Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 93.7%

Time: 32.3s

Alternatives: 29

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: 79.9% 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: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-285} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-285) (not (<= t_1 5e-210)))
     (+ x (* (- x t) (/ (- z y) (- a z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-285) || !(t_1 <= 5e-210)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-285)) .or. (.not. (t_1 <= 5d-210))) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-285) || !(t_1 <= 5e-210)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-285) or not (t_1 <= 5e-210):
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-285) || !(t_1 <= 5e-210))
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-285) || ~((t_1 <= 5e-210)))
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-285], N[Not[LessEqual[t$95$1, 5e-210]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000018e-285 or 5.0000000000000002e-210 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. div-sub 76.4%

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

      3. associate-*r/ 74.6%

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

      4. mul-1-neg 74.6%

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

      5. sub-neg 74.6%

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

      6. associate-/l* 76.4%

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

      7. associate-/l* 90.3%

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

      8. div-sub 90.5%

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

      9. associate-/r/ 94.3%

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

   5. Simplified 94.3%

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

   if -5.00000000000000018e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-210

   1. Initial program 3.7%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. associate--l+ 74.8%

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

      2. distribute-lft-out-- 74.8%

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

      3. div-sub 74.8%

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

      4. mul-1-neg 74.8%

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

      5. unsub-neg 74.8%

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

      6. distribute-rgt-out-- 74.8%

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

      7. associate-/l* 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-285} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 44.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -59:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t a))))
   (if (<= a -2.55e+160)
     x
     (if (<= a -59.0)
       t_1
       (if (<= a 2.8e-242)
         (- t (/ t (/ z y)))
         (if (<= a 6.2e-55)
           (* x (/ (- y a) z))
           (if (<= a 1.5e+38)
             (/ t (/ (- z a) z))
             (if (<= a 1.8e+91)
               (/ t (/ a (- y z)))
               (if (<= a 1.45e+96)
                 t
                 (if (<= a 7.6e+132)
                   x
                   (if (<= a 6.2e+160)
                     t_1
                     (if (<= a 1.35e+164) (* a (/ (- x) z)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -2.55e+160) {
		tmp = x;
	} else if (a <= -59.0) {
		tmp = t_1;
	} else if (a <= 2.8e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 6.2e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.5e+38) {
		tmp = t / ((z - a) / z);
	} else if (a <= 1.8e+91) {
		tmp = t / (a / (y - z));
	} else if (a <= 1.45e+96) {
		tmp = t;
	} else if (a <= 7.6e+132) {
		tmp = x;
	} else if (a <= 6.2e+160) {
		tmp = t_1;
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / a)
    if (a <= (-2.55d+160)) then
        tmp = x
    else if (a <= (-59.0d0)) then
        tmp = t_1
    else if (a <= 2.8d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 6.2d-55) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.5d+38) then
        tmp = t / ((z - a) / z)
    else if (a <= 1.8d+91) then
        tmp = t / (a / (y - z))
    else if (a <= 1.45d+96) then
        tmp = t
    else if (a <= 7.6d+132) then
        tmp = x
    else if (a <= 6.2d+160) then
        tmp = t_1
    else if (a <= 1.35d+164) then
        tmp = a * (-x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -2.55e+160) {
		tmp = x;
	} else if (a <= -59.0) {
		tmp = t_1;
	} else if (a <= 2.8e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 6.2e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.5e+38) {
		tmp = t / ((z - a) / z);
	} else if (a <= 1.8e+91) {
		tmp = t / (a / (y - z));
	} else if (a <= 1.45e+96) {
		tmp = t;
	} else if (a <= 7.6e+132) {
		tmp = x;
	} else if (a <= 6.2e+160) {
		tmp = t_1;
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / a)
	tmp = 0
	if a <= -2.55e+160:
		tmp = x
	elif a <= -59.0:
		tmp = t_1
	elif a <= 2.8e-242:
		tmp = t - (t / (z / y))
	elif a <= 6.2e-55:
		tmp = x * ((y - a) / z)
	elif a <= 1.5e+38:
		tmp = t / ((z - a) / z)
	elif a <= 1.8e+91:
		tmp = t / (a / (y - z))
	elif a <= 1.45e+96:
		tmp = t
	elif a <= 7.6e+132:
		tmp = x
	elif a <= 6.2e+160:
		tmp = t_1
	elif a <= 1.35e+164:
		tmp = a * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / a))
	tmp = 0.0
	if (a <= -2.55e+160)
		tmp = x;
	elseif (a <= -59.0)
		tmp = t_1;
	elseif (a <= 2.8e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 6.2e-55)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.5e+38)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (a <= 1.8e+91)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (a <= 1.45e+96)
		tmp = t;
	elseif (a <= 7.6e+132)
		tmp = x;
	elseif (a <= 6.2e+160)
		tmp = t_1;
	elseif (a <= 1.35e+164)
		tmp = Float64(a * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / a);
	tmp = 0.0;
	if (a <= -2.55e+160)
		tmp = x;
	elseif (a <= -59.0)
		tmp = t_1;
	elseif (a <= 2.8e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 6.2e-55)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.5e+38)
		tmp = t / ((z - a) / z);
	elseif (a <= 1.8e+91)
		tmp = t / (a / (y - z));
	elseif (a <= 1.45e+96)
		tmp = t;
	elseif (a <= 7.6e+132)
		tmp = x;
	elseif (a <= 6.2e+160)
		tmp = t_1;
	elseif (a <= 1.35e+164)
		tmp = a * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e+160], x, If[LessEqual[a, -59.0], t$95$1, If[LessEqual[a, 2.8e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-55], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+38], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+91], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+96], t, If[LessEqual[a, 7.6e+132], x, If[LessEqual[a, 6.2e+160], t$95$1, If[LessEqual[a, 1.35e+164], N[(a * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -2.5500000000000001e160 or 1.44999999999999989e96 < a < 7.60000000000000012e132 or 1.35000000000000003e164 < a

   1. Initial program 88.2%

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

   3. Taylor expanded in a around inf 64.8%

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

   if -2.5500000000000001e160 < a < -59 or 7.60000000000000012e132 < a < 6.1999999999999996e160

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 37.5%

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

      1. associate-/l* 52.1%

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

      2. associate-/r/ 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in a around inf 41.3%

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

   if -59 < a < 2.79999999999999983e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 2.79999999999999983e-242 < a < 6.19999999999999993e-55

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 6.19999999999999993e-55 < a < 1.5000000000000001e38

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 47.2%

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

      1. associate-/l* 64.8%

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

      2. associate-/r/ 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around 0 40.6%

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

      1. associate-*r/ 40.6%

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

      2. mul-1-neg 40.6%

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

      3. distribute-rgt-neg-out 40.6%

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

      4. associate-*l/ 52.1%

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

   8. Simplified 52.1%

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

      1. associate-*l/ 40.6%

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

      2. frac-2neg 40.6%

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

      3. add-sqr-sqrt 26.6%

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

      4. sqrt-unprod 15.4%

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

      5. sqr-neg 15.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.3%

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

      8. distribute-rgt-neg-out 2.3%

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

      9. add-sqr-sqrt 1.5%

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

      10. sqrt-unprod 8.9%

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

      11. sqr-neg 8.9%

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

      12. sqrt-unprod 13.7%

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

      13. add-sqr-sqrt 40.6%

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

      14. sub-neg 40.6%

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

      15. distribute-neg-in 40.6%

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

      16. add-sqr-sqrt 26.6%

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

      17. sqrt-unprod 15.3%

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

      18. sqr-neg 15.3%

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

      19. sqrt-unprod 0.8%

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

      20. add-sqr-sqrt 2.3%

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

      21. add-sqr-sqrt 1.5%

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

      22. sqrt-unprod 9.5%

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

      23. sqr-neg 9.5%

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

   10. Applied egg-rr 40.6%

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

       1. associate-/l* 58.2%

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

       2. +-commutative 58.2%

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

       3. unsub-neg 58.2%

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

   12. Simplified 58.2%

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

   if 1.5000000000000001e38 < a < 1.8e91

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 45.4%

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

      1. associate-/l* 45.9%

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

      2. associate-/r/ 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

   if 1.8e91 < a < 1.44999999999999989e96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if 6.1999999999999996e160 < a < 1.35000000000000003e164

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf 4.7%

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

      1. associate--l+ 4.7%

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

      2. distribute-lft-out-- 4.7%

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

      3. div-sub 4.7%

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

      4. mul-1-neg 4.7%

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

      5. unsub-neg 4.7%

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

      6. distribute-rgt-out-- 4.7%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 4.7%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around 0 4.7%

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

       1. mul-1-neg 4.7%

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

       2. distribute-neg-frac 4.7%

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

       3. distribute-lft-neg-out 4.7%

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

       4. associate-*r/ 100.0%

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

       5. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(-a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -59:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.41:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))))
   (if (<= a -4.6e+108)
     x
     (if (<= a -0.41)
       t_1
       (if (<= a 2.7e-242)
         (- t (/ t (/ z y)))
         (if (<= a 1.55e-49)
           (* x (/ (- y a) z))
           (if (<= a 1.55e+32)
             (/ t (/ (- z a) z))
             (if (<= a 3.3e+91)
               t_1
               (if (<= a 1.7e+96)
                 t
                 (if (<= a 2.8e+132)
                   x
                   (if (<= a 1.25e+164)
                     (* (- y z) (/ t a))
                     (if (<= a 1.35e+164) (* a (/ (- x) z)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -4.6e+108) {
		tmp = x;
	} else if (a <= -0.41) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.55e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.55e+32) {
		tmp = t / ((z - a) / z);
	} else if (a <= 3.3e+91) {
		tmp = t_1;
	} else if (a <= 1.7e+96) {
		tmp = t;
	} else if (a <= 2.8e+132) {
		tmp = x;
	} else if (a <= 1.25e+164) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / (t - x))
    if (a <= (-4.6d+108)) then
        tmp = x
    else if (a <= (-0.41d0)) then
        tmp = t_1
    else if (a <= 2.7d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 1.55d-49) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.55d+32) then
        tmp = t / ((z - a) / z)
    else if (a <= 3.3d+91) then
        tmp = t_1
    else if (a <= 1.7d+96) then
        tmp = t
    else if (a <= 2.8d+132) then
        tmp = x
    else if (a <= 1.25d+164) then
        tmp = (y - z) * (t / a)
    else if (a <= 1.35d+164) then
        tmp = a * (-x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -4.6e+108) {
		tmp = x;
	} else if (a <= -0.41) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.55e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.55e+32) {
		tmp = t / ((z - a) / z);
	} else if (a <= 3.3e+91) {
		tmp = t_1;
	} else if (a <= 1.7e+96) {
		tmp = t;
	} else if (a <= 2.8e+132) {
		tmp = x;
	} else if (a <= 1.25e+164) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	tmp = 0
	if a <= -4.6e+108:
		tmp = x
	elif a <= -0.41:
		tmp = t_1
	elif a <= 2.7e-242:
		tmp = t - (t / (z / y))
	elif a <= 1.55e-49:
		tmp = x * ((y - a) / z)
	elif a <= 1.55e+32:
		tmp = t / ((z - a) / z)
	elif a <= 3.3e+91:
		tmp = t_1
	elif a <= 1.7e+96:
		tmp = t
	elif a <= 2.8e+132:
		tmp = x
	elif a <= 1.25e+164:
		tmp = (y - z) * (t / a)
	elif a <= 1.35e+164:
		tmp = a * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	tmp = 0.0
	if (a <= -4.6e+108)
		tmp = x;
	elseif (a <= -0.41)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 1.55e-49)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.55e+32)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (a <= 3.3e+91)
		tmp = t_1;
	elseif (a <= 1.7e+96)
		tmp = t;
	elseif (a <= 2.8e+132)
		tmp = x;
	elseif (a <= 1.25e+164)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= 1.35e+164)
		tmp = Float64(a * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	tmp = 0.0;
	if (a <= -4.6e+108)
		tmp = x;
	elseif (a <= -0.41)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 1.55e-49)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.55e+32)
		tmp = t / ((z - a) / z);
	elseif (a <= 3.3e+91)
		tmp = t_1;
	elseif (a <= 1.7e+96)
		tmp = t;
	elseif (a <= 2.8e+132)
		tmp = x;
	elseif (a <= 1.25e+164)
		tmp = (y - z) * (t / a);
	elseif (a <= 1.35e+164)
		tmp = a * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+108], x, If[LessEqual[a, -0.41], t$95$1, If[LessEqual[a, 2.7e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-49], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+32], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+91], t$95$1, If[LessEqual[a, 1.7e+96], t, If[LessEqual[a, 2.8e+132], x, If[LessEqual[a, 1.25e+164], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+164], N[(a * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -4.5999999999999998e108 or 1.7e96 < a < 2.7999999999999999e132 or 1.35000000000000003e164 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in a around inf 59.3%

