Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 94.8%

Time: 23.5s

Alternatives: 30

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% 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: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -4e-262)
     (+ x (/ (- t x) (/ (- z a) (- z y))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -4e-262) {
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -4e-262)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(z - a) / Float64(z - y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return 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[LessEqual[t$95$1, -4e-262], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000005e-262

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*l/ 78.4%

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

      3. associate-*r/ 97.0%

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

      4. clear-num 97.0%

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

      5. un-div-inv 97.4%

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

   4. Applied egg-rr 97.4%

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

   if -4.00000000000000005e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. associate--l+ 90.2%

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

      2. distribute-lft-out-- 90.2%

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

      3. div-sub 90.2%

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

      4. mul-1-neg 90.2%

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

      5. unsub-neg 90.2%

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

      6. div-sub 90.2%

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

      7. associate-/l* 93.4%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

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

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. unsub-neg 91.8%

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

      4. *-commutative 91.8%

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

      5. associate-*l/ 80.0%

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

      6. associate-/l* 96.4%

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

      7. fma-neg 96.4%

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

      8. remove-double-neg 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-62}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-233}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+128}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+152} \lor \neg \left(z \leq 2.8 \cdot 10^{+223}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -1800.0)
     t_1
     (if (<= z -9.6e-62)
       (- x (* z (/ t a)))
       (if (<= z -1.25e-145)
         t_2
         (if (<= z -1.2e-145)
           (* z (/ t (- a)))
           (if (<= z -6e-216)
             (- x (* x (/ y a)))
             (if (<= z -2.1e-233)
               (* (- t x) (/ y a))
               (if (<= z -7.8e-260)
                 (* x (- 1.0 (/ y a)))
                 (if (<= z 2.2e+37)
                   t_2
                   (if (<= z 1.35e+128)
                     (/ (* t (- z y)) z)
                     (if (or (<= z 1.3e+152) (not (<= z 2.8e+223)))
                       t_1
                       (/ (- y a) (/ z x))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1800.0) {
		tmp = t_1;
	} else if (z <= -9.6e-62) {
		tmp = x - (z * (t / a));
	} else if (z <= -1.25e-145) {
		tmp = t_2;
	} else if (z <= -1.2e-145) {
		tmp = z * (t / -a);
	} else if (z <= -6e-216) {
		tmp = x - (x * (y / a));
	} else if (z <= -2.1e-233) {
		tmp = (t - x) * (y / a);
	} else if (z <= -7.8e-260) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.2e+37) {
		tmp = t_2;
	} else if (z <= 1.35e+128) {
		tmp = (t * (z - y)) / z;
	} else if ((z <= 1.3e+152) || !(z <= 2.8e+223)) {
		tmp = t_1;
	} else {
		tmp = (y - a) / (z / 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) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = x + ((y * t) / a)
    if (z <= (-1800.0d0)) then
        tmp = t_1
    else if (z <= (-9.6d-62)) then
        tmp = x - (z * (t / a))
    else if (z <= (-1.25d-145)) then
        tmp = t_2
    else if (z <= (-1.2d-145)) then
        tmp = z * (t / -a)
    else if (z <= (-6d-216)) then
        tmp = x - (x * (y / a))
    else if (z <= (-2.1d-233)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-7.8d-260)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.2d+37) then
        tmp = t_2
    else if (z <= 1.35d+128) then
        tmp = (t * (z - y)) / z
    else if ((z <= 1.3d+152) .or. (.not. (z <= 2.8d+223))) then
        tmp = t_1
    else
        tmp = (y - a) / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1800.0) {
		tmp = t_1;
	} else if (z <= -9.6e-62) {
		tmp = x - (z * (t / a));
	} else if (z <= -1.25e-145) {
		tmp = t_2;
	} else if (z <= -1.2e-145) {
		tmp = z * (t / -a);
	} else if (z <= -6e-216) {
		tmp = x - (x * (y / a));
	} else if (z <= -2.1e-233) {
		tmp = (t - x) * (y / a);
	} else if (z <= -7.8e-260) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.2e+37) {
		tmp = t_2;
	} else if (z <= 1.35e+128) {
		tmp = (t * (z - y)) / z;
	} else if ((z <= 1.3e+152) || !(z <= 2.8e+223)) {
		tmp = t_1;
	} else {
		tmp = (y - a) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -1800.0:
		tmp = t_1
	elif z <= -9.6e-62:
		tmp = x - (z * (t / a))
	elif z <= -1.25e-145:
		tmp = t_2
	elif z <= -1.2e-145:
		tmp = z * (t / -a)
	elif z <= -6e-216:
		tmp = x - (x * (y / a))
	elif z <= -2.1e-233:
		tmp = (t - x) * (y / a)
	elif z <= -7.8e-260:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.2e+37:
		tmp = t_2
	elif z <= 1.35e+128:
		tmp = (t * (z - y)) / z
	elif (z <= 1.3e+152) or not (z <= 2.8e+223):
		tmp = t_1
	else:
		tmp = (y - a) / (z / x)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1800.0)
		tmp = t_1;
	elseif (z <= -9.6e-62)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (z <= -1.25e-145)
		tmp = t_2;
	elseif (z <= -1.2e-145)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (z <= -6e-216)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= -2.1e-233)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -7.8e-260)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.2e+37)
		tmp = t_2;
	elseif (z <= 1.35e+128)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif ((z <= 1.3e+152) || !(z <= 2.8e+223))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - a) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1800.0)
		tmp = t_1;
	elseif (z <= -9.6e-62)
		tmp = x - (z * (t / a));
	elseif (z <= -1.25e-145)
		tmp = t_2;
	elseif (z <= -1.2e-145)
		tmp = z * (t / -a);
	elseif (z <= -6e-216)
		tmp = x - (x * (y / a));
	elseif (z <= -2.1e-233)
		tmp = (t - x) * (y / a);
	elseif (z <= -7.8e-260)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.2e+37)
		tmp = t_2;
	elseif (z <= 1.35e+128)
		tmp = (t * (z - y)) / z;
	elseif ((z <= 1.3e+152) || ~((z <= 2.8e+223)))
		tmp = t_1;
	else
		tmp = (y - a) / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1800.0], t$95$1, If[LessEqual[z, -9.6e-62], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-145], t$95$2, If[LessEqual[z, -1.2e-145], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-216], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-233], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-260], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+37], t$95$2, If[LessEqual[z, 1.35e+128], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, 1.3e+152], N[Not[LessEqual[z, 2.8e+223]], $MachinePrecision]], t$95$1, N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -1800 or 1.35000000000000001e128 < z < 1.3e152 or 2.7999999999999999e223 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. distribute-lft-out-- 69.1%

