t;
	elseif (x <= 6e+18)
		tmp = t * (y / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.7e+224], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e+67], x, If[LessEqual[x, -2.3e-158], t, If[LessEqual[x, 6e+18], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6999999999999999e224

   1. Initial program 64.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 34.6%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 34.6%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(\left(t - x\right) \cdot \left(y - z\right)\right)}{z}} \]

      2. *-commutative 34.6%

         \[\leadsto x + \frac{-1 \cdot \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right)}}{z} \]

      3. neg-mul-1 34.6%

         \[\leadsto x + \frac{\color{blue}{-\left(y - z\right) \cdot \left(t - x\right)}}{z} \]

      4. distribute-rgt-neg-in 34.6%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-\left(t - x\right)\right)}}{z} \]

      5. associate-/l* 43.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{z}{-\left(t - x\right)}}} \]

   5. Simplified 43.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{z}{-\left(t - x\right)}}} \]

   6. Taylor expanded in x around inf 42.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 58.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   if -2.6999999999999999e224 < x < -1.1499999999999999e67 or 6e18 < x

   1. Initial program 78.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{x} \]

   if -1.1499999999999999e67 < x < -2.2999999999999999e-158

   1. Initial program 74.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 32.8%

      \[\leadsto \color{blue}{t} \]

   if -2.2999999999999999e-158 < x < 6e18

   1. Initial program 84.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 84.6%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 84.4%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 84.4%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in t around inf 73.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   8. Taylor expanded in y around inf 42.3%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-158}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+79} \lor \neg \left(x \leq 2.5 \cdot 10^{+51}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+222)
   (* x (/ (- y a) z))
   (if (or (<= x -1.5e+79) (not (<= x 2.5e+51)))
     (- x (/ x (/ a y)))
     (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+222) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -1.5e+79) || !(x <= 2.5e+51)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t * ((y - z) / (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 <= (-6.8d+222)) then
        tmp = x * ((y - a) / z)
    else if ((x <= (-1.5d+79)) .or. (.not. (x <= 2.5d+51))) then
        tmp = x - (x / (a / y))
    else
        tmp = t * ((y - z) / (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 <= -6.8e+222) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -1.5e+79) || !(x <= 2.5e+51)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+222:
		tmp = x * ((y - a) / z)
	elif (x <= -1.5e+79) or not (x <= 2.5e+51):
		tmp = x - (x / (a / y))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+222)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif ((x <= -1.5e+79) || !(x <= 2.5e+51))
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+222)
		tmp = x * ((y - a) / z);
	elseif ((x <= -1.5e+79) || ~((x <= 2.5e+51)))
		tmp = x - (x / (a / y));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+222], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.5e+79], N[Not[LessEqual[x, 2.5e+51]], $MachinePrecision]], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.80000000000000032e222

   1. Initial program 64.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 42.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 42.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 42.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 50.0%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 50.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 50.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 50.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 76.7%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 76.7%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 70.2%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -6.80000000000000032e222 < x < -1.49999999999999987e79 or 2.5e51 < x

   1. Initial program 77.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 58.8%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   6. Taylor expanded in t around 0 56.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 56.5%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 61.9%

         \[\leadsto x - \color{blue}{\frac{x}{\frac{a}{y}}} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{x - \frac{x}{\frac{a}{y}}} \]

   if -1.49999999999999987e79 < x < 2.5e51

   1. Initial program 81.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 76.3%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 76.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 76.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in t around inf 65.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 65.2%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   7. Simplified 65.2%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+79} \lor \neg \left(x \leq 2.5 \cdot 10^{+51}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 1.65 \cdot 10^{+112}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -145000000.0) (not (<= z 1.65e+112)))
   (+ t (* y (/ (- x t) z)))
   (- x (/ (- x t) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -145000000.0) || !(z <= 1.65e+112)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - ((x - t) / (a / (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 <= (-145000000.0d0)) .or. (.not. (z <= 1.65d+112))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x - ((x - t) / (a / (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 <= -145000000.0) || !(z <= 1.65e+112)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - ((x - t) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -145000000.0) or not (z <= 1.65e+112):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x - ((x - t) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -145000000.0) || !(z <= 1.65e+112))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -145000000.0) || ~((z <= 1.65e+112)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x - ((x - t) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -145000000.0], N[Not[LessEqual[z, 1.65e+112]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e8 or 1.64999999999999995e112 < z

   1. Initial program 54.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 64.2%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 64.2%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 64.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 64.2%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 64.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 85.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 85.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 60.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 75.6%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   if -1.45e8 < z < 1.64999999999999995e112

   1. Initial program 93.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 77.1%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 84.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 1.65 \cdot 10^{+112}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+111}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -140000000.0) (not (<= z 3.1e+111)))
   (+ t (/ (- x t) (/ z (- y a))))
   (- x (/ (- x t) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -140000000.0) || !(z <= 3.1e+111)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((x - t) / (a / (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 <= (-140000000.0d0)) .or. (.not. (z <= 3.1d+111))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x - ((x - t) / (a / (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 <= -140000000.0) || !(z <= 3.1e+111)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((x - t) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -140000000.0) or not (z <= 3.1e+111):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x - ((x - t) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -140000000.0) || !(z <= 3.1e+111))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -140000000.0) || ~((z <= 3.1e+111)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x - ((x - t) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -140000000.0], N[Not[LessEqual[z, 3.1e+111]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e8 or 3.1e111 < z

   1. Initial program 54.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 64.2%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 64.2%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 64.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 64.2%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 64.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 85.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 85.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if -1.4e8 < z < 3.1e111

   1. Initial program 93.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 77.1%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 84.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+111}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+111}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -145000000.0) (not (<= z 3.1e+111)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -145000000.0) || !(z <= 3.1e+111)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-145000000.0d0)) .or. (.not. (z <= 3.1d+111))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -145000000.0) || !(z <= 3.1e+111)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -145000000.0) or not (z <= 3.1e+111):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -145000000.0) || !(z <= 3.1e+111))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -145000000.0) || ~((z <= 3.1e+111)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -145000000.0], N[Not[LessEqual[z, 3.1e+111]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e8 or 3.1e111 < z

   1. Initial program 54.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 64.2%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 64.2%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 64.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 64.2%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 64.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 85.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 85.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 60.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   8. Simplified 75.6%

      \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   if -1.45e8 < z < 3.1e111

   1. Initial program 93.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 79.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 79.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+111}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-27) t (if (<= z 1.72e+112) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-27) {
		tmp = t;
	} else if (z <= 1.72e+112) {
		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 <= (-1.8d-27)) then
        tmp = t
    else if (z <= 1.72d+112) 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 <= -1.8e-27) {
		tmp = t;
	} else if (z <= 1.72e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e-27:
		tmp = t
	elif z <= 1.72e+112:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 1.72e+112)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e-27)
		tmp = t;
	elseif (z <= 1.72e+112)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-27], t, If[LessEqual[z, 1.72e+112], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e-27 or 1.71999999999999997e112 < z

   1. Initial program 58.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 40.9%

      \[\leadsto \color{blue}{t} \]

   if -1.7999999999999999e-27 < z < 1.71999999999999997e112

   1. Initial program 93.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.8% 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 78.2%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 21.4%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 21.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))