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

   if -4.5999999999999998e108 < a < -0.409999999999999976 or 1.54999999999999997e32 < a < 3.30000000000000017e91

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. div-sub 57.0%

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

      2. associate-*r/ 53.3%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in a around inf 49.3%

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

   if -0.409999999999999976 < a < 2.7e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 2.7e-242 < a < 1.55e-49

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 1.55e-49 < a < 1.54999999999999997e32

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 39.7%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

      3. distribute-rgt-neg-out 39.0%

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

      4. associate-*l/ 52.2%

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

   8. Simplified 52.2%

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

      1. associate-*l/ 39.0%

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

      2. frac-2neg 39.0%

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

      3. add-sqr-sqrt 30.1%

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

      4. sqrt-unprod 17.4%

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

      5. sqr-neg 17.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.5%

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

      8. distribute-rgt-neg-out 2.5%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 2.9%

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

      11. sqr-neg 2.9%

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

      12. sqrt-unprod 8.5%

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

      13. add-sqr-sqrt 39.0%

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

      14. sub-neg 39.0%

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

      15. distribute-neg-in 39.0%

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

      16. add-sqr-sqrt 30.1%

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

      17. sqrt-unprod 17.1%

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

      18. sqr-neg 17.1%

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

      19. sqrt-unprod 0.9%

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

      20. add-sqr-sqrt 2.3%

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

      21. add-sqr-sqrt 1.5%

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

      22. sqrt-unprod 3.4%

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

      23. sqr-neg 3.4%

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

   10. Applied egg-rr 39.0%

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

       1. associate-/l* 59.1%

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

       2. +-commutative 59.1%

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

       3. unsub-neg 59.1%

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

   12. Simplified 59.1%

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

   if 3.30000000000000017e91 < a < 1.7e96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if 2.7999999999999999e132 < a < 1.24999999999999987e164

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 83.6%

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

      2. associate-/r/ 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in a around inf 68.5%

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

   if 1.24999999999999987e164 < a < 1.35000000000000003e164

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf 4.7%

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

      1. associate--l+ 4.7%

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

      2. distribute-lft-out-- 4.7%

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

      3. div-sub 4.7%

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

      4. mul-1-neg 4.7%

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

      5. unsub-neg 4.7%

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

      6. distribute-rgt-out-- 4.7%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 4.7%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around 0 4.7%

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

       1. mul-1-neg 4.7%

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

       2. distribute-neg-frac 4.7%

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

       3. distribute-lft-neg-out 4.7%

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

       4. associate-*r/ 100.0%

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

       5. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(-a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.41:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.72:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))))
   (if (<= a -9.5e+109)
     x
     (if (<= a -0.72)
       t_1
       (if (<= a 2.7e-242)
         (- t (/ t (/ z y)))
         (if (<= a 1.2e-54)
           (/ (* x (- y a)) z)
           (if (<= a 1.8e+29)
             (/ t (/ (- z a) z))
             (if (<= a 3.2e+91)
               t_1
               (if (<= a 1.7e+96)
                 t
                 (if (<= a 6.2e+132)
                   x
                   (if (<= a 7.2e+163)
                     (* (- y z) (/ t a))
                     (if (<= a 1.35e+164) (* a (/ (- x) z)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -9.5e+109) {
		tmp = x;
	} else if (a <= -0.72) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.2e-54) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.8e+29) {
		tmp = t / ((z - a) / z);
	} else if (a <= 3.2e+91) {
		tmp = t_1;
	} else if (a <= 1.7e+96) {
		tmp = t;
	} else if (a <= 6.2e+132) {
		tmp = x;
	} else if (a <= 7.2e+163) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / (t - x))
    if (a <= (-9.5d+109)) then
        tmp = x
    else if (a <= (-0.72d0)) then
        tmp = t_1
    else if (a <= 2.7d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 1.2d-54) then
        tmp = (x * (y - a)) / z
    else if (a <= 1.8d+29) then
        tmp = t / ((z - a) / z)
    else if (a <= 3.2d+91) then
        tmp = t_1
    else if (a <= 1.7d+96) then
        tmp = t
    else if (a <= 6.2d+132) then
        tmp = x
    else if (a <= 7.2d+163) then
        tmp = (y - z) * (t / a)
    else if (a <= 1.35d+164) then
        tmp = a * (-x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -9.5e+109) {
		tmp = x;
	} else if (a <= -0.72) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.2e-54) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.8e+29) {
		tmp = t / ((z - a) / z);
	} else if (a <= 3.2e+91) {
		tmp = t_1;
	} else if (a <= 1.7e+96) {
		tmp = t;
	} else if (a <= 6.2e+132) {
		tmp = x;
	} else if (a <= 7.2e+163) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	tmp = 0
	if a <= -9.5e+109:
		tmp = x
	elif a <= -0.72:
		tmp = t_1
	elif a <= 2.7e-242:
		tmp = t - (t / (z / y))
	elif a <= 1.2e-54:
		tmp = (x * (y - a)) / z
	elif a <= 1.8e+29:
		tmp = t / ((z - a) / z)
	elif a <= 3.2e+91:
		tmp = t_1
	elif a <= 1.7e+96:
		tmp = t
	elif a <= 6.2e+132:
		tmp = x
	elif a <= 7.2e+163:
		tmp = (y - z) * (t / a)
	elif a <= 1.35e+164:
		tmp = a * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	tmp = 0.0
	if (a <= -9.5e+109)
		tmp = x;
	elseif (a <= -0.72)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 1.2e-54)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 1.8e+29)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (a <= 3.2e+91)
		tmp = t_1;
	elseif (a <= 1.7e+96)
		tmp = t;
	elseif (a <= 6.2e+132)
		tmp = x;
	elseif (a <= 7.2e+163)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= 1.35e+164)
		tmp = Float64(a * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	tmp = 0.0;
	if (a <= -9.5e+109)
		tmp = x;
	elseif (a <= -0.72)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 1.2e-54)
		tmp = (x * (y - a)) / z;
	elseif (a <= 1.8e+29)
		tmp = t / ((z - a) / z);
	elseif (a <= 3.2e+91)
		tmp = t_1;
	elseif (a <= 1.7e+96)
		tmp = t;
	elseif (a <= 6.2e+132)
		tmp = x;
	elseif (a <= 7.2e+163)
		tmp = (y - z) * (t / a);
	elseif (a <= 1.35e+164)
		tmp = a * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+109], x, If[LessEqual[a, -0.72], t$95$1, If[LessEqual[a, 2.7e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-54], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.8e+29], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+91], t$95$1, If[LessEqual[a, 1.7e+96], t, If[LessEqual[a, 6.2e+132], x, If[LessEqual[a, 7.2e+163], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+164], N[(a * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -9.49999999999999972e109 or 1.7e96 < a < 6.1999999999999995e132 or 1.35000000000000003e164 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in a around inf 59.3%

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

   if -9.49999999999999972e109 < a < -0.71999999999999997 or 1.79999999999999988e29 < a < 3.19999999999999989e91

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. div-sub 57.0%

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

      2. associate-*r/ 53.3%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in a around inf 49.3%

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

   if -0.71999999999999997 < a < 2.7e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 2.7e-242 < a < 1.20000000000000007e-54

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

   if 1.20000000000000007e-54 < a < 1.79999999999999988e29

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 39.7%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

      3. distribute-rgt-neg-out 39.0%

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

      4. associate-*l/ 52.2%

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

   8. Simplified 52.2%

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

      1. associate-*l/ 39.0%

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

      2. frac-2neg 39.0%

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

      3. add-sqr-sqrt 30.1%

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

      4. sqrt-unprod 17.4%

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

      5. sqr-neg 17.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.5%

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

      8. distribute-rgt-neg-out 2.5%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 2.9%

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

      11. sqr-neg 2.9%

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

      12. sqrt-unprod 8.5%

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

      13. add-sqr-sqrt 39.0%

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

      14. sub-neg 39.0%

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

      15. distribute-neg-in 39.0%

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

      16. add-sqr-sqrt 30.1%

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

      17. sqrt-unprod 17.1%

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

      18. sqr-neg 17.1%

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

      19. sqrt-unprod 0.9%

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

      20. add-sqr-sqrt 2.3%

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

      21. add-sqr-sqrt 1.5%

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

      22. sqrt-unprod 3.4%

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

      23. sqr-neg 3.4%

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

   10. Applied egg-rr 39.0%

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

       1. associate-/l* 59.1%

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

       2. +-commutative 59.1%

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

       3. unsub-neg 59.1%

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

   12. Simplified 59.1%

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

   if 3.19999999999999989e91 < a < 1.7e96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if 6.1999999999999995e132 < a < 7.19999999999999955e163

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 83.6%

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

      2. associate-/r/ 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in a around inf 68.5%

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

   if 7.19999999999999955e163 < a < 1.35000000000000003e164

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf 4.7%

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

      1. associate--l+ 4.7%

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

      2. distribute-lft-out-- 4.7%

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

      3. div-sub 4.7%

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

      4. mul-1-neg 4.7%

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

      5. unsub-neg 4.7%

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

      6. distribute-rgt-out-- 4.7%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 4.7%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around 0 4.7%

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

       1. mul-1-neg 4.7%

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

       2. distribute-neg-frac 4.7%

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

       3. distribute-lft-neg-out 4.7%

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

       4. associate-*r/ 100.0%

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

       5. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(-a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.72:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))))
   (if (<= a -1.05e+106)
     x
     (if (<= a -1.65)
       t_1
       (if (<= a 1.2e-242)
         (- t (/ t (/ z y)))
         (if (<= a 3.8e-48)
           (/ (- x) (/ z (- a y)))
           (if (<= a 1.2e+29)
             (/ t (/ (- z a) z))
             (if (<= a 1.4e+91)
               t_1
               (if (<= a 1.12e+96)
                 t
                 (if (<= a 4e+131)
                   x
                   (if (<= a 1.3e+164)
                     (* (- y z) (/ t a))
                     (if (<= a 1.35e+164) (* a (/ (- x) z)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -1.05e+106) {
		tmp = x;
	} else if (a <= -1.65) {
		tmp = t_1;
	} else if (a <= 1.2e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 3.8e-48) {
		tmp = -x / (z / (a - y));
	} else if (a <= 1.2e+29) {
		tmp = t / ((z - a) / z);
	} else if (a <= 1.4e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else if (a <= 4e+131) {
		tmp = x;
	} else if (a <= 1.3e+164) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / (t - x))
    if (a <= (-1.05d+106)) then
        tmp = x
    else if (a <= (-1.65d0)) then
        tmp = t_1
    else if (a <= 1.2d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 3.8d-48) then
        tmp = -x / (z / (a - y))
    else if (a <= 1.2d+29) then
        tmp = t / ((z - a) / z)
    else if (a <= 1.4d+91) then
        tmp = t_1
    else if (a <= 1.12d+96) then
        tmp = t
    else if (a <= 4d+131) then
        tmp = x
    else if (a <= 1.3d+164) then
        tmp = (y - z) * (t / a)
    else if (a <= 1.35d+164) then
        tmp = a * (-x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -1.05e+106) {
		tmp = x;
	} else if (a <= -1.65) {
		tmp = t_1;
	} else if (a <= 1.2e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 3.8e-48) {
		tmp = -x / (z / (a - y));
	} else if (a <= 1.2e+29) {
		tmp = t / ((z - a) / z);
	} else if (a <= 1.4e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else if (a <= 4e+131) {
		tmp = x;
	} else if (a <= 1.3e+164) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = a * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	tmp = 0
	if a <= -1.05e+106:
		tmp = x
	elif a <= -1.65:
		tmp = t_1
	elif a <= 1.2e-242:
		tmp = t - (t / (z / y))
	elif a <= 3.8e-48:
		tmp = -x / (z / (a - y))
	elif a <= 1.2e+29:
		tmp = t / ((z - a) / z)
	elif a <= 1.4e+91:
		tmp = t_1
	elif a <= 1.12e+96:
		tmp = t
	elif a <= 4e+131:
		tmp = x
	elif a <= 1.3e+164:
		tmp = (y - z) * (t / a)
	elif a <= 1.35e+164:
		tmp = a * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	tmp = 0.0
	if (a <= -1.05e+106)
		tmp = x;
	elseif (a <= -1.65)
		tmp = t_1;
	elseif (a <= 1.2e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 3.8e-48)
		tmp = Float64(Float64(-x) / Float64(z / Float64(a - y)));
	elseif (a <= 1.2e+29)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (a <= 1.4e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	elseif (a <= 4e+131)
		tmp = x;
	elseif (a <= 1.3e+164)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= 1.35e+164)
		tmp = Float64(a * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	tmp = 0.0;
	if (a <= -1.05e+106)
		tmp = x;
	elseif (a <= -1.65)
		tmp = t_1;
	elseif (a <= 1.2e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 3.8e-48)
		tmp = -x / (z / (a - y));
	elseif (a <= 1.2e+29)
		tmp = t / ((z - a) / z);
	elseif (a <= 1.4e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	elseif (a <= 4e+131)
		tmp = x;
	elseif (a <= 1.3e+164)
		tmp = (y - z) * (t / a);
	elseif (a <= 1.35e+164)
		tmp = a * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+106], x, If[LessEqual[a, -1.65], t$95$1, If[LessEqual[a, 1.2e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-48], N[((-x) / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+29], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+91], t$95$1, If[LessEqual[a, 1.12e+96], t, If[LessEqual[a, 4e+131], x, If[LessEqual[a, 1.3e+164], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+164], N[(a * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.05000000000000002e106 or 1.1199999999999999e96 < a < 3.9999999999999996e131 or 1.35000000000000003e164 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in a around inf 59.3%