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

      3. div-sub 69.1%

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

      4. mul-1-neg 69.1%

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

      5. unsub-neg 69.1%

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

      6. div-sub 69.1%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 81.5%

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

      9. distribute-rgt-out-- 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in t around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. div-sub 75.6%

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

      3. mul-1-neg 75.6%

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

      4. associate-/l* 81.7%

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

      5. distribute-lft-neg-in 81.7%

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

      6. distribute-rgt-in 81.7%

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

      7. sub-neg 81.7%

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

      8. associate-/r/ 82.9%

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

   8. Simplified 82.9%

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

   9. Taylor expanded in t around 0 80.7%

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

       1. associate-*r/ 80.7%

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

       2. neg-mul-1 80.7%

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

   11. Simplified 80.7%

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

   12. Taylor expanded in y around inf 69.7%

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

       1. mul-1-neg 69.7%

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

       2. associate-/l* 74.3%

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

       3. distribute-rgt-neg-in 74.3%

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

       4. distribute-neg-frac2 74.3%

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

   14. Simplified 74.3%

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

   if -1800 < z < -9.59999999999999934e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 67.6%

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

   7. Taylor expanded in a around inf 67.5%

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

   if -9.59999999999999934e-62 < z < -1.2499999999999999e-145 or -7.79999999999999945e-260 < z < 2.2000000000000001e37

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*l/ 90.8%

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

      3. associate-*r/ 96.1%

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

      4. clear-num 96.0%

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

      5. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around 0 79.6%

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

   6. Taylor expanded in t around inf 62.3%

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

   if -1.2499999999999999e-145 < z < -1.20000000000000008e-145

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.4%

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

   4. Taylor expanded in a around inf 98.4%

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

   5. Taylor expanded in y around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-frac-neg2 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if -1.20000000000000008e-145 < z < -6.00000000000000025e-216

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. distribute-neg-frac 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

   if -6.00000000000000025e-216 < z < -2.0999999999999999e-233

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. div-sub 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in a around inf 99.2%

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

   7. Taylor expanded in y around 0 52.9%

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

   8. Taylor expanded in t around 0 52.9%

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

      1. neg-mul-1 52.9%

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

      2. associate-*r/ 76.5%

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

      3. +-commutative 76.5%

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

      4. associate-*r/ 99.6%

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

      5. distribute-lft-neg-out 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. sub-neg 99.6%

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

      8. *-commutative 99.6%

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

   10. Simplified 99.6%

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

   if -2.0999999999999999e-233 < z < -7.79999999999999945e-260

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

   if 2.2000000000000001e37 < z < 1.35000000000000001e128

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 64.0%

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

   4. Taylor expanded in a around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. associate-*r* 59.2%

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

      3. *-commutative 59.2%

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

      4. neg-mul-1 59.2%

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

   6. Simplified 59.2%

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

   if 1.3e152 < z < 2.7999999999999999e223

   1. Initial program 59.4%

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

   3. Taylor expanded in t around 0 10.9%

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

      1. neg-mul-1 10.9%

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

      2. distribute-neg-frac 10.9%

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

   5. Simplified 10.9%

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

      1. *-commutative 10.9%

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

      2. add-sqr-sqrt 1.8%

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

      3. sqrt-unprod 7.3%

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

      4. sqr-neg 7.3%

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

      5. sqrt-unprod 5.6%

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

      6. add-sqr-sqrt 7.0%

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

      7. cancel-sign-sub 7.0%

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

      8. distribute-frac-neg 7.0%

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

      9. *-commutative 7.0%

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

      10. add-sqr-sqrt 1.4%

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

      11. sqrt-unprod 10.7%

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

      12. sqr-neg 10.7%

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

      13. sqrt-unprod 9.5%

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

      14. add-sqr-sqrt 10.9%

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

   7. Applied egg-rr 10.9%

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

   8. Taylor expanded in z around inf 27.3%

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

   10. Simplified 43.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1800:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-62}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-233}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+128}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+152} \lor \neg \left(z \leq 2.8 \cdot 10^{+223}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+103}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= x -5.1e+100)
     (- x (/ x (/ a y)))
     (if (<= x -5.5e+70)
       t_1
       (if (<= x -3.5e+53)
         t_2
         (if (<= x -3.4e+32)
           (+ t (* x (/ y z)))
           (if (<= x -3e-40)
             t_2
             (if (<= x -1.55e-56)
               t_1
               (if (<= x -1.15e-86)
                 t_2
                 (if (<= x 1.46e+32)
                   t_1
                   (if (<= x 1.16e+103)
                     (- x (* z (/ t a)))
                     (if (<= x 2.1e+180) t_2 (- x (* x (/ y a)))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -5.1e+100) {
		tmp = x - (x / (a / y));
	} else if (x <= -5.5e+70) {
		tmp = t_1;
	} else if (x <= -3.5e+53) {
		tmp = t_2;
	} else if (x <= -3.4e+32) {
		tmp = t + (x * (y / z));
	} else if (x <= -3e-40) {
		tmp = t_2;
	} else if (x <= -1.55e-56) {
		tmp = t_1;
	} else if (x <= -1.15e-86) {
		tmp = t_2;
	} else if (x <= 1.46e+32) {
		tmp = t_1;
	} else if (x <= 1.16e+103) {
		tmp = x - (z * (t / a));
	} else if (x <= 2.1e+180) {
		tmp = t_2;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = y * ((t - x) / (a - z))
    if (x <= (-5.1d+100)) then
        tmp = x - (x / (a / y))
    else if (x <= (-5.5d+70)) then
        tmp = t_1
    else if (x <= (-3.5d+53)) then
        tmp = t_2
    else if (x <= (-3.4d+32)) then
        tmp = t + (x * (y / z))
    else if (x <= (-3d-40)) then
        tmp = t_2
    else if (x <= (-1.55d-56)) then
        tmp = t_1
    else if (x <= (-1.15d-86)) then
        tmp = t_2
    else if (x <= 1.46d+32) then
        tmp = t_1
    else if (x <= 1.16d+103) then
        tmp = x - (z * (t / a))
    else if (x <= 2.1d+180) then
        tmp = t_2
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -5.1e+100) {
		tmp = x - (x / (a / y));
	} else if (x <= -5.5e+70) {
		tmp = t_1;
	} else if (x <= -3.5e+53) {
		tmp = t_2;
	} else if (x <= -3.4e+32) {
		tmp = t + (x * (y / z));
	} else if (x <= -3e-40) {
		tmp = t_2;
	} else if (x <= -1.55e-56) {
		tmp = t_1;
	} else if (x <= -1.15e-86) {
		tmp = t_2;
	} else if (x <= 1.46e+32) {
		tmp = t_1;
	} else if (x <= 1.16e+103) {
		tmp = x - (z * (t / a));
	} else if (x <= 2.1e+180) {
		tmp = t_2;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if x <= -5.1e+100:
		tmp = x - (x / (a / y))
	elif x <= -5.5e+70:
		tmp = t_1
	elif x <= -3.5e+53:
		tmp = t_2
	elif x <= -3.4e+32:
		tmp = t + (x * (y / z))
	elif x <= -3e-40:
		tmp = t_2
	elif x <= -1.55e-56:
		tmp = t_1
	elif x <= -1.15e-86:
		tmp = t_2
	elif x <= 1.46e+32:
		tmp = t_1
	elif x <= 1.16e+103:
		tmp = x - (z * (t / a))
	elif x <= 2.1e+180:
		tmp = t_2
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (x <= -5.1e+100)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (x <= -5.5e+70)
		tmp = t_1;
	elseif (x <= -3.5e+53)
		tmp = t_2;
	elseif (x <= -3.4e+32)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (x <= -3e-40)
		tmp = t_2;
	elseif (x <= -1.55e-56)
		tmp = t_1;
	elseif (x <= -1.15e-86)
		tmp = t_2;
	elseif (x <= 1.46e+32)
		tmp = t_1;
	elseif (x <= 1.16e+103)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (x <= 2.1e+180)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (x <= -5.1e+100)
		tmp = x - (x / (a / y));
	elseif (x <= -5.5e+70)
		tmp = t_1;
	elseif (x <= -3.5e+53)
		tmp = t_2;
	elseif (x <= -3.4e+32)
		tmp = t + (x * (y / z));
	elseif (x <= -3e-40)
		tmp = t_2;
	elseif (x <= -1.55e-56)
		tmp = t_1;
	elseif (x <= -1.15e-86)
		tmp = t_2;
	elseif (x <= 1.46e+32)
		tmp = t_1;
	elseif (x <= 1.16e+103)
		tmp = x - (z * (t / a));
	elseif (x <= 2.1e+180)
		tmp = t_2;
	else
		tmp = x - (x * (y / a));
	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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e+100], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e+70], t$95$1, If[LessEqual[x, -3.5e+53], t$95$2, If[LessEqual[x, -3.4e+32], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-40], t$95$2, If[LessEqual[x, -1.55e-56], t$95$1, If[LessEqual[x, -1.15e-86], t$95$2, If[LessEqual[x, 1.46e+32], t$95$1, If[LessEqual[x, 1.16e+103], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+180], t$95$2, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.1000000000000001e100

