Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.9% → 91.0%

Time: 24.9s

Alternatives: 23

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: 80.9% 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: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-295} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -1e-295) (not (<= t_1 0.0)))
     (+ x (/ (- z y) (/ (- a z) (- x t))))
     (+ t (* (- t x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0)) {
		tmp = x + ((z - y) / ((a - z) / (x - t)));
	} else {
		tmp = t + ((t - x) * ((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) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((t - x) / (z - a)))
    if ((t_1 <= (-1d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((z - y) / ((a - z) / (x - t)))
    else
        tmp = t + ((t - x) * ((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 t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0)) {
		tmp = x + ((z - y) / ((a - z) / (x - t)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -1e-295) or not (t_1 <= 0.0):
		tmp = x + ((z - y) / ((a - z) / (x - t)))
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(a - z) / Float64(x - t))));
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -1e-295) || ~((t_1 <= 0.0)))
		tmp = x + ((z - y) / ((a - z) / (x - t)));
	else
		tmp = t + ((t - x) * ((a - y) / z));
	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[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $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)))) < -1.00000000000000006e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.8%

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

   4. Applied egg-rr 91.8%

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

   if -1.00000000000000006e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. distribute-lft-out-- 85.7%

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

      3. div-sub 85.6%

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

      4. mul-1-neg 85.6%

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

      5. unsub-neg 85.6%

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

      6. distribute-rgt-out-- 85.6%

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

      7. associate-/l* 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -1 \cdot 10^{-295} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{t - x}{a}\\ t_3 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+183}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a))))
        (t_2 (* y (/ (- t x) a)))
        (t_3 (* x (/ (- y a) z))))
   (if (<= z -7.8e+161)
     t
     (if (<= z -1.8e+47)
       t_3
       (if (<= z -1e-108)
         t_1
         (if (<= z -4.6e-160)
           t_2
           (if (<= z 7.5e-205)
             (+ x (/ (* y t) a))
             (if (<= z 2.9e-138)
               t_2
               (if (<= z 1.4e+16)
                 t_1
                 (if (<= z 3.7e+67)
                   (* t (/ y (- a z)))
                   (if (<= z 1.4e+114)
                     (+ x t)
                     (if (<= z 2.9e+183) t_3 t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = y * ((t - x) / a);
	double t_3 = x * ((y - a) / z);
	double tmp;
	if (z <= -7.8e+161) {
		tmp = t;
	} else if (z <= -1.8e+47) {
		tmp = t_3;
	} else if (z <= -1e-108) {
		tmp = t_1;
	} else if (z <= -4.6e-160) {
		tmp = t_2;
	} else if (z <= 7.5e-205) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.9e-138) {
		tmp = t_2;
	} else if (z <= 1.4e+16) {
		tmp = t_1;
	} else if (z <= 3.7e+67) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.4e+114) {
		tmp = x + t;
	} else if (z <= 2.9e+183) {
		tmp = t_3;
	} 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 = x + (t * (y / a))
    t_2 = y * ((t - x) / a)
    t_3 = x * ((y - a) / z)
    if (z <= (-7.8d+161)) then
        tmp = t
    else if (z <= (-1.8d+47)) then
        tmp = t_3
    else if (z <= (-1d-108)) then
        tmp = t_1
    else if (z <= (-4.6d-160)) then
        tmp = t_2
    else if (z <= 7.5d-205) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.9d-138) then
        tmp = t_2
    else if (z <= 1.4d+16) then
        tmp = t_1
    else if (z <= 3.7d+67) then
        tmp = t * (y / (a - z))
    else if (z <= 1.4d+114) then
        tmp = x + t
    else if (z <= 2.9d+183) then
        tmp = t_3
    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 + (t * (y / a));
	double t_2 = y * ((t - x) / a);
	double t_3 = x * ((y - a) / z);
	double tmp;
	if (z <= -7.8e+161) {
		tmp = t;
	} else if (z <= -1.8e+47) {
		tmp = t_3;
	} else if (z <= -1e-108) {
		tmp = t_1;
	} else if (z <= -4.6e-160) {
		tmp = t_2;
	} else if (z <= 7.5e-205) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.9e-138) {
		tmp = t_2;
	} else if (z <= 1.4e+16) {
		tmp = t_1;
	} else if (z <= 3.7e+67) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.4e+114) {
		tmp = x + t;
	} else if (z <= 2.9e+183) {
		tmp = t_3;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = y * ((t - x) / a)
	t_3 = x * ((y - a) / z)
	tmp = 0
	if z <= -7.8e+161:
		tmp = t
	elif z <= -1.8e+47:
		tmp = t_3
	elif z <= -1e-108:
		tmp = t_1
	elif z <= -4.6e-160:
		tmp = t_2
	elif z <= 7.5e-205:
		tmp = x + ((y * t) / a)
	elif z <= 2.9e-138:
		tmp = t_2
	elif z <= 1.4e+16:
		tmp = t_1
	elif z <= 3.7e+67:
		tmp = t * (y / (a - z))
	elif z <= 1.4e+114:
		tmp = x + t
	elif z <= 2.9e+183:
		tmp = t_3
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	t_3 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -7.8e+161)
		tmp = t;
	elseif (z <= -1.8e+47)
		tmp = t_3;
	elseif (z <= -1e-108)
		tmp = t_1;
	elseif (z <= -4.6e-160)
		tmp = t_2;
	elseif (z <= 7.5e-205)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.9e-138)
		tmp = t_2;
	elseif (z <= 1.4e+16)
		tmp = t_1;
	elseif (z <= 3.7e+67)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.4e+114)
		tmp = Float64(x + t);
	elseif (z <= 2.9e+183)
		tmp = t_3;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = y * ((t - x) / a);
	t_3 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -7.8e+161)
		tmp = t;
	elseif (z <= -1.8e+47)
		tmp = t_3;
	elseif (z <= -1e-108)
		tmp = t_1;
	elseif (z <= -4.6e-160)
		tmp = t_2;
	elseif (z <= 7.5e-205)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.9e-138)
		tmp = t_2;
	elseif (z <= 1.4e+16)
		tmp = t_1;
	elseif (z <= 3.7e+67)
		tmp = t * (y / (a - z));
	elseif (z <= 1.4e+114)
		tmp = x + t;
	elseif (z <= 2.9e+183)
		tmp = t_3;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+161], t, If[LessEqual[z, -1.8e+47], t$95$3, If[LessEqual[z, -1e-108], t$95$1, If[LessEqual[z, -4.6e-160], t$95$2, If[LessEqual[z, 7.5e-205], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-138], t$95$2, If[LessEqual[z, 1.4e+16], t$95$1, If[LessEqual[z, 3.7e+67], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+114], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.9e+183], t$95$3, t]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -7.8000000000000004e161 or 2.9000000000000001e183 < z