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

   if -1.05000000000000002e106 < a < -1.6499999999999999 or 1.2e29 < a < 1.3999999999999999e91

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. div-sub 57.0%

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

      2. associate-*r/ 53.3%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in a around inf 49.3%

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

   if -1.6499999999999999 < a < 1.2e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 1.2e-242 < a < 3.80000000000000002e-48

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-*l/ 57.6%

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

      4. distribute-lft-neg-in 57.6%

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

      5. distribute-neg-frac 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in t around 0 51.3%

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

       1. mul-1-neg 51.3%

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

       2. associate-/l* 51.4%

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

   11. Simplified 51.4%

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

   if 3.80000000000000002e-48 < a < 1.2e29

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 39.7%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

      3. distribute-rgt-neg-out 39.0%

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

      4. associate-*l/ 52.2%

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

   8. Simplified 52.2%

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

      1. associate-*l/ 39.0%

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

      2. frac-2neg 39.0%

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

      3. add-sqr-sqrt 30.1%

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

      4. sqrt-unprod 17.4%

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

      5. sqr-neg 17.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 2.5%

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

      8. distribute-rgt-neg-out 2.5%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 2.9%

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

      11. sqr-neg 2.9%

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

      12. sqrt-unprod 8.5%

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

      13. add-sqr-sqrt 39.0%

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

      14. sub-neg 39.0%

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

      15. distribute-neg-in 39.0%

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

      16. add-sqr-sqrt 30.1%

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

      17. sqrt-unprod 17.1%

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

      18. sqr-neg 17.1%

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

      19. sqrt-unprod 0.9%

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

      20. add-sqr-sqrt 2.3%

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

      21. add-sqr-sqrt 1.5%

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

      22. sqrt-unprod 3.4%

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

      23. sqr-neg 3.4%

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

   10. Applied egg-rr 39.0%

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

       1. associate-/l* 59.1%

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

       2. +-commutative 59.1%

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

       3. unsub-neg 59.1%

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

   12. Simplified 59.1%

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

   if 1.3999999999999999e91 < a < 1.1199999999999999e96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if 3.9999999999999996e131 < a < 1.3e164

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 83.6%

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

      2. associate-/r/ 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in a around inf 68.5%

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

   if 1.3e164 < a < 1.35000000000000003e164

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf 4.7%

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

      1. associate--l+ 4.7%

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

      2. distribute-lft-out-- 4.7%

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

      3. div-sub 4.7%

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

      4. mul-1-neg 4.7%

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

      5. unsub-neg 4.7%

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

      6. distribute-rgt-out-- 4.7%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 4.7%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around 0 4.7%

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

       1. mul-1-neg 4.7%

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

       2. distribute-neg-frac 4.7%

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

       3. distribute-lft-neg-out 4.7%

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

       4. associate-*r/ 100.0%

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

       5. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(-a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-235} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-210}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-235) (not (<= t_1 5e-210)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-235) || !(t_1 <= 5e-210)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-235)) .or. (.not. (t_1 <= 5d-210))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-235) || !(t_1 <= 5e-210)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-235) or not (t_1 <= 5e-210):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-235) || !(t_1 <= 5e-210))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-235) || ~((t_1 <= 5e-210)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-235], N[Not[LessEqual[t$95$1, 5e-210]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-236 or 5.0000000000000002e-210 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

   if -9.9999999999999996e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-210

   1. Initial program 6.4%

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

   3. Taylor expanded in z around inf 73.6%

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

      1. associate--l+ 73.6%

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

      2. distribute-lft-out-- 73.6%

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

      3. div-sub 73.6%

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

      4. mul-1-neg 73.6%

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

      5. unsub-neg 73.6%

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

      6. distribute-rgt-out-- 73.6%

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

      7. associate-/l* 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-235} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -16000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= x -16000000000.0)
     t_1
     (if (<= x -2.4e-36)
       (+ t (/ (* x y) z))
       (if (<= x -2.9e-133)
         t_1
         (if (<= x 6e-23)
           t_2
           (if (<= x 1.06e+114)
             t_1
             (if (<= x 3.15e+156) t_2 (* (- t x) (/ (- a y) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -16000000000.0) {
		tmp = t_1;
	} else if (x <= -2.4e-36) {
		tmp = t + ((x * y) / z);
	} else if (x <= -2.9e-133) {
		tmp = t_1;
	} else if (x <= 6e-23) {
		tmp = t_2;
	} else if (x <= 1.06e+114) {
		tmp = t_1;
	} else if (x <= 3.15e+156) {
		tmp = t_2;
	} else {
		tmp = (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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (x <= (-16000000000.0d0)) then
        tmp = t_1
    else if (x <= (-2.4d-36)) then
        tmp = t + ((x * y) / z)
    else if (x <= (-2.9d-133)) then
        tmp = t_1
    else if (x <= 6d-23) then
        tmp = t_2
    else if (x <= 1.06d+114) then
        tmp = t_1
    else if (x <= 3.15d+156) then
        tmp = t_2
    else
        tmp = (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 + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -16000000000.0) {
		tmp = t_1;
	} else if (x <= -2.4e-36) {
		tmp = t + ((x * y) / z);
	} else if (x <= -2.9e-133) {
		tmp = t_1;
	} else if (x <= 6e-23) {
		tmp = t_2;
	} else if (x <= 1.06e+114) {
		tmp = t_1;
	} else if (x <= 3.15e+156) {
		tmp = t_2;
	} else {
		tmp = (t - x) * ((a - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -16000000000.0:
		tmp = t_1
	elif x <= -2.4e-36:
		tmp = t + ((x * y) / z)
	elif x <= -2.9e-133:
		tmp = t_1
	elif x <= 6e-23:
		tmp = t_2
	elif x <= 1.06e+114:
		tmp = t_1
	elif x <= 3.15e+156:
		tmp = t_2
	else:
		tmp = (t - x) * ((a - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -16000000000.0)
		tmp = t_1;
	elseif (x <= -2.4e-36)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (x <= -2.9e-133)
		tmp = t_1;
	elseif (x <= 6e-23)
		tmp = t_2;
	elseif (x <= 1.06e+114)
		tmp = t_1;
	elseif (x <= 3.15e+156)
		tmp = t_2;
	else
		tmp = 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 + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -16000000000.0)
		tmp = t_1;
	elseif (x <= -2.4e-36)
		tmp = t + ((x * y) / z);
	elseif (x <= -2.9e-133)
		tmp = t_1;
	elseif (x <= 6e-23)
		tmp = t_2;
	elseif (x <= 1.06e+114)
		tmp = t_1;
	elseif (x <= 3.15e+156)
		tmp = t_2;
	else
		tmp = (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[(t - x), $MachinePrecision] * 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[x, -16000000000.0], t$95$1, If[LessEqual[x, -2.4e-36], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e-133], t$95$1, If[LessEqual[x, 6e-23], t$95$2, If[LessEqual[x, 1.06e+114], t$95$1, If[LessEqual[x, 3.15e+156], t$95$2, N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e10 or -2.4e-36 < x < -2.8999999999999998e-133 or 6.00000000000000006e-23 < x < 1.05999999999999993e114

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 60.8%

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

      1. associate-/l* 63.8%

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

      2. associate-/r/ 67.0%

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

   5. Simplified 67.0%

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

   if -1.6e10 < x < -2.4e-36

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. distribute-lft-out-- 71.1%

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

      3. div-sub 71.1%

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

      4. mul-1-neg 71.1%

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

      5. unsub-neg 71.1%

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

      6. distribute-rgt-out-- 71.1%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 72.0%

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

   7. Taylor expanded in t around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-lft-neg-out 81.4%

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

      3. *-commutative 81.4%

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

   9. Simplified 81.4%

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

   if -2.8999999999999998e-133 < x < 6.00000000000000006e-23 or 1.05999999999999993e114 < x < 3.14999999999999991e156

   1. Initial program 83.9%

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

      1. associate-*r/ 75.2%

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

      2. clear-num 75.2%

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

   4. Applied egg-rr 75.2%

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

   5. Taylor expanded in x around 0 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-/l* 69.2%

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

      3. associate-/r/ 77.8%

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

      4. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   if 3.14999999999999991e156 < x

   1. Initial program 63.7%

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

   3. Taylor expanded in z around inf 38.6%

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

      1. associate--l+ 38.6%

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

      2. distribute-lft-out-- 38.6%

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

      3. div-sub 41.3%

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

      4. mul-1-neg 41.3%

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

      5. unsub-neg 41.3%

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

      6. distribute-rgt-out-- 41.3%

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

      7. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in z around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. *-commutative 31.6%