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0 74.6%

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

      1. neg-mul-1 74.6%

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

      2. distribute-neg-frac 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in z around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

      1. clear-num 62.4%

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

      2. un-div-inv 62.4%

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

   10. Applied egg-rr 62.4%

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

   if -5.1000000000000001e100 < x < -5.49999999999999986e70 or -3.0000000000000002e-40 < x < -1.54999999999999994e-56 or -1.14999999999999998e-86 < x < 1.46000000000000005e32

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 64.5%

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

      1. associate-/l* 77.3%

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

   5. Simplified 77.3%

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

   if -5.49999999999999986e70 < x < -3.50000000000000019e53 or -3.39999999999999979e32 < x < -3.0000000000000002e-40 or -1.54999999999999994e-56 < x < -1.14999999999999998e-86 or 1.1600000000000001e103 < x < 2.1e180

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

   if -3.50000000000000019e53 < x < -3.39999999999999979e32

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. distribute-lft-out-- 99.5%

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

      3. div-sub 99.5%

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

      4. mul-1-neg 99.5%

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

      5. unsub-neg 99.5%

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

      6. div-sub 99.5%

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

      7. associate-/l* 99.5%

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

      8. associate-/l* 99.5%

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

      9. distribute-rgt-out-- 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in t around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. div-sub 99.5%

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

      3. mul-1-neg 99.5%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. distribute-rgt-in 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around 0 100.0%

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

       1. associate-*r/ 100.0%

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

       2. neg-mul-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around inf 99.5%

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

       1. mul-1-neg 99.5%

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

       2. associate-/l* 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

       4. distribute-neg-frac2 100.0%

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

   14. Simplified 100.0%

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

   if 1.46000000000000005e32 < x < 1.1600000000000001e103

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

      3. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around inf 72.7%

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

   7. Taylor expanded in a around inf 61.9%

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

   if 2.1e180 < x

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 69.7%

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

      1. neg-mul-1 69.7%

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

      2. distribute-neg-frac 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in z around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+103}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+49}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+117} \lor \neg \left(y \leq 2.25 \cdot 10^{+117}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -3.4e+34)
     t_1
     (if (<= y -9e-19)
       (+ x t)
       (if (<= y -2.2e-26)
         (/ z (/ a t))
         (if (<= y -3.7e-83)
           t
           (if (<= y -1.1e-107)
             x
             (if (<= y -1.05e-107)
               (* t (/ y a))
               (if (<= y 3e+49)
                 (+ x t)
                 (if (or (<= y 2.15e+117) (not (<= y 2.25e+117)))
                   t_1
                   t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -3.4e+34) {
		tmp = t_1;
	} else if (y <= -9e-19) {
		tmp = x + t;
	} else if (y <= -2.2e-26) {
		tmp = z / (a / t);
	} else if (y <= -3.7e-83) {
		tmp = t;
	} else if (y <= -1.1e-107) {
		tmp = x;
	} else if (y <= -1.05e-107) {
		tmp = t * (y / a);
	} else if (y <= 3e+49) {
		tmp = x + t;
	} else if ((y <= 2.15e+117) || !(y <= 2.25e+117)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-3.4d+34)) then
        tmp = t_1
    else if (y <= (-9d-19)) then
        tmp = x + t
    else if (y <= (-2.2d-26)) then
        tmp = z / (a / t)
    else if (y <= (-3.7d-83)) then
        tmp = t
    else if (y <= (-1.1d-107)) then
        tmp = x
    else if (y <= (-1.05d-107)) then
        tmp = t * (y / a)
    else if (y <= 3d+49) then
        tmp = x + t
    else if ((y <= 2.15d+117) .or. (.not. (y <= 2.25d+117))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -3.4e+34) {
		tmp = t_1;
	} else if (y <= -9e-19) {
		tmp = x + t;
	} else if (y <= -2.2e-26) {
		tmp = z / (a / t);
	} else if (y <= -3.7e-83) {
		tmp = t;
	} else if (y <= -1.1e-107) {
		tmp = x;
	} else if (y <= -1.05e-107) {
		tmp = t * (y / a);
	} else if (y <= 3e+49) {
		tmp = x + t;
	} else if ((y <= 2.15e+117) || !(y <= 2.25e+117)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -3.4e+34:
		tmp = t_1
	elif y <= -9e-19:
		tmp = x + t
	elif y <= -2.2e-26:
		tmp = z / (a / t)
	elif y <= -3.7e-83:
		tmp = t
	elif y <= -1.1e-107:
		tmp = x
	elif y <= -1.05e-107:
		tmp = t * (y / a)
	elif y <= 3e+49:
		tmp = x + t
	elif (y <= 2.15e+117) or not (y <= 2.25e+117):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.4e+34)
		tmp = t_1;
	elseif (y <= -9e-19)
		tmp = Float64(x + t);
	elseif (y <= -2.2e-26)
		tmp = Float64(z / Float64(a / t));
	elseif (y <= -3.7e-83)
		tmp = t;
	elseif (y <= -1.1e-107)
		tmp = x;
	elseif (y <= -1.05e-107)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 3e+49)
		tmp = Float64(x + t);
	elseif ((y <= 2.15e+117) || !(y <= 2.25e+117))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -3.4e+34)
		tmp = t_1;
	elseif (y <= -9e-19)
		tmp = x + t;
	elseif (y <= -2.2e-26)
		tmp = z / (a / t);
	elseif (y <= -3.7e-83)
		tmp = t;
	elseif (y <= -1.1e-107)
		tmp = x;
	elseif (y <= -1.05e-107)
		tmp = t * (y / a);
	elseif (y <= 3e+49)
		tmp = x + t;
	elseif ((y <= 2.15e+117) || ~((y <= 2.25e+117)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+34], t$95$1, If[LessEqual[y, -9e-19], N[(x + t), $MachinePrecision], If[LessEqual[y, -2.2e-26], N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-83], t, If[LessEqual[y, -1.1e-107], x, If[LessEqual[y, -1.05e-107], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+49], N[(x + t), $MachinePrecision], If[Or[LessEqual[y, 2.15e+117], N[Not[LessEqual[y, 2.25e+117]], $MachinePrecision]], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.3999999999999999e34 or 3.0000000000000002e49 < y < 2.14999999999999999e117 or 2.25e117 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. div-sub 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 42.3%