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 55.7%

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

   if -7.8000000000000004e161 < z < -1.80000000000000004e47 or 1.4e114 < z < 2.9000000000000001e183

   1. Initial program 65.2%

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

   3. Taylor expanded in x around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. unsub-neg 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in z around inf 42.6%

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

      1. mul-1-neg 42.6%

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

      2. neg-mul-1 42.6%

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

      3. sub-neg 42.6%

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

   8. Simplified 42.6%

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

   9. Taylor expanded in x around 0 42.6%

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

       1. div-sub 42.6%

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

       2. associate-/l* 35.0%

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

   11. Simplified 35.0%

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

       1. add0 35.0%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 42.6%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 42.6%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 42.6%

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

   15. Simplified 42.6%

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

   if -1.80000000000000004e47 < z < -1.00000000000000004e-108 or 2.89999999999999973e-138 < z < 1.4e16

   1. Initial program 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in t around inf 78.2%

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

   6. Taylor expanded in z around 0 52.6%

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

      1. +-commutative 52.6%

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

      2. associate-/l* 54.5%

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

   8. Simplified 54.5%

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

   if -1.00000000000000004e-108 < z < -4.5999999999999997e-160 or 7.4999999999999996e-205 < z < 2.89999999999999973e-138

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 77.6%

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

   4. Taylor expanded in a around inf 70.4%

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

      1. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   if -4.5999999999999997e-160 < z < 7.4999999999999996e-205

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in t around inf 71.3%

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

   if 1.4e16 < z < 3.6999999999999997e67

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 67.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around inf 34.3%

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

      1. associate-/l* 39.9%

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

   8. Simplified 39.9%

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

   if 3.6999999999999997e67 < z < 1.4e114

   1. Initial program 83.7%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in t around inf 81.0%

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

   6. Taylor expanded in z around inf 81.0%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-108}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (* y (/ (- t x) a))))
   (if (<= z -5.2e+161)
     t
     (if (<= z -6.5e+47)
       (* x (/ (- y a) z))
       (if (<= z -1.12e-108)
         t_1
         (if (<= z -6.5e-160)
           t_2
           (if (<= z 3.05e-204)
             t_1
             (if (<= z 1.15e-136)
               t_2
               (if (<= z 2.3e+16)
                 t_1
                 (if (<= z 3.2e+67)
                   (* t (/ y (- a z)))
                   (if (<= z 1.15e+114) (+ x t) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -5.2e+161) {
		tmp = t;
	} else if (z <= -6.5e+47) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.12e-108) {
		tmp = t_1;
	} else if (z <= -6.5e-160) {
		tmp = t_2;
	} else if (z <= 3.05e-204) {
		tmp = t_1;
	} else if (z <= 1.15e-136) {
		tmp = t_2;
	} else if (z <= 2.3e+16) {
		tmp = t_1;
	} else if (z <= 3.2e+67) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.15e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = y * ((t - x) / a)
    if (z <= (-5.2d+161)) then
        tmp = t
    else if (z <= (-6.5d+47)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.12d-108)) then
        tmp = t_1
    else if (z <= (-6.5d-160)) then
        tmp = t_2
    else if (z <= 3.05d-204) then
        tmp = t_1
    else if (z <= 1.15d-136) then
        tmp = t_2
    else if (z <= 2.3d+16) then
        tmp = t_1
    else if (z <= 3.2d+67) then
        tmp = t * (y / (a - z))
    else if (z <= 1.15d+114) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -5.2e+161) {
		tmp = t;
	} else if (z <= -6.5e+47) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.12e-108) {
		tmp = t_1;
	} else if (z <= -6.5e-160) {
		tmp = t_2;
	} else if (z <= 3.05e-204) {
		tmp = t_1;
	} else if (z <= 1.15e-136) {
		tmp = t_2;
	} else if (z <= 2.3e+16) {
		tmp = t_1;
	} else if (z <= 3.2e+67) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.15e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = y * ((t - x) / a)
	tmp = 0
	if z <= -5.2e+161:
		tmp = t
	elif z <= -6.5e+47:
		tmp = x * ((y - a) / z)
	elif z <= -1.12e-108:
		tmp = t_1
	elif z <= -6.5e-160:
		tmp = t_2
	elif z <= 3.05e-204:
		tmp = t_1
	elif z <= 1.15e-136:
		tmp = t_2
	elif z <= 2.3e+16:
		tmp = t_1
	elif z <= 3.2e+67:
		tmp = t * (y / (a - z))
	elif z <= 1.15e+114:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -5.2e+161)
		tmp = t;
	elseif (z <= -6.5e+47)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.12e-108)
		tmp = t_1;
	elseif (z <= -6.5e-160)
		tmp = t_2;
	elseif (z <= 3.05e-204)
		tmp = t_1;
	elseif (z <= 1.15e-136)
		tmp = t_2;
	elseif (z <= 2.3e+16)
		tmp = t_1;
	elseif (z <= 3.2e+67)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.15e+114)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -5.2e+161)
		tmp = t;
	elseif (z <= -6.5e+47)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.12e-108)
		tmp = t_1;
	elseif (z <= -6.5e-160)
		tmp = t_2;
	elseif (z <= 3.05e-204)
		tmp = t_1;
	elseif (z <= 1.15e-136)
		tmp = t_2;
	elseif (z <= 2.3e+16)
		tmp = t_1;
	elseif (z <= 3.2e+67)
		tmp = t * (y / (a - z));
	elseif (z <= 1.15e+114)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+161], t, If[LessEqual[z, -6.5e+47], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-108], t$95$1, If[LessEqual[z, -6.5e-160], t$95$2, If[LessEqual[z, 3.05e-204], t$95$1, If[LessEqual[z, 1.15e-136], t$95$2, If[LessEqual[z, 2.3e+16], t$95$1, If[LessEqual[z, 3.2e+67], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+114], N[(x + t), $MachinePrecision], t]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.1999999999999996e161 or 1.15e114 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 50.3%

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

   if -5.1999999999999996e161 < z < -6.49999999999999988e47

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in z around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. neg-mul-1 44.4%

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

      3. sub-neg 44.4%

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

   8. Simplified 44.4%

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

   9. Taylor expanded in x around 0 44.4%

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

       1. div-sub 44.4%

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

       2. associate-/l* 34.8%

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

   11. Simplified 34.8%

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

       1. add0 34.8%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 44.4%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 44.4%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 44.4%