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

      3. associate-*l/ 52.4%

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

      4. distribute-lft-neg-in 52.4%

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

      5. distribute-neg-frac 52.4%

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

   8. Simplified 52.4%

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

   9. Taylor expanded in y around 0 52.4%

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

       1. +-commutative 52.4%

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

       2. mul-1-neg 52.4%

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

       3. sub-neg 52.4%

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

       4. div-sub 52.4%

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

   11. Simplified 52.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -19000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-34}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= x -19000000.0)
     t_2
     (if (<= x -1.6e-34)
       (+ t (/ (* x y) z))
       (if (<= x -9.2e-143)
         (+ x (/ y (/ a (- t x))))
         (if (<= x 1.7e-12)
           t_1
           (if (<= x 1.3e+114)
             t_2
             (if (<= x 3.15e+156) t_1 (* (- t x) (/ (- a y) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (x <= -19000000.0) {
		tmp = t_2;
	} else if (x <= -1.6e-34) {
		tmp = t + ((x * y) / z);
	} else if (x <= -9.2e-143) {
		tmp = x + (y / (a / (t - x)));
	} else if (x <= 1.7e-12) {
		tmp = t_1;
	} else if (x <= 1.3e+114) {
		tmp = t_2;
	} else if (x <= 3.15e+156) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) * (y / a))
    if (x <= (-19000000.0d0)) then
        tmp = t_2
    else if (x <= (-1.6d-34)) then
        tmp = t + ((x * y) / z)
    else if (x <= (-9.2d-143)) then
        tmp = x + (y / (a / (t - x)))
    else if (x <= 1.7d-12) then
        tmp = t_1
    else if (x <= 1.3d+114) then
        tmp = t_2
    else if (x <= 3.15d+156) then
        tmp = t_1
    else
        tmp = (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 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (x <= -19000000.0) {
		tmp = t_2;
	} else if (x <= -1.6e-34) {
		tmp = t + ((x * y) / z);
	} else if (x <= -9.2e-143) {
		tmp = x + (y / (a / (t - x)));
	} else if (x <= 1.7e-12) {
		tmp = t_1;
	} else if (x <= 1.3e+114) {
		tmp = t_2;
	} else if (x <= 3.15e+156) {
		tmp = t_1;
	} else {
		tmp = (t - x) * ((a - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if x <= -19000000.0:
		tmp = t_2
	elif x <= -1.6e-34:
		tmp = t + ((x * y) / z)
	elif x <= -9.2e-143:
		tmp = x + (y / (a / (t - x)))
	elif x <= 1.7e-12:
		tmp = t_1
	elif x <= 1.3e+114:
		tmp = t_2
	elif x <= 3.15e+156:
		tmp = t_1
	else:
		tmp = (t - x) * ((a - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (x <= -19000000.0)
		tmp = t_2;
	elseif (x <= -1.6e-34)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (x <= -9.2e-143)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (x <= 1.7e-12)
		tmp = t_1;
	elseif (x <= 1.3e+114)
		tmp = t_2;
	elseif (x <= 3.15e+156)
		tmp = t_1;
	else
		tmp = 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 = t * ((y - z) / (a - z));
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (x <= -19000000.0)
		tmp = t_2;
	elseif (x <= -1.6e-34)
		tmp = t + ((x * y) / z);
	elseif (x <= -9.2e-143)
		tmp = x + (y / (a / (t - x)));
	elseif (x <= 1.7e-12)
		tmp = t_1;
	elseif (x <= 1.3e+114)
		tmp = t_2;
	elseif (x <= 3.15e+156)
		tmp = t_1;
	else
		tmp = (t - x) * ((a - y) / z);
	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]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -19000000.0], t$95$2, If[LessEqual[x, -1.6e-34], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e-143], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-12], t$95$1, If[LessEqual[x, 1.3e+114], t$95$2, If[LessEqual[x, 3.15e+156], t$95$1, N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.9e7 or 1.7e-12 < x < 1.3e114

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 57.1%

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

      1. associate-/l* 60.6%

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

      2. associate-/r/ 64.5%

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

   5. Simplified 64.5%

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

   if -1.9e7 < x < -1.60000000000000001e-34

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. distribute-lft-out-- 71.1%

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

      3. div-sub 71.1%

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

      4. mul-1-neg 71.1%

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

      5. unsub-neg 71.1%

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

      6. distribute-rgt-out-- 71.1%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 72.0%

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

   7. Taylor expanded in t around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-lft-neg-out 81.4%

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

      3. *-commutative 81.4%

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

   9. Simplified 81.4%

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

   if -1.60000000000000001e-34 < x < -9.20000000000000045e-143

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 76.1%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if -9.20000000000000045e-143 < x < 1.7e-12 or 1.3e114 < x < 3.14999999999999991e156

   1. Initial program 83.8%

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

      1. associate-*r/ 75.9%

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

      2. clear-num 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in x around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/l* 68.9%

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

      3. associate-/r/ 77.6%

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

      4. *-commutative 77.6%

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

   7. Simplified 77.6%

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

   if 3.14999999999999991e156 < x

   1. Initial program 63.7%

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

   3. Taylor expanded in z around inf 38.6%

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

      1. associate--l+ 38.6%

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

      2. distribute-lft-out-- 38.6%

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

      3. div-sub 41.3%

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

      4. mul-1-neg 41.3%

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

      5. unsub-neg 41.3%

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

      6. distribute-rgt-out-- 41.3%

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

      7. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in z around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. *-commutative 31.6%

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

      3. associate-*l/ 52.4%

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

      4. distribute-lft-neg-in 52.4%

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

      5. distribute-neg-frac 52.4%

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

   8. Simplified 52.4%

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

   9. Taylor expanded in y around 0 52.4%

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

       1. +-commutative 52.4%

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

       2. mul-1-neg 52.4%

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

       3. sub-neg 52.4%

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

       4. div-sub 52.4%

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

   11. Simplified 52.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-34}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+114}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -40:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t a))))
   (if (<= a -2.8e+155)
     x
     (if (<= a -40.0)
       t_1
       (if (<= a 2.8e-242)
         (* t (- 1.0 (/ y z)))
         (if (<= a 6e-53)
           (* x (/ (- y a) z))
           (if (<= a 1.2e+38)
             t
             (if (<= a 6e+90) t_1 (if (<= a 1.25e+96) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -2.8e+155) {
		tmp = x;
	} else if (a <= -40.0) {
		tmp = t_1;
	} else if (a <= 2.8e-242) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 6e-53) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.2e+38) {
		tmp = t;
	} else if (a <= 6e+90) {
		tmp = t_1;
	} else if (a <= 1.25e+96) {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / a)
    if (a <= (-2.8d+155)) then
        tmp = x
    else if (a <= (-40.0d0)) then
        tmp = t_1
    else if (a <= 2.8d-242) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 6d-53) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.2d+38) then
        tmp = t
    else if (a <= 6d+90) then
        tmp = t_1
    else if (a <= 1.25d+96) then
        tmp = 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 t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -2.8e+155) {
		tmp = x;
	} else if (a <= -40.0) {
		tmp = t_1;
	} else if (a <= 2.8e-242) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 6e-53) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.2e+38) {
		tmp = t;
	} else if (a <= 6e+90) {
		tmp = t_1;
	} else if (a <= 1.25e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / a)
	tmp = 0
	if a <= -2.8e+155:
		tmp = x
	elif a <= -40.0:
		tmp = t_1
	elif a <= 2.8e-242:
		tmp = t * (1.0 - (y / z))
	elif a <= 6e-53:
		tmp = x * ((y - a) / z)
	elif a <= 1.2e+38:
		tmp = t
	elif a <= 6e+90:
		tmp = t_1
	elif a <= 1.25e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / a))
	tmp = 0.0
	if (a <= -2.8e+155)
		tmp = x;
	elseif (a <= -40.0)
		tmp = t_1;
	elseif (a <= 2.8e-242)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 6e-53)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.2e+38)
		tmp = t;
	elseif (a <= 6e+90)
		tmp = t_1;
	elseif (a <= 1.25e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / a);
	tmp = 0.0;
	if (a <= -2.8e+155)
		tmp = x;
	elseif (a <= -40.0)
		tmp = t_1;
	elseif (a <= 2.8e-242)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 6e-53)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.2e+38)
		tmp = t;
	elseif (a <= 6e+90)
		tmp = t_1;
	elseif (a <= 1.25e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+155], x, If[LessEqual[a, -40.0], t$95$1, If[LessEqual[a, 2.8e-242], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-53], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+38], t, If[LessEqual[a, 6e+90], t$95$1, If[LessEqual[a, 1.25e+96], t, x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.80000000000000016e155 or 1.2500000000000001e96 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 58.9%

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

   if -2.80000000000000016e155 < a < -40 or 1.20000000000000009e38 < a < 5.99999999999999957e90

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 38.5%

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

      1. associate-/l* 48.1%

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

      2. associate-/r/ 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in a around inf 39.3%

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

   if -40 < a < 2.79999999999999983e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 65.3%

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

   if 2.79999999999999983e-242 < a < 6.0000000000000004e-53

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 6.0000000000000004e-53 < a < 1.20000000000000009e38 or 5.99999999999999957e90 < a < 1.2500000000000001e96

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf 59.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -40:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+90}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.36 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -88:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t a))))
   (if (<= a -1.36e+157)
     x
     (if (<= a -88.0)
       t_1
       (if (<= a 2.7e-242)
         (- t (/ t (/ z y)))
         (if (<= a 5.4e-49)
           (* x (/ (- y a) z))
           (if (<= a 1.2e+38)
             t
             (if (<= a 6e+90) t_1 (if (<= a 1.2e+96) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -1.36e+157) {
		tmp = x;
	} else if (a <= -88.0) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 5.4e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.2e+38) {
		tmp = t;
	} else if (a <= 6e+90) {
		tmp = t_1;
	} else if (a <= 1.2e+96) {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / a)
    if (a <= (-1.36d+157)) then
        tmp = x
    else if (a <= (-88.0d0)) then
        tmp = t_1
    else if (a <= 2.7d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 5.4d-49) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.2d+38) then
        tmp = t
    else if (a <= 6d+90) then
        tmp = t_1
    else if (a <= 1.2d+96) then
        tmp = 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 t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -1.36e+157) {
		tmp = x;
	} else if (a <= -88.0) {
		tmp = t_1;
	} else if (a <= 2.7e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 5.4e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.2e+38) {
		tmp = t;
	} else if (a <= 6e+90) {
		tmp = t_1;
	} else if (a <= 1.2e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / a)
	tmp = 0
	if a <= -1.36e+157:
		tmp = x
	elif a <= -88.0:
		tmp = t_1
	elif a <= 2.7e-242:
		tmp = t - (t / (z / y))
	elif a <= 5.4e-49:
		tmp = x * ((y - a) / z)
	elif a <= 1.2e+38:
		tmp = t
	elif a <= 6e+90:
		tmp = t_1
	elif a <= 1.2e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / a))
	tmp = 0.0
	if (a <= -1.36e+157)
		tmp = x;
	elseif (a <= -88.0)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 5.4e-49)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.2e+38)
		tmp = t;
	elseif (a <= 6e+90)
		tmp = t_1;
	elseif (a <= 1.2e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / a);
	tmp = 0.0;
	if (a <= -1.36e+157)
		tmp = x;
	elseif (a <= -88.0)
		tmp = t_1;
	elseif (a <= 2.7e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 5.4e-49)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.2e+38)
		tmp = t;
	elseif (a <= 6e+90)
		tmp = t_1;
	elseif (a <= 1.2e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.36e+157], x, If[LessEqual[a, -88.0], t$95$1, If[LessEqual[a, 2.7e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-49], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+38], t, If[LessEqual[a, 6e+90], t$95$1, If[LessEqual[a, 1.2e+96], t, x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.36e157 or 1.19999999999999996e96 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 58.9%

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

   if -1.36e157 < a < -88 or 1.20000000000000009e38 < a < 5.99999999999999957e90

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 38.5%

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

      1. associate-/l* 48.1%

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

      2. associate-/r/ 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in a around inf 39.3%

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

   if -88 < a < 2.7e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 2.7e-242 < a < 5.3999999999999999e-49

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 5.3999999999999999e-49 < a < 1.20000000000000009e38 or 5.99999999999999957e90 < a < 1.19999999999999996e96

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf 59.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -88:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+90}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -43:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+155)
   x
   (if (<= a -43.0)
     (* (- y z) (/ t a))
     (if (<= a 1.65e-242)
       (- t (/ t (/ z y)))
       (if (<= a 5.8e-49)
         (* x (/ (- y a) z))
         (if (<= a 1.25e+38)
           t
           (if (<= a 2.9e+91)
             (/ t (/ a (- y z)))
             (if (<= a 1.12e+96) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+155) {
		tmp = x;
	} else if (a <= -43.0) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.65e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 5.8e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.25e+38) {
		tmp = t;
	} else if (a <= 2.9e+91) {
		tmp = t / (a / (y - z));
	} else if (a <= 1.12e+96) {
		tmp = 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 (a <= (-2.5d+155)) then
        tmp = x
    else if (a <= (-43.0d0)) then
        tmp = (y - z) * (t / a)
    else if (a <= 1.65d-242) then
        tmp = t - (t / (z / y))
    else if (a <= 5.8d-49) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.25d+38) then
        tmp = t
    else if (a <= 2.9d+91) then
        tmp = t / (a / (y - z))
    else if (a <= 1.12d+96) then
        tmp = 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 (a <= -2.5e+155) {
		tmp = x;
	} else if (a <= -43.0) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.65e-242) {
		tmp = t - (t / (z / y));
	} else if (a <= 5.8e-49) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.25e+38) {
		tmp = t;
	} else if (a <= 2.9e+91) {
		tmp = t / (a / (y - z));
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+155:
		tmp = x
	elif a <= -43.0:
		tmp = (y - z) * (t / a)
	elif a <= 1.65e-242:
		tmp = t - (t / (z / y))
	elif a <= 5.8e-49:
		tmp = x * ((y - a) / z)
	elif a <= 1.25e+38:
		tmp = t
	elif a <= 2.9e+91:
		tmp = t / (a / (y - z))
	elif a <= 1.12e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+155)
		tmp = x;
	elseif (a <= -43.0)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= 1.65e-242)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 5.8e-49)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.25e+38)
		tmp = t;
	elseif (a <= 2.9e+91)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+155)
		tmp = x;
	elseif (a <= -43.0)
		tmp = (y - z) * (t / a);
	elseif (a <= 1.65e-242)
		tmp = t - (t / (z / y));
	elseif (a <= 5.8e-49)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.25e+38)
		tmp = t;
	elseif (a <= 2.9e+91)
		tmp = t / (a / (y - z));
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+155], x, If[LessEqual[a, -43.0], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-242], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-49], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+38], t, If[LessEqual[a, 2.9e+91], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+96], t, x]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.5e155 or 1.1199999999999999e96 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 58.9%