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

      1. associate-/l* 51.3%

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

   8. Simplified 51.3%

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

   if -3.3999999999999999e34 < y < -9.00000000000000026e-19 or -1.05e-107 < y < 3.0000000000000002e49

   1. Initial program 78.1%

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

   3. Taylor expanded in y around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around inf 65.4%

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

   7. Taylor expanded in z around inf 52.0%

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

      1. sub-neg 52.0%

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

      2. neg-mul-1 52.0%

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

      3. remove-double-neg 52.0%

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

   9. Simplified 52.0%

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

   if -9.00000000000000026e-19 < y < -2.2000000000000001e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.8%

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

   4. Taylor expanded in a around inf 50.0%

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

   5. Taylor expanded in y around 0 0.1%

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

      1. mul-1-neg 0.1%

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

      2. associate-/l* 0.1%

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

      3. distribute-lft-neg-in 0.1%

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

   7. Simplified 0.1%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 100.0%

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

      3. sqr-neg 100.0%

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

      4. sqrt-unprod 52.4%

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

      5. add-sqr-sqrt 52.4%

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

      6. associate-*r/ 52.4%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. clear-num 100.0%

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

      10. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -2.2000000000000001e-26 < y < -3.69999999999999995e-83 or 2.14999999999999999e117 < y < 2.25e117

   1. Initial program 83.6%

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

   3. Taylor expanded in z around inf 61.3%

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

   if -3.69999999999999995e-83 < y < -1.10000000000000006e-107

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf 78.4%

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

   if -1.10000000000000006e-107 < y < -1.05e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around inf 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+49}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+117} \lor \neg \left(y \leq 2.25 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+106}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= x -5e+106)
     (- x (/ x (/ a y)))
     (if (<= x -7.5e+68)
       t_2
       (if (<= x -3.8e+56)
         (* y (/ x (- z a)))
         (if (<= x -2.35e+26)
           t_1
           (if (<= x 2.5e+31)
             t_2
             (if (<= x 3.2e+102)
               (- x (* z (/ t a)))
               (if (<= x 9e+151)
                 (* x (/ (- y a) z))
                 (if (<= x 4.2e+225)
                   (* x (- 1.0 (/ y a)))
                   (if (<= x 3.6e+230) t_1 (- x (* x (/ y a))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -5e+106) {
		tmp = x - (x / (a / y));
	} else if (x <= -7.5e+68) {
		tmp = t_2;
	} else if (x <= -3.8e+56) {
		tmp = y * (x / (z - a));
	} else if (x <= -2.35e+26) {
		tmp = t_1;
	} else if (x <= 2.5e+31) {
		tmp = t_2;
	} else if (x <= 3.2e+102) {
		tmp = x - (z * (t / a));
	} else if (x <= 9e+151) {
		tmp = x * ((y - a) / z);
	} else if (x <= 4.2e+225) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 3.6e+230) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = t * ((y - z) / (a - z))
    if (x <= (-5d+106)) then
        tmp = x - (x / (a / y))
    else if (x <= (-7.5d+68)) then
        tmp = t_2
    else if (x <= (-3.8d+56)) then
        tmp = y * (x / (z - a))
    else if (x <= (-2.35d+26)) then
        tmp = t_1
    else if (x <= 2.5d+31) then
        tmp = t_2
    else if (x <= 3.2d+102) then
        tmp = x - (z * (t / a))
    else if (x <= 9d+151) then
        tmp = x * ((y - a) / z)
    else if (x <= 4.2d+225) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= 3.6d+230) then
        tmp = t_1
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -5e+106) {
		tmp = x - (x / (a / y));
	} else if (x <= -7.5e+68) {
		tmp = t_2;
	} else if (x <= -3.8e+56) {
		tmp = y * (x / (z - a));
	} else if (x <= -2.35e+26) {
		tmp = t_1;
	} else if (x <= 2.5e+31) {
		tmp = t_2;
	} else if (x <= 3.2e+102) {
		tmp = x - (z * (t / a));
	} else if (x <= 9e+151) {
		tmp = x * ((y - a) / z);
	} else if (x <= 4.2e+225) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 3.6e+230) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -5e+106:
		tmp = x - (x / (a / y))
	elif x <= -7.5e+68:
		tmp = t_2
	elif x <= -3.8e+56:
		tmp = y * (x / (z - a))
	elif x <= -2.35e+26:
		tmp = t_1
	elif x <= 2.5e+31:
		tmp = t_2
	elif x <= 3.2e+102:
		tmp = x - (z * (t / a))
	elif x <= 9e+151:
		tmp = x * ((y - a) / z)
	elif x <= 4.2e+225:
		tmp = x * (1.0 - (y / a))
	elif x <= 3.6e+230:
		tmp = t_1
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -5e+106)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (x <= -7.5e+68)
		tmp = t_2;
	elseif (x <= -3.8e+56)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (x <= -2.35e+26)
		tmp = t_1;
	elseif (x <= 2.5e+31)
		tmp = t_2;
	elseif (x <= 3.2e+102)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (x <= 9e+151)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= 4.2e+225)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= 3.6e+230)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -5e+106)
		tmp = x - (x / (a / y));
	elseif (x <= -7.5e+68)
		tmp = t_2;
	elseif (x <= -3.8e+56)
		tmp = y * (x / (z - a));
	elseif (x <= -2.35e+26)
		tmp = t_1;
	elseif (x <= 2.5e+31)
		tmp = t_2;
	elseif (x <= 3.2e+102)
		tmp = x - (z * (t / a));
	elseif (x <= 9e+151)
		tmp = x * ((y - a) / z);
	elseif (x <= 4.2e+225)
		tmp = x * (1.0 - (y / a));
	elseif (x <= 3.6e+230)
		tmp = t_1;
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+106], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e+68], t$95$2, If[LessEqual[x, -3.8e+56], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.35e+26], t$95$1, If[LessEqual[x, 2.5e+31], t$95$2, If[LessEqual[x, 3.2e+102], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+151], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+225], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+230], t$95$1, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -4.9999999999999998e106