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

   15. Simplified 44.4%

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

   if -6.49999999999999988e47 < z < -1.11999999999999992e-108 or -6.4999999999999996e-160 < z < 3.04999999999999987e-204 or 1.14999999999999999e-136 < z < 2.3e16

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 71.4%

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

   4. Taylor expanded in t around inf 62.2%

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

   if -1.11999999999999992e-108 < z < -6.4999999999999996e-160 or 3.04999999999999987e-204 < z < 1.14999999999999999e-136

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 77.6%

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

   4. Taylor expanded in a around inf 70.4%

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

      1. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   if 2.3e16 < z < 3.19999999999999983e67

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 67.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around inf 34.3%

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

      1. associate-/l* 39.9%

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

   8. Simplified 39.9%

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

   if 3.19999999999999983e67 < z < 1.15e114

   1. Initial program 83.7%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in t around inf 81.0%

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

   6. Taylor expanded in z around inf 81.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-204}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-295} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -1e-295) (not (<= t_1 0.0)))
     t_1
     (+ t (* (- t x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((t - x) * ((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) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((t - x) / (z - a)))
    if ((t_1 <= (-1d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((t - x) * ((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 t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -1e-295) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -1e-295) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -1e-295) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((t - x) * ((a - y) / z));
	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[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $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)))) < -1.00000000000000006e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

   if -1.00000000000000006e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. distribute-lft-out-- 85.7%

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

      3. div-sub 85.6%

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

      4. mul-1-neg 85.6%

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

      5. unsub-neg 85.6%

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

      6. distribute-rgt-out-- 85.6%

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

      7. associate-/l* 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -1 \cdot 10^{-295} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -700:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -700.0)
     t_2
     (if (<= t -1.9e-125)
       t_1
       (if (<= t -1.22e-174)
         t_2
         (if (<= t -1.25e-254)
           (/ (* x y) (- z a))
           (if (<= t 9.2e-302)
             (* x (/ (- y a) z))
             (if (<= t 1.35e-81) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -700.0) {
		tmp = t_2;
	} else if (t <= -1.9e-125) {
		tmp = t_1;
	} else if (t <= -1.22e-174) {
		tmp = t_2;
	} else if (t <= -1.25e-254) {
		tmp = (x * y) / (z - a);
	} else if (t <= 9.2e-302) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.35e-81) {
		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 - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-700.0d0)) then
        tmp = t_2
    else if (t <= (-1.9d-125)) then
        tmp = t_1
    else if (t <= (-1.22d-174)) then
        tmp = t_2
    else if (t <= (-1.25d-254)) then
        tmp = (x * y) / (z - a)
    else if (t <= 9.2d-302) then
        tmp = x * ((y - a) / z)
    else if (t <= 1.35d-81) 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 - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -700.0) {
		tmp = t_2;
	} else if (t <= -1.9e-125) {
		tmp = t_1;
	} else if (t <= -1.22e-174) {
		tmp = t_2;
	} else if (t <= -1.25e-254) {
		tmp = (x * y) / (z - a);
	} else if (t <= 9.2e-302) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.35e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -700.0:
		tmp = t_2
	elif t <= -1.9e-125:
		tmp = t_1
	elif t <= -1.22e-174:
		tmp = t_2
	elif t <= -1.25e-254:
		tmp = (x * y) / (z - a)
	elif t <= 9.2e-302:
		tmp = x * ((y - a) / z)
	elif t <= 1.35e-81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -700.0)
		tmp = t_2;
	elseif (t <= -1.9e-125)
		tmp = t_1;
	elseif (t <= -1.22e-174)
		tmp = t_2;
	elseif (t <= -1.25e-254)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (t <= 9.2e-302)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 1.35e-81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -700.0)
		tmp = t_2;
	elseif (t <= -1.9e-125)
		tmp = t_1;
	elseif (t <= -1.22e-174)
		tmp = t_2;
	elseif (t <= -1.25e-254)
		tmp = (x * y) / (z - a);
	elseif (t <= 9.2e-302)
		tmp = x * ((y - a) / z);
	elseif (t <= 1.35e-81)
		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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -700.0], t$95$2, If[LessEqual[t, -1.9e-125], t$95$1, If[LessEqual[t, -1.22e-174], t$95$2, If[LessEqual[t, -1.25e-254], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-302], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-81], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -700 or -1.9000000000000001e-125 < t < -1.2200000000000001e-174 or 1.34999999999999995e-81 < t

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 56.0%

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

      1. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if -700 < t < -1.9000000000000001e-125 or 9.20000000000000007e-302 < t < 1.34999999999999995e-81

   1. Initial program 78.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. Taylor expanded in t around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. unsub-neg 59.1%

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

      3. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

   if -1.2200000000000001e-174 < t < -1.2500000000000001e-254

   1. Initial program 55.6%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. distribute-lft-neg-out 84.7%

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

      4. *-commutative 84.7%

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

   8. Simplified 84.7%

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

   if -1.2500000000000001e-254 < t < 9.20000000000000007e-302

   1. Initial program 50.9%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in z around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. neg-mul-1 74.9%

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

      3. sub-neg 74.9%

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

   8. Simplified 74.9%

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

   9. Taylor expanded in x around 0 74.9%

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

       1. div-sub 74.9%

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

       2. associate-/l* 59.2%

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

   11. Simplified 59.2%

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

       1. add0 59.2%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 74.9%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 74.9%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 74.9%

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

   15. Simplified 74.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -700:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-125}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-81}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+161)
   t
   (if (<= z -1.56e+47)
     (* x (/ (- y a) z))
     (if (<= z 8.5e-188)
       (+ x (/ (* y t) a))
       (if (<= z 3.5e-26)
         (- x (* x (/ y a)))
         (if (<= z 3.3e+67)
           (* t (/ (- y z) a))
           (if (<= z 1.06e+114) (+ x t) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+161) {
		tmp = t;
	} else if (z <= -1.56e+47) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.5e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.5e-26) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.3e+67) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.06e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.4d+161)) then
        tmp = t
    else if (z <= (-1.56d+47)) then
        tmp = x * ((y - a) / z)
    else if (z <= 8.5d-188) then
        tmp = x + ((y * t) / a)
    else if (z <= 3.5d-26) then
        tmp = x - (x * (y / a))
    else if (z <= 3.3d+67) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.06d+114) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+161) {
		tmp = t;
	} else if (z <= -1.56e+47) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.5e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.5e-26) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.3e+67) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.06e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+161:
		tmp = t
	elif z <= -1.56e+47:
		tmp = x * ((y - a) / z)
	elif z <= 8.5e-188:
		tmp = x + ((y * t) / a)
	elif z <= 3.5e-26:
		tmp = x - (x * (y / a))
	elif z <= 3.3e+67:
		tmp = t * ((y - z) / a)
	elif z <= 1.06e+114:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+161)
		tmp = t;
	elseif (z <= -1.56e+47)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 8.5e-188)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 3.5e-26)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 3.3e+67)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.06e+114)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+161)
		tmp = t;
	elseif (z <= -1.56e+47)
		tmp = x * ((y - a) / z);
	elseif (z <= 8.5e-188)
		tmp = x + ((y * t) / a);
	elseif (z <= 3.5e-26)
		tmp = x - (x * (y / a));
	elseif (z <= 3.3e+67)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.06e+114)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+161], t, If[LessEqual[z, -1.56e+47], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-188], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-26], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+67], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+114], N[(x + t), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.4e161 or 1.05999999999999993e114 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 50.3%