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

   if -2.5e155 < a < -43

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 35.4%

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

      1. associate-/l* 47.9%

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

      2. associate-/r/ 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in a around inf 37.6%

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

   if -43 < a < 1.64999999999999991e-242

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 75.0%

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

   7. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   if 1.64999999999999991e-242 < a < 5.8e-49

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 5.8e-49 < a < 1.24999999999999992e38 or 2.90000000000000014e91 < a < 1.1199999999999999e96

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 62.5%

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

   if 1.24999999999999992e38 < a < 2.90000000000000014e91

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 45.4%

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

      1. associate-/l* 45.9%

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

      2. associate-/r/ 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -43:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-242}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4e+99)
   x
   (if (<= a 2.75e-242)
     (* t (- 1.0 (/ y z)))
     (if (<= a 4.6e-48)
       (* x (/ (- y a) z))
       (if (<= a 1.9e+38)
         t
         (if (<= a 1.15e+91) (* t (/ y (- a z))) (if (<= a 1.55e+96) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e+99) {
		tmp = x;
	} else if (a <= 2.75e-242) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 4.6e-48) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.9e+38) {
		tmp = t;
	} else if (a <= 1.15e+91) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.55e+96) {
		tmp = 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 (a <= (-4d+99)) then
        tmp = x
    else if (a <= 2.75d-242) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 4.6d-48) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.9d+38) then
        tmp = t
    else if (a <= 1.15d+91) then
        tmp = t * (y / (a - z))
    else if (a <= 1.55d+96) then
        tmp = 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 (a <= -4e+99) {
		tmp = x;
	} else if (a <= 2.75e-242) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 4.6e-48) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.9e+38) {
		tmp = t;
	} else if (a <= 1.15e+91) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.55e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4e+99:
		tmp = x
	elif a <= 2.75e-242:
		tmp = t * (1.0 - (y / z))
	elif a <= 4.6e-48:
		tmp = x * ((y - a) / z)
	elif a <= 1.9e+38:
		tmp = t
	elif a <= 1.15e+91:
		tmp = t * (y / (a - z))
	elif a <= 1.55e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4e+99)
		tmp = x;
	elseif (a <= 2.75e-242)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 4.6e-48)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.9e+38)
		tmp = t;
	elseif (a <= 1.15e+91)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 1.55e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4e+99)
		tmp = x;
	elseif (a <= 2.75e-242)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 4.6e-48)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.9e+38)
		tmp = t;
	elseif (a <= 1.15e+91)
		tmp = t * (y / (a - z));
	elseif (a <= 1.55e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4e+99], x, If[LessEqual[a, 2.75e-242], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-48], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+38], t, If[LessEqual[a, 1.15e+91], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+96], t, x]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.9999999999999999e99 or 1.5499999999999999e96 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 53.7%

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

   if -3.9999999999999999e99 < a < 2.7499999999999999e-242

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. distribute-lft-out-- 64.7%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. distribute-rgt-out-- 65.8%

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

      7. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in y around inf 62.7%

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

   7. Taylor expanded in t around inf 53.7%

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

   if 2.7499999999999999e-242 < a < 4.6000000000000001e-48

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. distribute-rgt-out-- 72.6%

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

      7. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 51.3%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in x around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. times-frac 51.3%

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

       3. /-rgt-identity 51.3%

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

   11. Simplified 51.3%

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

   if 4.6000000000000001e-48 < a < 1.8999999999999999e38 or 1.14999999999999996e91 < a < 1.5499999999999999e96

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 62.5%

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

   if 1.8999999999999999e38 < a < 1.14999999999999996e91

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. div-sub 51.9%

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

      2. associate-*r/ 51.8%

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

      3. associate-/l* 51.7%

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

      4. associate-/r/ 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in t around inf 39.3%

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

      1. associate-*r/ 39.2%

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

   8. Simplified 39.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.85:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-245}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))))
   (if (<= a -2.2e+106)
     x
     (if (<= a -1.85)
       t_1
       (if (<= a 2.5e-245)
         (- t (/ t (/ z y)))
         (if (<= a 1.65e+38)
           (+ t (/ (* x y) z))
           (if (<= a 2.95e+91) t_1 (if (<= a 1.12e+96) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -2.2e+106) {
		tmp = x;
	} else if (a <= -1.85) {
		tmp = t_1;
	} else if (a <= 2.5e-245) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.65e+38) {
		tmp = t + ((x * y) / z);
	} else if (a <= 2.95e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y / (a / (t - x))
    if (a <= (-2.2d+106)) then
        tmp = x
    else if (a <= (-1.85d0)) then
        tmp = t_1
    else if (a <= 2.5d-245) then
        tmp = t - (t / (z / y))
    else if (a <= 1.65d+38) then
        tmp = t + ((x * y) / z)
    else if (a <= 2.95d+91) then
        tmp = t_1
    else if (a <= 1.12d+96) then
        tmp = 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 t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -2.2e+106) {
		tmp = x;
	} else if (a <= -1.85) {
		tmp = t_1;
	} else if (a <= 2.5e-245) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.65e+38) {
		tmp = t + ((x * y) / z);
	} else if (a <= 2.95e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	tmp = 0
	if a <= -2.2e+106:
		tmp = x
	elif a <= -1.85:
		tmp = t_1
	elif a <= 2.5e-245:
		tmp = t - (t / (z / y))
	elif a <= 1.65e+38:
		tmp = t + ((x * y) / z)
	elif a <= 2.95e+91:
		tmp = t_1
	elif a <= 1.12e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	tmp = 0.0
	if (a <= -2.2e+106)
		tmp = x;
	elseif (a <= -1.85)
		tmp = t_1;
	elseif (a <= 2.5e-245)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 1.65e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (a <= 2.95e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	tmp = 0.0;
	if (a <= -2.2e+106)
		tmp = x;
	elseif (a <= -1.85)
		tmp = t_1;
	elseif (a <= 2.5e-245)
		tmp = t - (t / (z / y));
	elseif (a <= 1.65e+38)
		tmp = t + ((x * y) / z);
	elseif (a <= 2.95e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+106], x, If[LessEqual[a, -1.85], t$95$1, If[LessEqual[a, 2.5e-245], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.95e+91], t$95$1, If[LessEqual[a, 1.12e+96], t, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.19999999999999992e106 or 1.1199999999999999e96 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 54.8%

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

   if -2.19999999999999992e106 < a < -1.8500000000000001 or 1.65e38 < a < 2.9500000000000001e91

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. div-sub 57.3%

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

      2. associate-*r/ 53.4%

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

      3. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in a around inf 49.1%

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

   if -1.8500000000000001 < a < 2.4999999999999998e-245

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. distribute-lft-out-- 77.2%

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

      3. div-sub 78.7%

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

      4. mul-1-neg 78.7%

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

      5. unsub-neg 78.7%

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

      6. distribute-rgt-out-- 78.7%

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

      7. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around inf 74.7%

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

   7. Taylor expanded in t around inf 60.8%

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

      1. associate-/l* 64.8%

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

   9. Simplified 64.8%

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

   if 2.4999999999999998e-245 < a < 1.65e38

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. distribute-lft-out-- 68.3%

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

      3. div-sub 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-out-- 68.3%

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

      7. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in y around inf 63.0%

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

   7. Taylor expanded in t around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. distribute-lft-neg-out 63.1%

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

      3. *-commutative 63.1%

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

   9. Simplified 63.1%

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

   if 2.9500000000000001e91 < a < 1.1199999999999999e96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.85:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-245}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -42:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))))
   (if (<= a -1.4e+110)
     x
     (if (<= a -42.0)
       t_1
       (if (<= a 2.5e-245)
         (* t (+ (/ (- a y) z) 1.0))
         (if (<= a 2.3e+38)
           (+ t (/ (* x y) z))
           (if (<= a 3.5e+91) t_1 (if (<= a 1.46e+96) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -1.4e+110) {
		tmp = x;
	} else if (a <= -42.0) {
		tmp = t_1;
	} else if (a <= 2.5e-245) {
		tmp = t * (((a - y) / z) + 1.0);
	} else if (a <= 2.3e+38) {
		tmp = t + ((x * y) / z);
	} else if (a <= 3.5e+91) {
		tmp = t_1;
	} else if (a <= 1.46e+96) {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y / (a / (t - x))
    if (a <= (-1.4d+110)) then
        tmp = x
    else if (a <= (-42.0d0)) then
        tmp = t_1
    else if (a <= 2.5d-245) then
        tmp = t * (((a - y) / z) + 1.0d0)
    else if (a <= 2.3d+38) then
        tmp = t + ((x * y) / z)
    else if (a <= 3.5d+91) then
        tmp = t_1
    else if (a <= 1.46d+96) then
        tmp = 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 t_1 = y / (a / (t - x));
	double tmp;
	if (a <= -1.4e+110) {
		tmp = x;
	} else if (a <= -42.0) {
		tmp = t_1;
	} else if (a <= 2.5e-245) {
		tmp = t * (((a - y) / z) + 1.0);
	} else if (a <= 2.3e+38) {
		tmp = t + ((x * y) / z);
	} else if (a <= 3.5e+91) {
		tmp = t_1;
	} else if (a <= 1.46e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	tmp = 0
	if a <= -1.4e+110:
		tmp = x
	elif a <= -42.0:
		tmp = t_1
	elif a <= 2.5e-245:
		tmp = t * (((a - y) / z) + 1.0)
	elif a <= 2.3e+38:
		tmp = t + ((x * y) / z)
	elif a <= 3.5e+91:
		tmp = t_1
	elif a <= 1.46e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	tmp = 0.0
	if (a <= -1.4e+110)
		tmp = x;
	elseif (a <= -42.0)
		tmp = t_1;
	elseif (a <= 2.5e-245)
		tmp = Float64(t * Float64(Float64(Float64(a - y) / z) + 1.0));
	elseif (a <= 2.3e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (a <= 3.5e+91)
		tmp = t_1;
	elseif (a <= 1.46e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	tmp = 0.0;
	if (a <= -1.4e+110)
		tmp = x;
	elseif (a <= -42.0)
		tmp = t_1;
	elseif (a <= 2.5e-245)
		tmp = t * (((a - y) / z) + 1.0);
	elseif (a <= 2.3e+38)
		tmp = t + ((x * y) / z);
	elseif (a <= 3.5e+91)
		tmp = t_1;
	elseif (a <= 1.46e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+110], x, If[LessEqual[a, -42.0], t$95$1, If[LessEqual[a, 2.5e-245], N[(t * N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+91], t$95$1, If[LessEqual[a, 1.46e+96], t, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999993e110 or 1.4600000000000001e96 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 54.8%

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

   if -1.39999999999999993e110 < a < -42 or 2.3000000000000001e38 < a < 3.50000000000000001e91

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. div-sub 57.3%

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

      2. associate-*r/ 53.4%

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

      3. associate-/l* 57.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

   6. Taylor expanded in a around inf 49.1%

      \[\leadsto \frac{y}{\color{blue}{\frac{a}{t - x}}} \]

   if -42 < a < 2.4999999999999998e-245

   1. Initial program 70.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 77.2%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 78.7%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 78.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 78.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 78.7%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 80.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around -inf 64.8%

      \[\leadsto \color{blue}{t \cdot \left(1 + -1 \cdot \frac{y - a}{z}\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 64.8%

         \[\leadsto t \cdot \left(1 + \color{blue}{\left(-\frac{y - a}{z}\right)}\right) \]

      2. unsub-neg 64.8%

         \[\leadsto t \cdot \color{blue}{\left(1 - \frac{y - a}{z}\right)} \]