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0 74.6%

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

      1. neg-mul-1 74.6%

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

      2. distribute-neg-frac 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in z around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

      3. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

      1. clear-num 62.4%

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

      2. un-div-inv 62.4%

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

   10. Applied egg-rr 62.4%

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

   if -4.9999999999999998e106 < x < -7.49999999999999959e68 or -2.3499999999999999e26 < x < 2.50000000000000013e31

   1. Initial program 88.0%

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

   3. Taylor expanded in x around 0 58.8%

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

      1. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   if -7.49999999999999959e68 < x < -3.79999999999999996e56

   1. Initial program 83.6%

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

   3. Taylor expanded in y around inf 83.5%

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

      1. div-sub 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in t around 0 68.1%

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

      1. neg-mul-1 68.1%

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

      2. distribute-neg-frac 68.1%

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

   8. Simplified 68.1%

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

   if -3.79999999999999996e56 < x < -2.3499999999999999e26 or 4.2e225 < x < 3.60000000000000019e230

   1. Initial program 19.4%

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

   3. Taylor expanded in z around inf 88.0%

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

      1. associate--l+ 88.0%

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

      2. distribute-lft-out-- 88.0%

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

      3. div-sub 88.0%

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

      4. mul-1-neg 88.0%

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

      5. unsub-neg 88.0%

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

      6. div-sub 88.0%

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

      7. associate-/l* 99.6%

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

      8. associate-/l* 99.6%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. div-sub 88.0%

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

      3. mul-1-neg 88.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. distribute-rgt-in 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around 0 100.0%

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

       1. associate-*r/ 100.0%

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

       2. neg-mul-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around inf 63.0%

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

       1. mul-1-neg 63.0%

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

       2. associate-/l* 74.9%

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

       3. distribute-rgt-neg-in 74.9%

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

       4. distribute-neg-frac2 74.9%

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

   14. Simplified 74.9%

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

   if 2.50000000000000013e31 < x < 3.1999999999999999e102

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

      3. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around inf 72.7%

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

   7. Taylor expanded in a around inf 61.9%

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

   if 3.1999999999999999e102 < x < 8.9999999999999997e151

   1. Initial program 55.7%

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

   3. Taylor expanded in x around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. unsub-neg 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in z around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. sub-neg 65.3%

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

      4. distribute-lft-out-- 65.3%

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

      5. sub-neg 65.3%

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

      6. mul-1-neg 65.3%

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

      7. mul-1-neg 65.3%

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

      8. remove-double-neg 65.3%

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

   8. Simplified 65.3%

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

   if 8.9999999999999997e151 < x < 4.2e225

   1. Initial program 82.1%

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

   3. Taylor expanded in x around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. unsub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around 0 59.3%

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

   if 3.60000000000000019e230 < x

   1. Initial program 82.6%

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

   3. Taylor expanded in t around 0 82.6%

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

      1. neg-mul-1 82.6%

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

      2. distribute-neg-frac 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

      3. associate-/l* 64.2%

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

   8. Simplified 64.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+106}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+230}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -7300:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-60}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-217}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-233}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -7300.0)
     t_1
     (if (<= z -7.4e-60)
       (- x (* z (/ t a)))
       (if (<= z -1.25e-145)
         t_2
         (if (<= z -1.2e-145)
           (* z (/ t (- a)))
           (if (<= z -9.2e-217)
             (- x (* x (/ y a)))
             (if (<= z -8.2e-233)
               (* (- t x) (/ y a))
               (if (<= z -2.7e-261)
                 (* x (- 1.0 (/ y a)))
                 (if (<= z 4.2e-20) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -7300.0) {
		tmp = t_1;
	} else if (z <= -7.4e-60) {
		tmp = x - (z * (t / a));
	} else if (z <= -1.25e-145) {
		tmp = t_2;
	} else if (z <= -1.2e-145) {
		tmp = z * (t / -a);
	} else if (z <= -9.2e-217) {
		tmp = x - (x * (y / a));
	} else if (z <= -8.2e-233) {
		tmp = (t - x) * (y / a);
	} else if (z <= -2.7e-261) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e-20) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = x + ((y * t) / a)
    if (z <= (-7300.0d0)) then
        tmp = t_1
    else if (z <= (-7.4d-60)) then
        tmp = x - (z * (t / a))
    else if (z <= (-1.25d-145)) then
        tmp = t_2
    else if (z <= (-1.2d-145)) then
        tmp = z * (t / -a)
    else if (z <= (-9.2d-217)) then
        tmp = x - (x * (y / a))
    else if (z <= (-8.2d-233)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-2.7d-261)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.2d-20) then
        tmp = t_2
    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 + (x * (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -7300.0) {
		tmp = t_1;
	} else if (z <= -7.4e-60) {
		tmp = x - (z * (t / a));
	} else if (z <= -1.25e-145) {
		tmp = t_2;
	} else if (z <= -1.2e-145) {
		tmp = z * (t / -a);
	} else if (z <= -9.2e-217) {
		tmp = x - (x * (y / a));
	} else if (z <= -8.2e-233) {
		tmp = (t - x) * (y / a);
	} else if (z <= -2.7e-261) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e-20) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -7300.0:
		tmp = t_1
	elif z <= -7.4e-60:
		tmp = x - (z * (t / a))
	elif z <= -1.25e-145:
		tmp = t_2
	elif z <= -1.2e-145:
		tmp = z * (t / -a)
	elif z <= -9.2e-217:
		tmp = x - (x * (y / a))
	elif z <= -8.2e-233:
		tmp = (t - x) * (y / a)
	elif z <= -2.7e-261:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.2e-20:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -7300.0)
		tmp = t_1;
	elseif (z <= -7.4e-60)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (z <= -1.25e-145)
		tmp = t_2;
	elseif (z <= -1.2e-145)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (z <= -9.2e-217)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= -8.2e-233)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -2.7e-261)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.2e-20)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -7300.0)
		tmp = t_1;
	elseif (z <= -7.4e-60)
		tmp = x - (z * (t / a));
	elseif (z <= -1.25e-145)
		tmp = t_2;
	elseif (z <= -1.2e-145)
		tmp = z * (t / -a);
	elseif (z <= -9.2e-217)
		tmp = x - (x * (y / a));
	elseif (z <= -8.2e-233)
		tmp = (t - x) * (y / a);
	elseif (z <= -2.7e-261)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.2e-20)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7300.0], t$95$1, If[LessEqual[z, -7.4e-60], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-145], t$95$2, If[LessEqual[z, -1.2e-145], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-217], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-233], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-261], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-20], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -7300 or 4.1999999999999998e-20 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 64.5%