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

   if -4.4e161 < z < -1.55999999999999998e47

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in z around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. neg-mul-1 44.4%

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

      3. sub-neg 44.4%

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

   8. Simplified 44.4%

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

   9. Taylor expanded in x around 0 44.4%

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

       1. div-sub 44.4%

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

       2. associate-/l* 34.8%

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

   11. Simplified 34.8%

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

       1. add0 34.8%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 44.4%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 44.4%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 44.4%

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

   15. Simplified 44.4%

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

   if -1.55999999999999998e47 < z < 8.5000000000000004e-188

   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 74.7%

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

   4. Taylor expanded in t around inf 61.1%

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

   if 8.5000000000000004e-188 < z < 3.49999999999999985e-26

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 79.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

   if 3.49999999999999985e-26 < z < 3.3000000000000003e67

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 62.8%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in a around inf 35.9%

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

   if 3.3000000000000003e67 < z < 1.05999999999999993e114

   1. Initial program 83.7%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in t around inf 81.0%

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

   6. Taylor expanded in z around inf 81.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+159)
   t
   (if (<= z -2.6e+44)
     (* x (/ (- y a) z))
     (if (<= z 8.8e-188)
       (+ x (/ (* y t) a))
       (if (<= z 3.7e-26)
         (- x (* x (/ y a)))
         (if (<= z 3.2e+67)
           (/ t (/ a (- y z)))
           (if (<= z 1.02e+114) (+ x t) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+159) {
		tmp = t;
	} else if (z <= -2.6e+44) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.8e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.7e-26) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.2e+67) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.02e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+159)) then
        tmp = t
    else if (z <= (-2.6d+44)) then
        tmp = x * ((y - a) / z)
    else if (z <= 8.8d-188) then
        tmp = x + ((y * t) / a)
    else if (z <= 3.7d-26) then
        tmp = x - (x * (y / a))
    else if (z <= 3.2d+67) then
        tmp = t / (a / (y - z))
    else if (z <= 1.02d+114) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+159) {
		tmp = t;
	} else if (z <= -2.6e+44) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.8e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.7e-26) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.2e+67) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.02e+114) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+159:
		tmp = t
	elif z <= -2.6e+44:
		tmp = x * ((y - a) / z)
	elif z <= 8.8e-188:
		tmp = x + ((y * t) / a)
	elif z <= 3.7e-26:
		tmp = x - (x * (y / a))
	elif z <= 3.2e+67:
		tmp = t / (a / (y - z))
	elif z <= 1.02e+114:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+159)
		tmp = t;
	elseif (z <= -2.6e+44)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 8.8e-188)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 3.7e-26)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 3.2e+67)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 1.02e+114)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+159)
		tmp = t;
	elseif (z <= -2.6e+44)
		tmp = x * ((y - a) / z);
	elseif (z <= 8.8e-188)
		tmp = x + ((y * t) / a);
	elseif (z <= 3.7e-26)
		tmp = x - (x * (y / a));
	elseif (z <= 3.2e+67)
		tmp = t / (a / (y - z));
	elseif (z <= 1.02e+114)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+159], t, If[LessEqual[z, -2.6e+44], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-188], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-26], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+67], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+114], N[(x + t), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.2e159 or 1.01999999999999999e114 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 50.3%

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

   if -1.2e159 < z < -2.5999999999999999e44

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 33.7%

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

      1. mul-1-neg 33.7%

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

      2. unsub-neg 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in z around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. neg-mul-1 44.4%

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

      3. sub-neg 44.4%

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

   8. Simplified 44.4%

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

   9. Taylor expanded in x around 0 44.4%

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

       1. div-sub 44.4%

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

       2. associate-/l* 34.8%

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

   11. Simplified 34.8%

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

       1. add0 34.8%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 44.4%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 44.4%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 44.4%

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

   15. Simplified 44.4%

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

   if -2.5999999999999999e44 < z < 8.7999999999999998e-188

   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 74.7%

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

   4. Taylor expanded in t around inf 61.1%

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

   if 8.7999999999999998e-188 < z < 3.6999999999999999e-26

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 79.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

   if 3.6999999999999999e-26 < z < 3.19999999999999983e67

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 62.8%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in a around inf 35.9%

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

      1. clear-num 35.9%

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

      2. un-div-inv 36.0%

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

   8. Applied egg-rr 36.0%

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

   if 3.19999999999999983e67 < z < 1.01999999999999999e114

   1. Initial program 83.7%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in t around inf 81.0%

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

   6. Taylor expanded in z around inf 81.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+114}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 10^{-187}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))))
   (if (<= z -2e+150)
     t_1
     (if (<= z -1.85e+57)
       (* x (/ (- y a) z))
       (if (<= z -1.9e-26)
         (+ x t)
         (if (<= z 1e-187)
           (+ x (/ (* y t) a))
           (if (<= z 2.9e-26) (- x (* x (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -2e+150) {
		tmp = t_1;
	} else if (z <= -1.85e+57) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.9e-26) {
		tmp = x + t;
	} else if (z <= 1e-187) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.9e-26) {
		tmp = x - (x * (y / a));
	} 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 * (z / (z - a))
    if (z <= (-2d+150)) then
        tmp = t_1
    else if (z <= (-1.85d+57)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.9d-26)) then
        tmp = x + t
    else if (z <= 1d-187) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.9d-26) then
        tmp = x - (x * (y / a))
    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 * (z / (z - a));
	double tmp;
	if (z <= -2e+150) {
		tmp = t_1;
	} else if (z <= -1.85e+57) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.9e-26) {
		tmp = x + t;
	} else if (z <= 1e-187) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.9e-26) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -2e+150:
		tmp = t_1
	elif z <= -1.85e+57:
		tmp = x * ((y - a) / z)
	elif z <= -1.9e-26:
		tmp = x + t
	elif z <= 1e-187:
		tmp = x + ((y * t) / a)
	elif z <= 2.9e-26:
		tmp = x - (x * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -2e+150)
		tmp = t_1;
	elseif (z <= -1.85e+57)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.9e-26)
		tmp = Float64(x + t);
	elseif (z <= 1e-187)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.9e-26)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -2e+150)
		tmp = t_1;
	elseif (z <= -1.85e+57)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.9e-26)
		tmp = x + t;
	elseif (z <= 1e-187)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.9e-26)
		tmp = x - (x * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+150], t$95$1, If[LessEqual[z, -1.85e+57], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-26], N[(x + t), $MachinePrecision], If[LessEqual[z, 1e-187], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-26], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999996e150 or 2.8999999999999998e-26 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in x around 0 41.0%