   8. Simplified 64.8%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y - a}{z}\right)} \]

   if 2.4999999999999998e-245 < a < 2.3000000000000001e38

   1. Initial program 69.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 68.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 68.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 68.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 68.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 68.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 68.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 76.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 76.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 63.0%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around 0 63.1%

      \[\leadsto t - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{z} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.1%

         \[\leadsto t - \frac{\color{blue}{-x \cdot y}}{z} \]

      2. distribute-lft-neg-out 63.1%

         \[\leadsto t - \frac{\color{blue}{\left(-x\right) \cdot y}}{z} \]

      3. *-commutative 63.1%

         \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   9. Simplified 63.1%

      \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   if 3.50000000000000001e91 < a < 1.4600000000000001e96

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -42:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1100000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-222}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+106)
   x
   (if (<= a -2.6e+58)
     (/ t (/ a y))
     (if (<= a -1100000000.0)
       x
       (if (<= a 3.6e-222)
         t
         (if (<= a 2.5e-42) (* y (/ x z)) (if (<= a 1.35e+38) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+106) {
		tmp = x;
	} else if (a <= -2.6e+58) {
		tmp = t / (a / y);
	} else if (a <= -1100000000.0) {
		tmp = x;
	} else if (a <= 3.6e-222) {
		tmp = t;
	} else if (a <= 2.5e-42) {
		tmp = y * (x / z);
	} else if (a <= 1.35e+38) {
		tmp = 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 (a <= (-1.15d+106)) then
        tmp = x
    else if (a <= (-2.6d+58)) then
        tmp = t / (a / y)
    else if (a <= (-1100000000.0d0)) then
        tmp = x
    else if (a <= 3.6d-222) then
        tmp = t
    else if (a <= 2.5d-42) then
        tmp = y * (x / z)
    else if (a <= 1.35d+38) then
        tmp = 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 (a <= -1.15e+106) {
		tmp = x;
	} else if (a <= -2.6e+58) {
		tmp = t / (a / y);
	} else if (a <= -1100000000.0) {
		tmp = x;
	} else if (a <= 3.6e-222) {
		tmp = t;
	} else if (a <= 2.5e-42) {
		tmp = y * (x / z);
	} else if (a <= 1.35e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+106:
		tmp = x
	elif a <= -2.6e+58:
		tmp = t / (a / y)
	elif a <= -1100000000.0:
		tmp = x
	elif a <= 3.6e-222:
		tmp = t
	elif a <= 2.5e-42:
		tmp = y * (x / z)
	elif a <= 1.35e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+106)
		tmp = x;
	elseif (a <= -2.6e+58)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -1100000000.0)
		tmp = x;
	elseif (a <= 3.6e-222)
		tmp = t;
	elseif (a <= 2.5e-42)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 1.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+106)
		tmp = x;
	elseif (a <= -2.6e+58)
		tmp = t / (a / y);
	elseif (a <= -1100000000.0)
		tmp = x;
	elseif (a <= 3.6e-222)
		tmp = t;
	elseif (a <= 2.5e-42)
		tmp = y * (x / z);
	elseif (a <= 1.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+106], x, If[LessEqual[a, -2.6e+58], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1100000000.0], x, If[LessEqual[a, 3.6e-222], t, If[LessEqual[a, 2.5e-42], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+38], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1500000000000001e106 or -2.59999999999999988e58 < a < -1.1e9 or 1.34999999999999998e38 < a

   1. Initial program 85.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{x} \]

   if -1.1500000000000001e106 < a < -2.59999999999999988e58

   1. Initial program 93.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

      2. associate-/r/ 64.8%

         \[\leadsto \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

   6. Taylor expanded in z around 0 37.7%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 38.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -1.1e9 < a < 3.59999999999999974e-222 or 2.50000000000000001e-42 < a < 1.34999999999999998e38

   1. Initial program 70.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.6%

      \[\leadsto \color{blue}{t} \]

   if 3.59999999999999974e-222 < a < 2.50000000000000001e-42

   1. Initial program 71.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 65.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 65.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 65.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 65.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 65.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 72.3%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 47.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 48.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 47.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   8. Simplified 47.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Taylor expanded in y around inf 41.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. associate-*l/ 41.6%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

       2. *-commutative 41.6%

          \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   11. Simplified 41.6%

       \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1100000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-222}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -13000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e+110)
   x
   (if (<= a -7.2e+56)
     (/ t (/ a y))
     (if (<= a -13000000000000.0)
       x
       (if (<= a 2.4e-244)
         t
         (if (<= a 1.65e-46) (/ (* x y) z) (if (<= a 2.4e+38) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+110) {
		tmp = x;
	} else if (a <= -7.2e+56) {
		tmp = t / (a / y);
	} else if (a <= -13000000000000.0) {
		tmp = x;
	} else if (a <= 2.4e-244) {
		tmp = t;
	} else if (a <= 1.65e-46) {
		tmp = (x * y) / z;
	} else if (a <= 2.4e+38) {
		tmp = 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 (a <= (-1.8d+110)) then
        tmp = x
    else if (a <= (-7.2d+56)) then
        tmp = t / (a / y)
    else if (a <= (-13000000000000.0d0)) then
        tmp = x
    else if (a <= 2.4d-244) then
        tmp = t
    else if (a <= 1.65d-46) then
        tmp = (x * y) / z
    else if (a <= 2.4d+38) then
        tmp = 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 (a <= -1.8e+110) {
		tmp = x;
	} else if (a <= -7.2e+56) {
		tmp = t / (a / y);
	} else if (a <= -13000000000000.0) {
		tmp = x;
	} else if (a <= 2.4e-244) {
		tmp = t;
	} else if (a <= 1.65e-46) {
		tmp = (x * y) / z;
	} else if (a <= 2.4e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e+110:
		tmp = x
	elif a <= -7.2e+56:
		tmp = t / (a / y)
	elif a <= -13000000000000.0:
		tmp = x
	elif a <= 2.4e-244:
		tmp = t
	elif a <= 1.65e-46:
		tmp = (x * y) / z
	elif a <= 2.4e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e+110)
		tmp = x;
	elseif (a <= -7.2e+56)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -13000000000000.0)
		tmp = x;
	elseif (a <= 2.4e-244)
		tmp = t;
	elseif (a <= 1.65e-46)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.4e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e+110)
		tmp = x;
	elseif (a <= -7.2e+56)
		tmp = t / (a / y);
	elseif (a <= -13000000000000.0)
		tmp = x;
	elseif (a <= 2.4e-244)
		tmp = t;
	elseif (a <= 1.65e-46)
		tmp = (x * y) / z;
	elseif (a <= 2.4e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e+110], x, If[LessEqual[a, -7.2e+56], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -13000000000000.0], x, If[LessEqual[a, 2.4e-244], t, If[LessEqual[a, 1.65e-46], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.4e+38], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7999999999999998e110 or -7.19999999999999996e56 < a < -1.3e13 or 2.40000000000000017e38 < a

   1. Initial program 85.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{x} \]

   if -1.7999999999999998e110 < a < -7.19999999999999996e56

   1. Initial program 93.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

      2. associate-/r/ 64.8%

         \[\leadsto \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{t}{a - z} \cdot \left(y - z\right)} \]

   6. Taylor expanded in z around 0 37.7%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 38.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -1.3e13 < a < 2.40000000000000016e-244 or 1.65000000000000007e-46 < a < 2.40000000000000017e38

   1. Initial program 72.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.7%

      \[\leadsto \color{blue}{t} \]

   if 2.40000000000000016e-244 < a < 1.65000000000000007e-46

   1. Initial program 66.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.6%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 70.6%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 70.6%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 70.6%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 70.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 70.6%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 70.6%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 76.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 50.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 50.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 44.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   8. Simplified 44.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Taylor expanded in y around inf 41.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -13000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -0.97:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-80}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -0.97)
     t_1
     (if (<= a 5.6e-124)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 1.9e-80)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 1.18e+38) (+ t (/ (* x y) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -0.97) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.9e-80) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1.18e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / a))
    if (a <= (-0.97d0)) then
        tmp = t_1
    else if (a <= 5.6d-124) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.9d-80) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 1.18d+38) then
        tmp = t + ((x * y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -0.97) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.9e-80) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1.18e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -0.97:
		tmp = t_1
	elif a <= 5.6e-124:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.9e-80:
		tmp = x + ((t - x) * (y / a))
	elif a <= 1.18e+38:
		tmp = t + ((x * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -0.97)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.9e-80)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 1.18e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -0.97)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.9e-80)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 1.18e+38)
		tmp = t + ((x * y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.97], t$95$1, If[LessEqual[a, 5.6e-124], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-80], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.96999999999999997 or 1.18e38 < a

   1. Initial program 86.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 76.1%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}} \]

   if -0.96999999999999997 < a < 5.59999999999999996e-124

   1. Initial program 68.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 79.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 79.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 80.6%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 80.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 80.6%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 80.6%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 84.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 75.5%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   if 5.59999999999999996e-124 < a < 1.89999999999999983e-80

   1. Initial program 87.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.8%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 98.2%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]

   if 1.89999999999999983e-80 < a < 1.18e38

   1. Initial program 70.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 66.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 61.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around 0 66.6%

      \[\leadsto t - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{z} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.6%

         \[\leadsto t - \frac{\color{blue}{-x \cdot y}}{z} \]

      2. distribute-lft-neg-out 66.6%

         \[\leadsto t - \frac{\color{blue}{\left(-x\right) \cdot y}}{z} \]

      3. *-commutative 66.6%

         \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   9. Simplified 66.6%

      \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.97:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-80}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 69.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -5.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- x t) (/ (- z y) a)))))
   (if (<= a -5.3)
     t_1
     (if (<= a 5.6e-124)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 7.4e-82)
         t_1
         (if (<= a 1.18e+38)
           (+ t (/ (* x y) z))
           (+ x (* (- y z) (/ (- t x) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -5.3) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 7.4e-82) {
		tmp = t_1;
	} else if (a <= 1.18e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * ((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) :: t_1
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / a))
    if (a <= (-5.3d0)) then
        tmp = t_1
    else if (a <= 5.6d-124) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 7.4d-82) then
        tmp = t_1
    else if (a <= 1.18d+38) then
        tmp = t + ((x * y) / z)
    else
        tmp = x + ((y - z) * ((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 t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -5.3) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 7.4e-82) {
		tmp = t_1;
	} else if (a <= 1.18e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / a))
	tmp = 0
	if a <= -5.3:
		tmp = t_1
	elif a <= 5.6e-124:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 7.4e-82:
		tmp = t_1
	elif a <= 1.18e+38:
		tmp = t + ((x * y) / z)
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -5.3)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 7.4e-82)
		tmp = t_1;
	elseif (a <= 1.18e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -5.3)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 7.4e-82)
		tmp = t_1;
	elseif (a <= 1.18e+38)
		tmp = t + ((x * y) / z);
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3], t$95$1, If[LessEqual[a, 5.6e-124], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e-82], t$95$1, If[LessEqual[a, 1.18e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.29999999999999982 or 5.59999999999999996e-124 < a < 7.4000000000000002e-82

   1. Initial program 88.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.5%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. div-sub 75.5%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      3. associate-*r/ 67.8%

         \[\leadsto x + \left(\color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      4. mul-1-neg 67.8%

         \[\leadsto x + \left(\frac{y \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      5. sub-neg 67.8%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{a - z} - \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      6. associate-/l* 75.5%

         \[\leadsto x + \left(\color{blue}{\frac{y}{\frac{a - z}{t - x}}} - \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      7. associate-/l* 88.1%

         \[\leadsto x + \left(\frac{y}{\frac{a - z}{t - x}} - \color{blue}{\frac{z}{\frac{a - z}{t - x}}}\right) \]

      8. div-sub 88.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

      9. associate-/r/ 91.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 91.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   6. Taylor expanded in a around inf 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{a}} \cdot \left(t - x\right) \]

   if -5.29999999999999982 < a < 5.59999999999999996e-124

   1. Initial program 68.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 79.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 79.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 80.6%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 80.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 80.6%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 80.6%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 84.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 75.5%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   if 7.4000000000000002e-82 < a < 1.18e38

   1. Initial program 70.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 66.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 61.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around 0 66.6%

      \[\leadsto t - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{z} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.6%

         \[\leadsto t - \frac{\color{blue}{-x \cdot y}}{z} \]