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

      1. associate--l+ 64.5%

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

      2. distribute-lft-out-- 64.5%

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

      3. div-sub 64.5%

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

      4. mul-1-neg 64.5%

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

      5. unsub-neg 64.5%

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

      6. div-sub 64.5%

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

      7. associate-/l* 69.7%

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

      8. associate-/l* 74.6%

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

      9. distribute-rgt-out-- 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. div-sub 68.6%

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

      3. mul-1-neg 68.6%

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

      4. associate-/l* 74.0%

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

      5. distribute-lft-neg-in 74.0%

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

      6. distribute-rgt-in 74.0%

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

      7. sub-neg 74.0%

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

      8. associate-/r/ 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in t around 0 69.4%

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

       1. associate-*r/ 69.4%

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

       2. neg-mul-1 69.4%

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

   11. Simplified 69.4%

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

   12. Taylor expanded in y around inf 58.0%

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

       1. mul-1-neg 58.0%

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

       2. associate-/l* 61.7%

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

       3. distribute-rgt-neg-in 61.7%

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

       4. distribute-neg-frac2 61.7%

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

   14. Simplified 61.7%

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

   if -7300 < z < -7.4000000000000005e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 67.6%

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

   7. Taylor expanded in a around inf 67.5%

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

   if -7.4000000000000005e-60 < z < -1.2499999999999999e-145 or -2.6999999999999999e-261 < z < 4.1999999999999998e-20

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 90.4%

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

      3. associate-*r/ 95.5%

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

      4. clear-num 95.5%

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

      5. un-div-inv 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around 0 85.1%

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

   6. Taylor expanded in t around inf 65.7%

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

   if -1.2499999999999999e-145 < z < -1.20000000000000008e-145

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.4%

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

   4. Taylor expanded in a around inf 98.4%

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

   5. Taylor expanded in y around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-frac-neg2 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   if -1.20000000000000008e-145 < z < -9.20000000000000019e-217

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. distribute-neg-frac 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

   if -9.20000000000000019e-217 < z < -8.2000000000000009e-233

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. div-sub 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in a around inf 99.2%

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

   7. Taylor expanded in y around 0 52.9%

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

   8. Taylor expanded in t around 0 52.9%

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

      1. neg-mul-1 52.9%

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

      2. associate-*r/ 76.5%

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

      3. +-commutative 76.5%

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

      4. associate-*r/ 99.6%

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

      5. distribute-lft-neg-out 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. sub-neg 99.6%

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

      8. *-commutative 99.6%

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

   10. Simplified 99.6%

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

   if -8.2000000000000009e-233 < z < -2.6999999999999999e-261

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7300:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-60}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-217}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-233}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -16200:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.4e+40)
     t
     (if (<= z -16200.0)
       (- x (* x (/ y a)))
       (if (<= z -8000.0)
         t
         (if (<= z -5.4e-48)
           (- x (* z (/ t a)))
           (if (<= z 8.2e-293)
             (* x (- 1.0 (/ y a)))
             (if (<= z 4.5e-77)
               t_1
               (if (<= z 4e-44)
                 (* y (/ (- t x) a))
                 (if (<= z 2.45e+42) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+40) {
		tmp = t;
	} else if (z <= -16200.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -8000.0) {
		tmp = t;
	} else if (z <= -5.4e-48) {
		tmp = x - (z * (t / a));
	} else if (z <= 8.2e-293) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.5e-77) {
		tmp = t_1;
	} else if (z <= 4e-44) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.45e+42) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.4d+40)) then
        tmp = t
    else if (z <= (-16200.0d0)) then
        tmp = x - (x * (y / a))
    else if (z <= (-8000.0d0)) then
        tmp = t
    else if (z <= (-5.4d-48)) then
        tmp = x - (z * (t / a))
    else if (z <= 8.2d-293) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.5d-77) then
        tmp = t_1
    else if (z <= 4d-44) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.45d+42) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+40) {
		tmp = t;
	} else if (z <= -16200.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -8000.0) {
		tmp = t;
	} else if (z <= -5.4e-48) {
		tmp = x - (z * (t / a));
	} else if (z <= 8.2e-293) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.5e-77) {
		tmp = t_1;
	} else if (z <= 4e-44) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.45e+42) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.4e+40:
		tmp = t
	elif z <= -16200.0:
		tmp = x - (x * (y / a))
	elif z <= -8000.0:
		tmp = t
	elif z <= -5.4e-48:
		tmp = x - (z * (t / a))
	elif z <= 8.2e-293:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.5e-77:
		tmp = t_1
	elif z <= 4e-44:
		tmp = y * ((t - x) / a)
	elif z <= 2.45e+42:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.4e+40)
		tmp = t;
	elseif (z <= -16200.0)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= -8000.0)
		tmp = t;
	elseif (z <= -5.4e-48)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (z <= 8.2e-293)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.5e-77)
		tmp = t_1;
	elseif (z <= 4e-44)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.45e+42)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.4e+40)
		tmp = t;
	elseif (z <= -16200.0)
		tmp = x - (x * (y / a));
	elseif (z <= -8000.0)
		tmp = t;
	elseif (z <= -5.4e-48)
		tmp = x - (z * (t / a));
	elseif (z <= 8.2e-293)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.5e-77)
		tmp = t_1;
	elseif (z <= 4e-44)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.45e+42)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+40], t, If[LessEqual[z, -16200.0], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8000.0], t, If[LessEqual[z, -5.4e-48], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-293], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-77], t$95$1, If[LessEqual[z, 4e-44], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+42], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.4000000000000001e40 or -16200 < z < -8e3 or 2.4500000000000001e42 < z