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

      1. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. neg-mul-1 50.9%

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

      2. distribute-neg-frac2 50.9%

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

   8. Simplified 50.9%

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

   if -1.99999999999999996e150 < z < -1.85000000000000003e57

   1. Initial program 64.4%

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

   3. Taylor expanded in x around inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. unsub-neg 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in z around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. neg-mul-1 52.2%

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

      3. sub-neg 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in x around 0 52.2%

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

       1. div-sub 52.2%

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

       2. associate-/l* 45.6%

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

   11. Simplified 45.6%

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

       1. add0 45.6%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 52.2%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 52.2%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 52.2%

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

   15. Simplified 52.2%

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

   if -1.85000000000000003e57 < z < -1.90000000000000007e-26

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in t around inf 81.3%

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

   6. Taylor expanded in z around inf 57.9%

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

   if -1.90000000000000007e-26 < z < 1e-187

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 80.8%

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

   4. Taylor expanded in t around inf 63.8%

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

   if 1e-187 < z < 2.8999999999999998e-26

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 79.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 10^{-187}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -78000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- y z) (- z a)) 1.0)))
        (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -78000000000.0)
     t_2
     (if (<= t -2.2e-140)
       t_1
       (if (<= t -4.2e-261)
         (/ (* y (- x t)) (- z a))
         (if (<= t 3.25e-81) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((y - z) / (z - a)) + 1.0);
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -78000000000.0) {
		tmp = t_2;
	} else if (t <= -2.2e-140) {
		tmp = t_1;
	} else if (t <= -4.2e-261) {
		tmp = (y * (x - t)) / (z - a);
	} else if (t <= 3.25e-81) {
		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 - z) / (z - a)) + 1.0d0)
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-78000000000.0d0)) then
        tmp = t_2
    else if (t <= (-2.2d-140)) then
        tmp = t_1
    else if (t <= (-4.2d-261)) then
        tmp = (y * (x - t)) / (z - a)
    else if (t <= 3.25d-81) 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 - z) / (z - a)) + 1.0);
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -78000000000.0) {
		tmp = t_2;
	} else if (t <= -2.2e-140) {
		tmp = t_1;
	} else if (t <= -4.2e-261) {
		tmp = (y * (x - t)) / (z - a);
	} else if (t <= 3.25e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((y - z) / (z - a)) + 1.0)
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -78000000000.0:
		tmp = t_2
	elif t <= -2.2e-140:
		tmp = t_1
	elif t <= -4.2e-261:
		tmp = (y * (x - t)) / (z - a)
	elif t <= 3.25e-81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -78000000000.0)
		tmp = t_2;
	elseif (t <= -2.2e-140)
		tmp = t_1;
	elseif (t <= -4.2e-261)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	elseif (t <= 3.25e-81)
		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 - z) / (z - a)) + 1.0);
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -78000000000.0)
		tmp = t_2;
	elseif (t <= -2.2e-140)
		tmp = t_1;
	elseif (t <= -4.2e-261)
		tmp = (y * (x - t)) / (z - a);
	elseif (t <= 3.25e-81)
		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[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -78000000000.0], t$95$2, If[LessEqual[t, -2.2e-140], t$95$1, If[LessEqual[t, -4.2e-261], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e-81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8e10 or 3.2500000000000001e-81 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 54.9%

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

      1. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

   if -7.8e10 < t < -2.1999999999999999e-140 or -4.19999999999999991e-261 < t < 3.2500000000000001e-81

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   5. Simplified 66.8%

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

   if -2.1999999999999999e-140 < t < -4.19999999999999991e-261

   1. Initial program 55.9%

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

   3. Taylor expanded in y around -inf 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -78000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z \cdot t}{z - a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.3e+32)
     t_1
     (if (<= z -2.1e-103)
       (+ x (/ (* z t) (- z a)))
       (if (<= z -2.4e-154)
         (* y (/ (- t x) (- a z)))
         (if (<= z 3.4e-26) (- x (/ (* y (- x t)) a)) t_1))))))

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 <= -3.3e+32) {
		tmp = t_1;
	} else if (z <= -2.1e-103) {
		tmp = x + ((z * t) / (z - a));
	} else if (z <= -2.4e-154) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.4e-26) {
		tmp = x - ((y * (x - t)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-3.3d+32)) then
        tmp = t_1
    else if (z <= (-2.1d-103)) then
        tmp = x + ((z * t) / (z - a))
    else if (z <= (-2.4d-154)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 3.4d-26) then
        tmp = x - ((y * (x - t)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.3e+32) {
		tmp = t_1;
	} else if (z <= -2.1e-103) {
		tmp = x + ((z * t) / (z - a));
	} else if (z <= -2.4e-154) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.4e-26) {
		tmp = x - ((y * (x - t)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3.3e+32:
		tmp = t_1
	elif z <= -2.1e-103:
		tmp = x + ((z * t) / (z - a))
	elif z <= -2.4e-154:
		tmp = y * ((t - x) / (a - z))
	elif z <= 3.4e-26:
		tmp = x - ((y * (x - t)) / a)
	else:
		tmp = t_1
	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 <= -3.3e+32)
		tmp = t_1;
	elseif (z <= -2.1e-103)
		tmp = Float64(x + Float64(Float64(z * t) / Float64(z - a)));
	elseif (z <= -2.4e-154)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 3.4e-26)
		tmp = Float64(x - Float64(Float64(y * Float64(x - t)) / a));
	else
		tmp = t_1;
	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 <= -3.3e+32)
		tmp = t_1;
	elseif (z <= -2.1e-103)
		tmp = x + ((z * t) / (z - a));
	elseif (z <= -2.4e-154)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 3.4e-26)
		tmp = x - ((y * (x - t)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+32], t$95$1, If[LessEqual[z, -2.1e-103], N[(x + N[(N[(z * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-154], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-26], N[(x - N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3000000000000002e32 or 3.40000000000000013e-26 < z