      2. distribute-lft-neg-out 66.6%

         \[\leadsto t - \frac{\color{blue}{\left(-x\right) \cdot y}}{z} \]

      3. *-commutative 66.6%

         \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   9. Simplified 66.6%

      \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   if 1.18e38 < a

   1. Initial program 84.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 75.0%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-82}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -70:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- x t) (/ (- z y) a)))))
   (if (<= a -70.0)
     t_1
     (if (<= a 5.3e-124)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= a 2.1e-82)
         t_1
         (if (<= a 1.55e+38)
           (+ t (/ (* x y) z))
           (+ x (* (- y z) (/ (- t x) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -70.0) {
		tmp = t_1;
	} else if (a <= 5.3e-124) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 2.1e-82) {
		tmp = t_1;
	} else if (a <= 1.55e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * ((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) :: t_1
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / a))
    if (a <= (-70.0d0)) then
        tmp = t_1
    else if (a <= 5.3d-124) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (a <= 2.1d-82) then
        tmp = t_1
    else if (a <= 1.55d+38) then
        tmp = t + ((x * y) / z)
    else
        tmp = x + ((y - z) * ((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 t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -70.0) {
		tmp = t_1;
	} else if (a <= 5.3e-124) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 2.1e-82) {
		tmp = t_1;
	} else if (a <= 1.55e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / a))
	tmp = 0
	if a <= -70.0:
		tmp = t_1
	elif a <= 5.3e-124:
		tmp = t + (((t - x) * (a - y)) / z)
	elif a <= 2.1e-82:
		tmp = t_1
	elif a <= 1.55e+38:
		tmp = t + ((x * y) / z)
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -70.0)
		tmp = t_1;
	elseif (a <= 5.3e-124)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (a <= 2.1e-82)
		tmp = t_1;
	elseif (a <= 1.55e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -70.0)
		tmp = t_1;
	elseif (a <= 5.3e-124)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (a <= 2.1e-82)
		tmp = t_1;
	elseif (a <= 1.55e+38)
		tmp = t + ((x * y) / z);
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -70.0], t$95$1, If[LessEqual[a, 5.3e-124], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-82], t$95$1, If[LessEqual[a, 1.55e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -70 or 5.2999999999999997e-124 < a < 2.1e-82

   1. Initial program 88.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.5%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. div-sub 75.5%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      3. associate-*r/ 67.8%

         \[\leadsto x + \left(\color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      4. mul-1-neg 67.8%

         \[\leadsto x + \left(\frac{y \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      5. sub-neg 67.8%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{a - z} - \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      6. associate-/l* 75.5%

         \[\leadsto x + \left(\color{blue}{\frac{y}{\frac{a - z}{t - x}}} - \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      7. associate-/l* 88.1%

         \[\leadsto x + \left(\frac{y}{\frac{a - z}{t - x}} - \color{blue}{\frac{z}{\frac{a - z}{t - x}}}\right) \]

      8. div-sub 88.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

      9. associate-/r/ 91.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 91.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   6. Taylor expanded in a around inf 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{a}} \cdot \left(t - x\right) \]

   if -70 < a < 5.2999999999999997e-124

   1. Initial program 68.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 79.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 79.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 80.6%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 80.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 80.6%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 80.6%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 84.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in z around 0 80.6%

      \[\leadsto t - \color{blue}{\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   if 2.1e-82 < a < 1.55000000000000009e38

   1. Initial program 70.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 66.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 61.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around 0 66.6%

      \[\leadsto t - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{z} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.6%

         \[\leadsto t - \frac{\color{blue}{-x \cdot y}}{z} \]

      2. distribute-lft-neg-out 66.6%

         \[\leadsto t - \frac{\color{blue}{\left(-x\right) \cdot y}}{z} \]

      3. *-commutative 66.6%

         \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   9. Simplified 66.6%

      \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   if 1.55000000000000009e38 < a

   1. Initial program 84.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 75.0%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -70:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ t_2 := x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -30.5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a)))))
        (t_2 (+ x (* (- x t) (/ (- z y) a)))))
   (if (<= a -30.5)
     t_2
     (if (<= a 1.1e-124)
       t_1
       (if (<= a 1.65e-85)
         t_2
         (if (<= a 6.2e+28) t_1 (+ x (* (- y z) (/ (- t x) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -30.5) {
		tmp = t_2;
	} else if (a <= 1.1e-124) {
		tmp = t_1;
	} else if (a <= 1.65e-85) {
		tmp = t_2;
	} else if (a <= 6.2e+28) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    t_2 = x + ((x - t) * ((z - y) / a))
    if (a <= (-30.5d0)) then
        tmp = t_2
    else if (a <= 1.1d-124) then
        tmp = t_1
    else if (a <= 1.65d-85) then
        tmp = t_2
    else if (a <= 6.2d+28) then
        tmp = t_1
    else
        tmp = x + ((y - z) * ((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 t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -30.5) {
		tmp = t_2;
	} else if (a <= 1.1e-124) {
		tmp = t_1;
	} else if (a <= 1.65e-85) {
		tmp = t_2;
	} else if (a <= 6.2e+28) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	t_2 = x + ((x - t) * ((z - y) / a))
	tmp = 0
	if a <= -30.5:
		tmp = t_2
	elif a <= 1.1e-124:
		tmp = t_1
	elif a <= 1.65e-85:
		tmp = t_2
	elif a <= 6.2e+28:
		tmp = t_1
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	t_2 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -30.5)
		tmp = t_2;
	elseif (a <= 1.1e-124)
		tmp = t_1;
	elseif (a <= 1.65e-85)
		tmp = t_2;
	elseif (a <= 6.2e+28)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	t_2 = x + ((x - t) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -30.5)
		tmp = t_2;
	elseif (a <= 1.1e-124)
		tmp = t_1;
	elseif (a <= 1.65e-85)
		tmp = t_2;
	elseif (a <= 6.2e+28)
		tmp = t_1;
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -30.5], t$95$2, If[LessEqual[a, 1.1e-124], t$95$1, If[LessEqual[a, 1.65e-85], t$95$2, If[LessEqual[a, 6.2e+28], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -30.5 or 1.0999999999999999e-124 < a < 1.64999999999999986e-85

   1. Initial program 88.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.5%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. div-sub 75.5%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      3. associate-*r/ 67.8%

         \[\leadsto x + \left(\color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      4. mul-1-neg 67.8%

         \[\leadsto x + \left(\frac{y \cdot \left(t - x\right)}{a - z} + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      5. sub-neg 67.8%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{a - z} - \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      6. associate-/l* 75.5%

         \[\leadsto x + \left(\color{blue}{\frac{y}{\frac{a - z}{t - x}}} - \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      7. associate-/l* 88.1%

         \[\leadsto x + \left(\frac{y}{\frac{a - z}{t - x}} - \color{blue}{\frac{z}{\frac{a - z}{t - x}}}\right) \]

      8. div-sub 88.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

      9. associate-/r/ 91.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 91.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   6. Taylor expanded in a around inf 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{a}} \cdot \left(t - x\right) \]

   if -30.5 < a < 1.0999999999999999e-124 or 1.64999999999999986e-85 < a < 6.2000000000000001e28

   1. Initial program 68.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 77.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 78.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 78.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 78.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 83.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if 6.2000000000000001e28 < a

   1. Initial program 85.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 74.1%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -30.5:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -8.4e-97)
     t_2
     (if (<= t 4.9e-237)
       t_1
       (if (<= t 3.8e-100) x (if (<= t 6.5e-28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -8.4e-97) {
		tmp = t_2;
	} else if (t <= 4.9e-237) {
		tmp = t_1;
	} else if (t <= 3.8e-100) {
		tmp = x;
	} else if (t <= 6.5e-28) {
		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 = (t - x) * (y / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-8.4d-97)) then
        tmp = t_2
    else if (t <= 4.9d-237) then
        tmp = t_1
    else if (t <= 3.8d-100) then
        tmp = x
    else if (t <= 6.5d-28) 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 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -8.4e-97) {
		tmp = t_2;
	} else if (t <= 4.9e-237) {
		tmp = t_1;
	} else if (t <= 3.8e-100) {
		tmp = x;
	} else if (t <= 6.5e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -8.4e-97:
		tmp = t_2
	elif t <= 4.9e-237:
		tmp = t_1
	elif t <= 3.8e-100:
		tmp = x
	elif t <= 6.5e-28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -8.4e-97)
		tmp = t_2;
	elseif (t <= 4.9e-237)
		tmp = t_1;
	elseif (t <= 3.8e-100)
		tmp = x;
	elseif (t <= 6.5e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -8.4e-97)
		tmp = t_2;
	elseif (t <= 4.9e-237)
		tmp = t_1;
	elseif (t <= 3.8e-100)
		tmp = x;
	elseif (t <= 6.5e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.4e-97], t$95$2, If[LessEqual[t, 4.9e-237], t$95$1, If[LessEqual[t, 3.8e-100], x, If[LessEqual[t, 6.5e-28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4000000000000005e-97 or 6.50000000000000043e-28 < t

   1. Initial program 84.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 63.1%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 63.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 63.1%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in x around 0 50.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 63.4%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

      3. associate-/r/ 67.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

      4. *-commutative 67.6%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -8.4000000000000005e-97 < t < 4.9000000000000001e-237 or 3.79999999999999997e-100 < t < 6.50000000000000043e-28

   1. Initial program 72.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 49.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 51.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 49.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 53.4%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   if 4.9000000000000001e-237 < t < 3.79999999999999997e-100

   1. Initial program 64.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-28}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 56.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-20}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1e-95)
     t_1
     (if (<= t 5.2e-240)
       (* (- t x) (/ y (- a z)))
       (if (<= t 1.5e-99)
         x
         (if (<= t 2e-20) (* (- t x) (/ (- a y) z)) 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 (t <= -1e-95) {
		tmp = t_1;
	} else if (t <= 5.2e-240) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 1.5e-99) {
		tmp = x;
	} else if (t <= 2e-20) {
		tmp = (t - x) * ((a - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1d-95)) then
        tmp = t_1
    else if (t <= 5.2d-240) then
        tmp = (t - x) * (y / (a - z))
    else if (t <= 1.5d-99) then
        tmp = x
    else if (t <= 2d-20) then
        tmp = (t - x) * ((a - y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1e-95) {
		tmp = t_1;
	} else if (t <= 5.2e-240) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 1.5e-99) {
		tmp = x;
	} else if (t <= 2e-20) {
		tmp = (t - x) * ((a - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1e-95:
		tmp = t_1
	elif t <= 5.2e-240:
		tmp = (t - x) * (y / (a - z))
	elif t <= 1.5e-99:
		tmp = x
	elif t <= 2e-20:
		tmp = (t - x) * ((a - y) / z)
	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 (t <= -1e-95)
		tmp = t_1;
	elseif (t <= 5.2e-240)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (t <= 1.5e-99)
		tmp = x;
	elseif (t <= 2e-20)
		tmp = Float64(Float64(t - x) * Float64(Float64(a - y) / z));
	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 (t <= -1e-95)
		tmp = t_1;
	elseif (t <= 5.2e-240)
		tmp = (t - x) * (y / (a - z));
	elseif (t <= 1.5e-99)
		tmp = x;
	elseif (t <= 2e-20)
		tmp = (t - x) * ((a - y) / z);
	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[t, -1e-95], t$95$1, If[LessEqual[t, 5.2e-240], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-99], x, If[LessEqual[t, 2e-20], N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.99999999999999989e-96 or 1.99999999999999989e-20 < t

   1. Initial program 84.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 62.8%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 62.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 62.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in x around 0 50.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. *-commutative 50.1%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 63.1%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

      3. associate-/r/ 67.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

      4. *-commutative 67.4%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 67.4%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -9.99999999999999989e-96 < t < 5.19999999999999984e-240

   1. Initial program 74.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 48.7%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 50.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 48.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 53.0%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 53.0%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   if 5.19999999999999984e-240 < t < 1.50000000000000003e-99

   1. Initial program 64.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.8%

      \[\leadsto \color{blue}{x} \]

   if 1.50000000000000003e-99 < t < 1.99999999999999989e-20

   1. Initial program 68.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 59.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 59.2%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 59.2%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 59.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 59.2%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 59.2%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 67.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in z around 0 51.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto \color{blue}{-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      2. *-commutative 51.1%

         \[\leadsto -\frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      3. associate-*l/ 58.8%

         \[\leadsto -\color{blue}{\frac{y - a}{z} \cdot \left(t - x\right)} \]