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 52.3%

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

   if -1.4000000000000001e40 < z < -16200

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 83.9%

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

      1. neg-mul-1 83.9%

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

      2. distribute-neg-frac 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. associate-/l* 83.5%

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

   8. Simplified 83.5%

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

   if -8e3 < z < -5.40000000000000023e-48

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 67.6%

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

   7. Taylor expanded in a around inf 67.7%

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

   if -5.40000000000000023e-48 < z < 8.19999999999999975e-293

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. unsub-neg 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in z around 0 70.4%

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

   if 8.19999999999999975e-293 < z < 4.5000000000000001e-77 or 3.99999999999999981e-44 < z < 2.4500000000000001e42

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l/ 92.3%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.2%

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

      5. un-div-inv 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in z around 0 75.7%

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

   6. Taylor expanded in t around inf 61.5%

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

   if 4.5000000000000001e-77 < z < 3.99999999999999981e-44

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 99.5%

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

      1. div-sub 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf 84.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -16200:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -58000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{-15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-237}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.4e+42)
     t
     (if (<= z -58000.0)
       t_1
       (if (<= z -7.1e-15)
         (+ x t)
         (if (<= z -8.5e-109)
           (* t (/ y (- a z)))
           (if (<= z -2e-216)
             t_1
             (if (<= z -3.4e-237)
               (* (- t x) (/ y a))
               (if (<= z 4e-77)
                 t_1
                 (if (<= z 5.9e+35) (* t (/ (- y z) a)) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t;
	} else if (z <= -58000.0) {
		tmp = t_1;
	} else if (z <= -7.1e-15) {
		tmp = x + t;
	} else if (z <= -8.5e-109) {
		tmp = t * (y / (a - z));
	} else if (z <= -2e-216) {
		tmp = t_1;
	} else if (z <= -3.4e-237) {
		tmp = (t - x) * (y / a);
	} else if (z <= 4e-77) {
		tmp = t_1;
	} else if (z <= 5.9e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-3.4d+42)) then
        tmp = t
    else if (z <= (-58000.0d0)) then
        tmp = t_1
    else if (z <= (-7.1d-15)) then
        tmp = x + t
    else if (z <= (-8.5d-109)) then
        tmp = t * (y / (a - z))
    else if (z <= (-2d-216)) then
        tmp = t_1
    else if (z <= (-3.4d-237)) then
        tmp = (t - x) * (y / a)
    else if (z <= 4d-77) then
        tmp = t_1
    else if (z <= 5.9d+35) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.4e+42) {
		tmp = t;
	} else if (z <= -58000.0) {
		tmp = t_1;
	} else if (z <= -7.1e-15) {
		tmp = x + t;
	} else if (z <= -8.5e-109) {
		tmp = t * (y / (a - z));
	} else if (z <= -2e-216) {
		tmp = t_1;
	} else if (z <= -3.4e-237) {
		tmp = (t - x) * (y / a);
	} else if (z <= 4e-77) {
		tmp = t_1;
	} else if (z <= 5.9e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.4e+42:
		tmp = t
	elif z <= -58000.0:
		tmp = t_1
	elif z <= -7.1e-15:
		tmp = x + t
	elif z <= -8.5e-109:
		tmp = t * (y / (a - z))
	elif z <= -2e-216:
		tmp = t_1
	elif z <= -3.4e-237:
		tmp = (t - x) * (y / a)
	elif z <= 4e-77:
		tmp = t_1
	elif z <= 5.9e+35:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.4e+42)
		tmp = t;
	elseif (z <= -58000.0)
		tmp = t_1;
	elseif (z <= -7.1e-15)
		tmp = Float64(x + t);
	elseif (z <= -8.5e-109)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -2e-216)
		tmp = t_1;
	elseif (z <= -3.4e-237)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 4e-77)
		tmp = t_1;
	elseif (z <= 5.9e+35)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.4e+42)
		tmp = t;
	elseif (z <= -58000.0)
		tmp = t_1;
	elseif (z <= -7.1e-15)
		tmp = x + t;
	elseif (z <= -8.5e-109)
		tmp = t * (y / (a - z));
	elseif (z <= -2e-216)
		tmp = t_1;
	elseif (z <= -3.4e-237)
		tmp = (t - x) * (y / a);
	elseif (z <= 4e-77)
		tmp = t_1;
	elseif (z <= 5.9e+35)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+42], t, If[LessEqual[z, -58000.0], t$95$1, If[LessEqual[z, -7.1e-15], N[(x + t), $MachinePrecision], If[LessEqual[z, -8.5e-109], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-216], t$95$1, If[LessEqual[z, -3.4e-237], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-77], t$95$1, If[LessEqual[z, 5.9e+35], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.39999999999999975e42 or 5.89999999999999985e35 < z

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 50.9%

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

   if -3.39999999999999975e42 < z < -58000 or -8.50000000000000005e-109 < z < -2.0000000000000001e-216 or -3.4000000000000002e-237 < z < 3.9999999999999997e-77

   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 inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around 0 70.1%

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

   if -58000 < z < -7.1000000000000002e-15

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf 99.6%

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

   7. Taylor expanded in z around inf 76.1%

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

      1. sub-neg 76.1%

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

      2. neg-mul-1 76.1%

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

      3. remove-double-neg 76.1%

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

   9. Simplified 76.1%

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

   if -7.1000000000000002e-15 < z < -8.50000000000000005e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 54.0%

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

      1. div-sub 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in t around inf 35.7%

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

      1. associate-/l* 48.9%

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

   8. Simplified 48.9%

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

   if -2.0000000000000001e-216 < z < -3.4000000000000002e-237

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. div-sub 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in a around inf 99.4%

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

   7. Taylor expanded in y around 0 62.3%

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

   8. Taylor expanded in t around 0 62.3%

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

      1. neg-mul-1 62.3%

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

      2. associate-*r/ 81.2%

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

      3. +-commutative 81.2%

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

      4. associate-*r/ 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. distribute-rgt-in 99.7%