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 39.6%

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

      1. associate-/l* 63.8%

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

   5. Simplified 63.8%

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

   if -3.3000000000000002e32 < z < -2.10000000000000005e-103

   1. Initial program 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in t around inf 78.2%

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

   6. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r/ 67.5%

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

      4. unsub-neg 67.5%

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

      5. associate-*r/ 67.6%

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

      6. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if -2.10000000000000005e-103 < z < -2.39999999999999987e-154

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 90.3%

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

      1. div-sub 90.3%

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

   5. Simplified 90.3%

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

   if -2.39999999999999987e-154 < z < 3.40000000000000013e-26

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 83.9%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z \cdot t}{z - a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-128} \lor \neg \left(z \leq 9 \cdot 10^{-67}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+139)
   (* t (/ (- y z) (- a z)))
   (if (or (<= z -2.4e-128) (not (<= z 9e-67)))
     (+ x (/ (- z y) (/ (- z a) t)))
     (- x (* (/ (- y z) a) (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+139) {
		tmp = t * ((y - z) / (a - z));
	} else if ((z <= -2.4e-128) || !(z <= 9e-67)) {
		tmp = x + ((z - y) / ((z - a) / t));
	} else {
		tmp = x - (((y - z) / a) * (x - 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 <= (-8.2d+139)) then
        tmp = t * ((y - z) / (a - z))
    else if ((z <= (-2.4d-128)) .or. (.not. (z <= 9d-67))) then
        tmp = x + ((z - y) / ((z - a) / t))
    else
        tmp = x - (((y - z) / a) * (x - 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 <= -8.2e+139) {
		tmp = t * ((y - z) / (a - z));
	} else if ((z <= -2.4e-128) || !(z <= 9e-67)) {
		tmp = x + ((z - y) / ((z - a) / t));
	} else {
		tmp = x - (((y - z) / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+139:
		tmp = t * ((y - z) / (a - z))
	elif (z <= -2.4e-128) or not (z <= 9e-67):
		tmp = x + ((z - y) / ((z - a) / t))
	else:
		tmp = x - (((y - z) / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+139)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((z <= -2.4e-128) || !(z <= 9e-67))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(z - a) / t)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+139)
		tmp = t * ((y - z) / (a - z));
	elseif ((z <= -2.4e-128) || ~((z <= 9e-67)))
		tmp = x + ((z - y) / ((z - a) / t));
	else
		tmp = x - (((y - z) / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+139], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.4e-128], N[Not[LessEqual[z, 9e-67]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000004e139

   1. Initial program 53.0%

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

   3. Taylor expanded in x around 0 32.6%

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

      1. associate-/l* 63.4%

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

   5. Simplified 63.4%

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

   if -8.2000000000000004e139 < z < -2.3999999999999998e-128 or 9.00000000000000031e-67 < z

   1. Initial program 83.5%

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

      1. clear-num 83.3%

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

      2. un-div-inv 84.0%

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

   4. Applied egg-rr 84.0%

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

   5. Taylor expanded in t around inf 72.1%

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

   if -2.3999999999999998e-128 < z < 9.00000000000000031e-67

   1. Initial program 91.4%

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

   3. Taylor expanded in a around inf 89.2%

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

      1. associate-/l* 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-128} \lor \neg \left(z \leq 9 \cdot 10^{-67}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -3.5e+42)
     t_1
     (if (<= z -6.5e-126)
       (+ x (/ (- z y) (/ (- z a) t)))
       (if (<= z 0.66) (- x (* (/ (- y z) a) (- x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -3.5e+42) {
		tmp = t_1;
	} else if (z <= -6.5e-126) {
		tmp = x + ((z - y) / ((z - a) / t));
	} else if (z <= 0.66) {
		tmp = x - (((y - z) / a) * (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 - x) * ((a - y) / z))
    if (z <= (-3.5d+42)) then
        tmp = t_1
    else if (z <= (-6.5d-126)) then
        tmp = x + ((z - y) / ((z - a) / t))
    else if (z <= 0.66d0) then
        tmp = x - (((y - z) / a) * (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 - x) * ((a - y) / z));
	double tmp;
	if (z <= -3.5e+42) {
		tmp = t_1;
	} else if (z <= -6.5e-126) {
		tmp = x + ((z - y) / ((z - a) / t));
	} else if (z <= 0.66) {
		tmp = x - (((y - z) / a) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -3.5e+42:
		tmp = t_1
	elif z <= -6.5e-126:
		tmp = x + ((z - y) / ((z - a) / t))
	elif z <= 0.66:
		tmp = x - (((y - z) / a) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -3.5e+42)
		tmp = t_1;
	elseif (z <= -6.5e-126)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(z - a) / t)));
	elseif (z <= 0.66)
		tmp = Float64(x - Float64(Float64(Float64(y - z) / a) * 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 - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -3.5e+42)
		tmp = t_1;
	elseif (z <= -6.5e-126)
		tmp = x + ((z - y) / ((z - a) / t));
	elseif (z <= 0.66)
		tmp = x - (((y - z) / a) * (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[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+42], t$95$1, If[LessEqual[z, -6.5e-126], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x - N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000023e42 or 0.660000000000000031 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. distribute-lft-out-- 58.8%

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

      3. div-sub 58.8%

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

      4. mul-1-neg 58.8%

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

      5. unsub-neg 58.8%

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

      6. distribute-rgt-out-- 58.9%

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

      7. associate-/l* 76.8%

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

   5. Simplified 76.8%

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

   if -3.50000000000000023e42 < z < -6.50000000000000014e-126

   1. Initial program 93.8%

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

      1. clear-num 93.8%

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

      2. un-div-inv 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in t around inf 82.3%

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

   if -6.50000000000000014e-126 < z < 0.660000000000000031

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf 86.1%

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

      1. associate-/l* 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-90} \lor \neg \left(z \leq 0.43\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+137)
   t
   (if (or (<= z -4.5e-90) (not (<= z 0.43))) (+ x t) (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+137) {
		tmp = t;
	} else if ((z <= -4.5e-90) || !(z <= 0.43)) {
		tmp = x + t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+137)) then
        tmp = t
    else if ((z <= (-4.5d-90)) .or. (.not. (z <= 0.43d0))) then
        tmp = x + t
    else
        tmp = y * ((t - x) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+137) {
		tmp = t;
	} else if ((z <= -4.5e-90) || !(z <= 0.43)) {
		tmp = x + t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+137:
		tmp = t
	elif (z <= -4.5e-90) or not (z <= 0.43):
		tmp = x + t
	else:
		tmp = y * ((t - x) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+137)
		tmp = t;
	elseif ((z <= -4.5e-90) || !(z <= 0.43))
		tmp = Float64(x + t);
	else
		tmp = Float64(y * Float64(Float64(t - x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+137)
		tmp = t;
	elseif ((z <= -4.5e-90) || ~((z <= 0.43)))
		tmp = x + t;
	else
		tmp = y * ((t - x) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+137], t, If[Or[LessEqual[z, -4.5e-90], N[Not[LessEqual[z, 0.43]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000003e137