      4. distribute-lft-neg-in 58.8%

         \[\leadsto \color{blue}{\left(-\frac{y - a}{z}\right) \cdot \left(t - x\right)} \]

      5. distribute-neg-frac 58.8%

         \[\leadsto \color{blue}{\frac{-\left(y - a\right)}{z}} \cdot \left(t - x\right) \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{-\left(y - a\right)}{z} \cdot \left(t - x\right)} \]

   9. Taylor expanded in y around 0 58.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{z} + \frac{a}{z}\right)} \cdot \left(t - x\right) \]
   10. Step-by-step derivation

       1. +-commutative 58.8%

          \[\leadsto \color{blue}{\left(\frac{a}{z} + -1 \cdot \frac{y}{z}\right)} \cdot \left(t - x\right) \]

       2. mul-1-neg 58.8%

          \[\leadsto \left(\frac{a}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \cdot \left(t - x\right) \]

       3. sub-neg 58.8%

          \[\leadsto \color{blue}{\left(\frac{a}{z} - \frac{y}{z}\right)} \cdot \left(t - x\right) \]

       4. div-sub 58.8%

          \[\leadsto \color{blue}{\frac{a - y}{z}} \cdot \left(t - x\right) \]

   11. Simplified 58.8%

       \[\leadsto \color{blue}{\frac{a - y}{z}} \cdot \left(t - x\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-20}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.9:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -7.9)
     t_1
     (if (<= a 5.6e-124)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 1.04e-85)
         t_1
         (if (<= a 1.25e+38)
           (+ t (/ (* x y) z))
           (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.9) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.04e-85) {
		tmp = t_1;
	} else if (a <= 1.25e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-7.9d0)) then
        tmp = t_1
    else if (a <= 5.6d-124) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.04d-85) then
        tmp = t_1
    else if (a <= 1.25d+38) then
        tmp = t + ((x * y) / z)
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.9) {
		tmp = t_1;
	} else if (a <= 5.6e-124) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.04e-85) {
		tmp = t_1;
	} else if (a <= 1.25e+38) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -7.9:
		tmp = t_1
	elif a <= 5.6e-124:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.04e-85:
		tmp = t_1
	elif a <= 1.25e+38:
		tmp = t + ((x * y) / z)
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -7.9)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.04e-85)
		tmp = t_1;
	elseif (a <= 1.25e+38)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -7.9)
		tmp = t_1;
	elseif (a <= 5.6e-124)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.04e-85)
		tmp = t_1;
	elseif (a <= 1.25e+38)
		tmp = t + ((x * y) / z);
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.9], t$95$1, If[LessEqual[a, 5.6e-124], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.04e-85], t$95$1, If[LessEqual[a, 1.25e+38], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.9000000000000004 or 5.59999999999999996e-124 < a < 1.04e-85

   1. Initial program 88.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 59.4%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 69.9%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]

   if -7.9000000000000004 < a < 5.59999999999999996e-124

   1. Initial program 68.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 79.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 79.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 80.6%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 80.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 80.6%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 80.6%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 84.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 75.5%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   if 1.04e-85 < a < 1.24999999999999992e38

   1. Initial program 70.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 66.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.5%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 61.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around 0 66.6%

      \[\leadsto t - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{z} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.6%

         \[\leadsto t - \frac{\color{blue}{-x \cdot y}}{z} \]

      2. distribute-lft-neg-out 66.6%

         \[\leadsto t - \frac{\color{blue}{\left(-x\right) \cdot y}}{z} \]

      3. *-commutative 66.6%

         \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   9. Simplified 66.6%

      \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

   if 1.24999999999999992e38 < a

   1. Initial program 84.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 59.5%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   5. Simplified 67.7%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.9:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 56.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-240}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.25e-123)
     t_1
     (if (<= t 2.5e-240) (* (- x) (/ y (- a z))) (if (<= t 4.5e-169) x 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 (t <= -2.25e-123) {
		tmp = t_1;
	} else if (t <= 2.5e-240) {
		tmp = -x * (y / (a - z));
	} else if (t <= 4.5e-169) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-2.25d-123)) then
        tmp = t_1
    else if (t <= 2.5d-240) then
        tmp = -x * (y / (a - z))
    else if (t <= 4.5d-169) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.25e-123) {
		tmp = t_1;
	} else if (t <= 2.5e-240) {
		tmp = -x * (y / (a - z));
	} else if (t <= 4.5e-169) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.25e-123:
		tmp = t_1
	elif t <= 2.5e-240:
		tmp = -x * (y / (a - z))
	elif t <= 4.5e-169:
		tmp = x
	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 (t <= -2.25e-123)
		tmp = t_1;
	elseif (t <= 2.5e-240)
		tmp = Float64(Float64(-x) * Float64(y / Float64(a - z)));
	elseif (t <= 4.5e-169)
		tmp = x;
	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 (t <= -2.25e-123)
		tmp = t_1;
	elseif (t <= 2.5e-240)
		tmp = -x * (y / (a - z));
	elseif (t <= 4.5e-169)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e-123], t$95$1, If[LessEqual[t, 2.5e-240], N[((-x) * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-169], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.24999999999999997e-123 or 4.4999999999999999e-169 < t

   1. Initial program 80.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 63.3%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 63.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   4. Applied egg-rr 63.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot t}}{a - z} \]

      2. associate-/l* 57.8%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

      3. associate-/r/ 63.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

      4. *-commutative 63.0%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -2.24999999999999997e-123 < t < 2.5000000000000002e-240

   1. Initial program 76.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.1%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 50.1%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 51.8%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 50.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 53.2%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   6. Taylor expanded in t around 0 47.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 47.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{a - z}} \]

      2. mul-1-neg 47.1%

         \[\leadsto \frac{\color{blue}{-x \cdot y}}{a - z} \]

      3. distribute-lft-neg-out 47.1%

         \[\leadsto \frac{\color{blue}{\left(-x\right) \cdot y}}{a - z} \]

      4. associate-*r/ 48.5%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{y}{a - z}} \]

      5. distribute-lft-neg-out 48.5%

         \[\leadsto \color{blue}{-x \cdot \frac{y}{a - z}} \]

      6. distribute-rgt-neg-in 48.5%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y}{a - z}\right)} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{x \cdot \left(-\frac{y}{a - z}\right)} \]

   if 2.5000000000000002e-240 < t < 4.4999999999999999e-169

   1. Initial program 69.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-240}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+99)
   x
   (if (<= a 2.55e+38)
     (* t (- 1.0 (/ y z)))
     (if (<= a 2.8e+91) (* t (/ y (- a z))) (if (<= a 1.12e+96) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+99) {
		tmp = x;
	} else if (a <= 2.55e+38) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 2.8e+91) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.12e+96) {
		tmp = 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 (a <= (-4.8d+99)) then
        tmp = x
    else if (a <= 2.55d+38) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 2.8d+91) then
        tmp = t * (y / (a - z))
    else if (a <= 1.12d+96) then
        tmp = 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 (a <= -4.8e+99) {
		tmp = x;
	} else if (a <= 2.55e+38) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 2.8e+91) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+99:
		tmp = x
	elif a <= 2.55e+38:
		tmp = t * (1.0 - (y / z))
	elif a <= 2.8e+91:
		tmp = t * (y / (a - z))
	elif a <= 1.12e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+99)
		tmp = x;
	elseif (a <= 2.55e+38)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 2.8e+91)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+99)
		tmp = x;
	elseif (a <= 2.55e+38)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 2.8e+91)
		tmp = t * (y / (a - z));
	elseif (a <= 1.12e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+99], x, If[LessEqual[a, 2.55e+38], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+91], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+96], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.8000000000000002e99 or 1.1199999999999999e96 < a

   1. Initial program 87.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 53.7%

      \[\leadsto \color{blue}{x} \]

   if -4.8000000000000002e99 < a < 2.5500000000000001e38

   1. Initial program 73.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 65.7%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.4%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.4%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.4%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 71.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 62.6%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if 2.5500000000000001e38 < a < 2.7999999999999999e91

   1. Initial program 82.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 51.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 51.9%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 51.8%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 51.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 51.7%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   6. Taylor expanded in t around inf 39.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 39.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if 2.7999999999999999e91 < a < 1.1199999999999999e96

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3250000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-225}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3250000.0)
   x
   (if (<= a 3.3e-225)
     t
     (if (<= a 4.5e-47) (* y (/ x z)) (if (<= a 2.4e+38) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3250000.0) {
		tmp = x;
	} else if (a <= 3.3e-225) {
		tmp = t;
	} else if (a <= 4.5e-47) {
		tmp = y * (x / z);
	} else if (a <= 2.4e+38) {
		tmp = 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 (a <= (-3250000.0d0)) then
        tmp = x
    else if (a <= 3.3d-225) then
        tmp = t
    else if (a <= 4.5d-47) then
        tmp = y * (x / z)
    else if (a <= 2.4d+38) then
        tmp = 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 (a <= -3250000.0) {
		tmp = x;
	} else if (a <= 3.3e-225) {
		tmp = t;
	} else if (a <= 4.5e-47) {
		tmp = y * (x / z);
	} else if (a <= 2.4e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3250000.0:
		tmp = x
	elif a <= 3.3e-225:
		tmp = t
	elif a <= 4.5e-47:
		tmp = y * (x / z)
	elif a <= 2.4e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3250000.0)
		tmp = x;
	elseif (a <= 3.3e-225)
		tmp = t;
	elseif (a <= 4.5e-47)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 2.4e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3250000.0)
		tmp = x;
	elseif (a <= 3.3e-225)
		tmp = t;
	elseif (a <= 4.5e-47)
		tmp = y * (x / z);
	elseif (a <= 2.4e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3250000.0], x, If[LessEqual[a, 3.3e-225], t, If[LessEqual[a, 4.5e-47], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+38], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.25e6 or 2.40000000000000017e38 < a

   1. Initial program 86.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.7%

      \[\leadsto \color{blue}{x} \]

   if -3.25e6 < a < 3.3000000000000001e-225 or 4.5e-47 < a < 2.40000000000000017e38

   1. Initial program 70.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.6%

      \[\leadsto \color{blue}{t} \]

   if 3.3000000000000001e-225 < a < 4.5e-47

   1. Initial program 71.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 65.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 65.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 65.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 65.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 65.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 72.3%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 47.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 48.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 47.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   8. Simplified 47.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Taylor expanded in y around inf 41.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. associate-*l/ 41.6%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

       2. *-commutative 41.6%

          \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   11. Simplified 41.6%

       \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3250000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-225}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+98) x (if (<= a 1.65e+38) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= 1.65e+38) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.8d+98)) then
        tmp = x
    else if (a <= 1.65d+38) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= 1.65e+38) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+98:
		tmp = x
	elif a <= 1.65e+38:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= 1.65e+38)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= 1.65e+38)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+98], x, If[LessEqual[a, 1.65e+38], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.80000000000000034e98 or 1.65e38 < a

   1. Initial program 86.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.6%

      \[\leadsto \color{blue}{x} \]

   if -8.80000000000000034e98 < a < 1.65e38

   1. Initial program 73.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 65.7%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.4%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.4%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 66.4%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 71.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 62.6%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -275000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -275000.0) x (if (<= a 2.05e+38) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -275000.0) {
		tmp = x;
	} else if (a <= 2.05e+38) {
		tmp = 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 (a <= (-275000.0d0)) then
        tmp = x
    else if (a <= 2.05d+38) then
        tmp = 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 (a <= -275000.0) {
		tmp = x;
	} else if (a <= 2.05e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -275000.0:
		tmp = x
	elif a <= 2.05e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -275000.0)
		tmp = x;
	elseif (a <= 2.05e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -275000.0)
		tmp = x;
	elseif (a <= 2.05e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -275000.0], x, If[LessEqual[a, 2.05e+38], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -275000 or 2.0500000000000002e38 < a

   1. Initial program 86.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.7%

      \[\leadsto \color{blue}{x} \]

   if -275000 < a < 2.0500000000000002e38

   1. Initial program 70.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 38.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -275000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 26.1% 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 79.0%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 24.6%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 24.6%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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)))))