   1. Initial program 53.0%

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

   3. Taylor expanded in z around inf 47.7%

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

   if -3.30000000000000003e137 < z < -4.50000000000000009e-90 or 0.429999999999999993 < z

   1. Initial program 79.9%

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

      1. clear-num 79.7%

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

      2. un-div-inv 80.6%

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

   4. Applied egg-rr 80.6%

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

   5. Taylor expanded in t around inf 68.7%

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

   6. Taylor expanded in z around inf 40.8%

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

   if -4.50000000000000009e-90 < z < 0.429999999999999993

   1. Initial program 93.1%

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

   3. Taylor expanded in y around -inf 60.6%

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

   4. Taylor expanded in a around inf 53.0%

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

      1. associate-/l* 56.5%

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

   6. Simplified 56.5%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-90} \lor \neg \left(z \leq 0.43\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+34)
   (* t (/ (- z y) z))
   (if (<= z 9.2e-188)
     (+ x (/ (* y t) a))
     (if (<= z 4.7e-26) (- x (* x (/ y a))) (* t (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+34) {
		tmp = t * ((z - y) / z);
	} else if (z <= 9.2e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.7e-26) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d+34)) then
        tmp = t * ((z - y) / z)
    else if (z <= 9.2d-188) then
        tmp = x + ((y * t) / a)
    else if (z <= 4.7d-26) then
        tmp = x - (x * (y / a))
    else
        tmp = t * (z / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+34) {
		tmp = t * ((z - y) / z);
	} else if (z <= 9.2e-188) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.7e-26) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+34:
		tmp = t * ((z - y) / z)
	elif z <= 9.2e-188:
		tmp = x + ((y * t) / a)
	elif z <= 4.7e-26:
		tmp = x - (x * (y / a))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+34)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= 9.2e-188)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 4.7e-26)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+34)
		tmp = t * ((z - y) / z);
	elseif (z <= 9.2e-188)
		tmp = x + ((y * t) / a);
	elseif (z <= 4.7e-26)
		tmp = x - (x * (y / a));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+34], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-188], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-26], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999996e34

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0 33.9%

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

      1. associate-/l* 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in a around 0 51.1%

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

      1. associate-*r/ 51.1%

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

      2. neg-mul-1 51.1%

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

   8. Simplified 51.1%

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

   if -4.5999999999999996e34 < z < 9.1999999999999999e-188

   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 75.3%

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

   4. Taylor expanded in t around inf 61.6%

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

   if 9.1999999999999999e-188 < z < 4.69999999999999989e-26

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 79.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

   if 4.69999999999999989e-26 < z

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0 43.7%

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

      1. associate-/l* 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in y around 0 48.0%

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

      1. neg-mul-1 48.0%

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

      2. distribute-neg-frac2 48.0%

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

   8. Simplified 48.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+33} \lor \neg \left(z \leq 0.9\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+33) (not (<= z 0.9)))
   (* t (/ (- y z) (- a z)))
   (- x (* (/ (- y z) a) (- x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+33) || !(z <= 0.9)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (((y - z) / a) * (x - 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 <= (-2.7d+33)) .or. (.not. (z <= 0.9d0))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - (((y - z) / a) * (x - 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 <= -2.7e+33) || !(z <= 0.9)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (((y - z) / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+33) or not (z <= 0.9):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - (((y - z) / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+33) || !(z <= 0.9))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e+33) || ~((z <= 0.9)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - (((y - z) / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+33], N[Not[LessEqual[z, 0.9]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999991e33 or 0.900000000000000022 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in x around 0 38.7%

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

      1. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -2.69999999999999991e33 < z < 0.900000000000000022

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 80.7%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+33} \lor \neg \left(z \leq 0.9\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-45} \lor \neg \left(z \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e-45) (not (<= z 3.7e-26)))
   (* t (/ (- y z) (- a z)))
   (- x (/ (* y (- x t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e-45) || !(z <= 3.7e-26)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((y * (x - t)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.25d-45)) .or. (.not. (z <= 3.7d-26))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - ((y * (x - t)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e-45) || !(z <= 3.7e-26)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((y * (x - t)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e-45) or not (z <= 3.7e-26):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - ((y * (x - t)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e-45) || !(z <= 3.7e-26))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(x - t)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e-45) || ~((z <= 3.7e-26)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - ((y * (x - t)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e-45], N[Not[LessEqual[z, 3.7e-26]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999994e-45 or 3.6999999999999999e-26 < z

   1. Initial program 72.8%

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

   3. Taylor expanded in x around 0 40.5%

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

      1. associate-/l* 62.1%

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

   5. Simplified 62.1%

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

   if -1.24999999999999994e-45 < z < 3.6999999999999999e-26

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 81.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-45} \lor \neg \left(z \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-26} \lor \neg \left(z \leq 1.35 \cdot 10^{-42}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+138)
   t
   (if (or (<= z -1.2e-26) (not (<= z 1.35e-42))) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+138) {
		tmp = t;
	} else if ((z <= -1.2e-26) || !(z <= 1.35e-42)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d+138)) then
        tmp = t
    else if ((z <= (-1.2d-26)) .or. (.not. (z <= 1.35d-42))) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+138) {
		tmp = t;
	} else if ((z <= -1.2e-26) || !(z <= 1.35e-42)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+138:
		tmp = t
	elif (z <= -1.2e-26) or not (z <= 1.35e-42):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+138)
		tmp = t;
	elseif ((z <= -1.2e-26) || !(z <= 1.35e-42))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+138)
		tmp = t;
	elseif ((z <= -1.2e-26) || ~((z <= 1.35e-42)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+138], t, If[Or[LessEqual[z, -1.2e-26], N[Not[LessEqual[z, 1.35e-42]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000016e138

   1. Initial program 53.0%

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

   3. Taylor expanded in z around inf 47.7%

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

   if -5.00000000000000016e138 < z < -1.2e-26 or 1.35e-42 < z

   1. Initial program 81.2%

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

      1. clear-num 80.9%

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

      2. un-div-inv 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in t around inf 69.5%

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

   6. Taylor expanded in z around inf 40.5%

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

   if -1.2e-26 < z < 1.35e-42

   1. Initial program 91.6%

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

   3. Taylor expanded in a around inf 32.9%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-26} \lor \neg \left(z \leq 1.35 \cdot 10^{-42}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 40.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+70}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.3e-54)
   (* t (/ y (- a z)))
   (if (<= y 1.75e+70) (+ x t) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e-54) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.75e+70) {
		tmp = x + t;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.3d-54)) then
        tmp = t * (y / (a - z))
    else if (y <= 1.75d+70) then
        tmp = x + t
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e-54) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.75e+70) {
		tmp = x + t;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.3e-54:
		tmp = t * (y / (a - z))
	elif y <= 1.75e+70:
		tmp = x + t
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.3e-54)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= 1.75e+70)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.3e-54)
		tmp = t * (y / (a - z));
	elseif (y <= 1.75e+70)
		tmp = x + t;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.3e-54], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+70], N[(x + t), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000001e-54

   1. Initial program 80.4%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around inf 39.0%

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

      1. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

   if -1.30000000000000001e-54 < y < 1.75000000000000001e70

   1. Initial program 82.3%

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

      1. clear-num 82.2%

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

      2. un-div-inv 82.8%

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

   4. Applied egg-rr 82.8%

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

   5. Taylor expanded in t around inf 78.1%

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

   6. Taylor expanded in z around inf 47.9%

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

   if 1.75000000000000001e70 < y

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in z around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. neg-mul-1 37.3%

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

      3. sub-neg 37.3%

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

   8. Simplified 37.3%

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

   9. Taylor expanded in x around 0 37.1%

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

       1. div-sub 37.3%

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

       2. associate-/l* 26.4%

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

   11. Simplified 26.4%

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

       1. add0 26.4%

          \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z} + 0} \]

       2. associate-/l* 37.3%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} + 0 \]

   13. Applied egg-rr 37.3%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z} + 0} \]
   14. Step-by-step derivation

       1. add0 37.3%

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

   15. Simplified 37.3%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+70}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12800000000000 \lor \neg \left(y \leq 1.65 \cdot 10^{+132}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -12800000000000.0) (not (<= y 1.65e+132)))
   (* t (/ y a))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -12800000000000.0) || !(y <= 1.65e+132)) {
		tmp = t * (y / a);
	} else {
		tmp = x + 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 ((y <= (-12800000000000.0d0)) .or. (.not. (y <= 1.65d+132))) then
        tmp = t * (y / a)
    else
        tmp = x + 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 ((y <= -12800000000000.0) || !(y <= 1.65e+132)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -12800000000000.0) or not (y <= 1.65e+132):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -12800000000000.0) || !(y <= 1.65e+132))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -12800000000000.0) || ~((y <= 1.65e+132)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -12800000000000.0], N[Not[LessEqual[y, 1.65e+132]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.28e13 or 1.65000000000000015e132 < y

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in z around 0 30.0%

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

      1. associate-/l* 30.8%

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

   8. Simplified 30.8%

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

   if -1.28e13 < y < 1.65000000000000015e132

   1. Initial program 79.3%

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

      1. clear-num 79.2%

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

      2. un-div-inv 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in t around inf 72.9%

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

   6. Taylor expanded in z around inf 43.8%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12800000000000 \lor \neg \left(y \leq 1.65 \cdot 10^{+132}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -72000000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -72000000000.0)
   (* t (/ y a))
   (if (<= y 8.5e+69) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -72000000000.0) {
		tmp = t * (y / a);
	} else if (y <= 8.5e+69) {
		tmp = x + t;
	} else {
		tmp = x * (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 (y <= (-72000000000.0d0)) then
        tmp = t * (y / a)
    else if (y <= 8.5d+69) then
        tmp = x + t
    else
        tmp = x * (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 (y <= -72000000000.0) {
		tmp = t * (y / a);
	} else if (y <= 8.5e+69) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -72000000000.0:
		tmp = t * (y / a)
	elif y <= 8.5e+69:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -72000000000.0)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 8.5e+69)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -72000000000.0)
		tmp = t * (y / a);
	elseif (y <= 8.5e+69)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -72000000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+69], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e10

   1. Initial program 85.0%

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

   3. Taylor expanded in x around 0 45.8%

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

      1. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. associate-/l* 35.2%

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

   8. Simplified 35.2%

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

   if -7.2e10 < y < 8.5000000000000002e69

   1. Initial program 80.2%

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

      1. clear-num 80.0%

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

      2. un-div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in z around inf 45.5%

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

   if 8.5000000000000002e69 < y

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 35.5%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -72000000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+70}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e-55)
   (* t (/ y (- a z)))
   (if (<= y 1.55e+70) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e-55) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.55e+70) {
		tmp = x + t;
	} else {
		tmp = x * (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 (y <= (-3.8d-55)) then
        tmp = t * (y / (a - z))
    else if (y <= 1.55d+70) then
        tmp = x + t
    else
        tmp = x * (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 (y <= -3.8e-55) {
		tmp = t * (y / (a - z));
	} else if (y <= 1.55e+70) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e-55:
		tmp = t * (y / (a - z))
	elif y <= 1.55e+70:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e-55)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= 1.55e+70)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.8e-55)
		tmp = t * (y / (a - z));
	elseif (y <= 1.55e+70)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e-55], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+70], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999997e-55

   1. Initial program 80.4%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around inf 39.0%

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

      1. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

   if -3.7999999999999997e-55 < y < 1.55000000000000015e70

   1. Initial program 82.3%

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

      1. clear-num 82.2%

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

      2. un-div-inv 82.8%

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

   4. Applied egg-rr 82.8%

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

   5. Taylor expanded in t around inf 78.1%

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

   6. Taylor expanded in z around inf 47.9%

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

   if 1.55000000000000015e70 < y

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in a around 0 35.5%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+70}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+33}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.72:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.85e+33) t (if (<= z 0.72) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.85e+33) {
		tmp = t;
	} else if (z <= 0.72) {
		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 <= (-3.85d+33)) then
        tmp = t
    else if (z <= 0.72d0) 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 <= -3.85e+33) {
		tmp = t;
	} else if (z <= 0.72) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.85e+33:
		tmp = t
	elif z <= 0.72:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.85e+33)
		tmp = t;
	elseif (z <= 0.72)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.85e+33)
		tmp = t;
	elseif (z <= 0.72)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.85e+33], t, If[LessEqual[z, 0.72], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.84999999999999982e33 or 0.71999999999999997 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 39.5%

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

   if -3.84999999999999982e33 < z < 0.71999999999999997

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 32.6%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+33}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.72:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.4% 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 81.9%

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

3. Taylor expanded in z around inf 22.3%

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

4. Final simplification 22.3%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))))