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

      7. sub-neg 99.7%

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

      8. *-commutative 99.7%

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

   10. Simplified 99.7%

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

   if 3.9999999999999997e-77 < z < 5.89999999999999985e35

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 53.7%

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

   4. Taylor expanded in a around inf 43.0%

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

      1. associate-/l* 53.8%

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

   6. Simplified 53.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 9: 46.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -12200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.1e+39)
     t
     (if (<= z -12200.0)
       t_1
       (if (<= z -1.5e-17)
         (+ x t)
         (if (<= z -3.2e-108)
           (* t (/ y (- a z)))
           (if (<= z -4.9e-216)
             t_1
             (if (<= z -3.5e-236)
               (* y (/ (- t x) a))
               (if (<= z 4.6e-77)
                 t_1
                 (if (<= z 4.5e+35) (* t (/ (- y z) a)) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+39) {
		tmp = t;
	} else if (z <= -12200.0) {
		tmp = t_1;
	} else if (z <= -1.5e-17) {
		tmp = x + t;
	} else if (z <= -3.2e-108) {
		tmp = t * (y / (a - z));
	} else if (z <= -4.9e-216) {
		tmp = t_1;
	} else if (z <= -3.5e-236) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.6e-77) {
		tmp = t_1;
	} else if (z <= 4.5e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.1d+39)) then
        tmp = t
    else if (z <= (-12200.0d0)) then
        tmp = t_1
    else if (z <= (-1.5d-17)) then
        tmp = x + t
    else if (z <= (-3.2d-108)) then
        tmp = t * (y / (a - z))
    else if (z <= (-4.9d-216)) then
        tmp = t_1
    else if (z <= (-3.5d-236)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.6d-77) then
        tmp = t_1
    else if (z <= 4.5d+35) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+39) {
		tmp = t;
	} else if (z <= -12200.0) {
		tmp = t_1;
	} else if (z <= -1.5e-17) {
		tmp = x + t;
	} else if (z <= -3.2e-108) {
		tmp = t * (y / (a - z));
	} else if (z <= -4.9e-216) {
		tmp = t_1;
	} else if (z <= -3.5e-236) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.6e-77) {
		tmp = t_1;
	} else if (z <= 4.5e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.1e+39:
		tmp = t
	elif z <= -12200.0:
		tmp = t_1
	elif z <= -1.5e-17:
		tmp = x + t
	elif z <= -3.2e-108:
		tmp = t * (y / (a - z))
	elif z <= -4.9e-216:
		tmp = t_1
	elif z <= -3.5e-236:
		tmp = y * ((t - x) / a)
	elif z <= 4.6e-77:
		tmp = t_1
	elif z <= 4.5e+35:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.1e+39)
		tmp = t;
	elseif (z <= -12200.0)
		tmp = t_1;
	elseif (z <= -1.5e-17)
		tmp = Float64(x + t);
	elseif (z <= -3.2e-108)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -4.9e-216)
		tmp = t_1;
	elseif (z <= -3.5e-236)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.6e-77)
		tmp = t_1;
	elseif (z <= 4.5e+35)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.1e+39)
		tmp = t;
	elseif (z <= -12200.0)
		tmp = t_1;
	elseif (z <= -1.5e-17)
		tmp = x + t;
	elseif (z <= -3.2e-108)
		tmp = t * (y / (a - z));
	elseif (z <= -4.9e-216)
		tmp = t_1;
	elseif (z <= -3.5e-236)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.6e-77)
		tmp = t_1;
	elseif (z <= 4.5e+35)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+39], t, If[LessEqual[z, -12200.0], t$95$1, If[LessEqual[z, -1.5e-17], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.2e-108], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-216], t$95$1, If[LessEqual[z, -3.5e-236], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-77], t$95$1, If[LessEqual[z, 4.5e+35], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.0999999999999999e39 or 4.4999999999999997e35 < z

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 50.9%

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

   if -2.0999999999999999e39 < z < -12200 or -3.2e-108 < z < -4.9000000000000001e-216 or -3.49999999999999994e-236 < z < 4.59999999999999997e-77

   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 inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around 0 70.1%

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

   if -12200 < z < -1.50000000000000003e-17

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf 99.6%

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

   7. Taylor expanded in z around inf 76.1%

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

      1. sub-neg 76.1%

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

      2. neg-mul-1 76.1%

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

      3. remove-double-neg 76.1%

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

   9. Simplified 76.1%

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

   if -1.50000000000000003e-17 < z < -3.2e-108

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 54.0%

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

      1. div-sub 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in t around inf 35.7%

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

      1. associate-/l* 48.9%

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

   8. Simplified 48.9%

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

   if -4.9000000000000001e-216 < z < -3.49999999999999994e-236

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. div-sub 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in a around inf 99.4%

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

   if 4.59999999999999997e-77 < z < 4.4999999999999997e35

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 53.7%

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

   4. Taylor expanded in a around inf 43.0%

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

      1. associate-/l* 53.8%

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

   6. Simplified 53.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 10: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-262} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-262) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- z a) (- z y))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-262) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-262)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((z - a) / (z - y)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-262) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-262) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((z - a) / (z - y)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-262) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(z - a) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-262) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-262], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000005e-262 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l/ 79.2%

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

      3. associate-*r/ 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 96.9%

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

   4. Applied egg-rr 96.9%

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

   if -4.00000000000000005e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. associate--l+ 90.2%

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

      2. distribute-lft-out-- 90.2%

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

      3. div-sub 90.2%

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

      4. mul-1-neg 90.2%

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

      5. unsub-neg 90.2%

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

      6. div-sub 90.2%

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

      7. associate-/l* 93.4%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-262} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-142} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-142) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-142) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-142)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-142) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-142) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-142) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-142) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-142], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.0000000000000002e-142 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.3%

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

   if -4.0000000000000002e-142 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   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 84.7%

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

      1. associate--l+ 84.7%

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

      2. distribute-lft-out-- 84.7%

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

      3. div-sub 84.7%

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

      4. mul-1-neg 84.7%

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

      5. unsub-neg 84.7%

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

      6. div-sub 84.7%

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

      7. associate-/l* 87.7%

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

      8. associate-/l* 93.6%

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

      9. distribute-rgt-out-- 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-142} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+147} \lor \neg \left(z \leq 9.5 \cdot 10^{+257}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.6e+45)
     t_1
     (if (<= z 2.15e-13)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 2.9e+85)
         t_2
         (if (<= z 2.8e+87)
           x
           (if (<= z 4.6e+118)
             t_2
             (if (or (<= z 3.3e+147) (not (<= z 9.5e+257)))
               t_1
               (+ t (/ (* y (- x t)) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.6e+45) {
		tmp = t_1;
	} else if (z <= 2.15e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if (z <= 4.6e+118) {
		tmp = t_2;
	} else if ((z <= 3.3e+147) || !(z <= 9.5e+257)) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-3.6d+45)) then
        tmp = t_1
    else if (z <= 2.15d-13) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.9d+85) then
        tmp = t_2
    else if (z <= 2.8d+87) then
        tmp = x
    else if (z <= 4.6d+118) then
        tmp = t_2
    else if ((z <= 3.3d+147) .or. (.not. (z <= 9.5d+257))) then
        tmp = t_1
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.6e+45) {
		tmp = t_1;
	} else if (z <= 2.15e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if (z <= 4.6e+118) {
		tmp = t_2;
	} else if ((z <= 3.3e+147) || !(z <= 9.5e+257)) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3.6e+45:
		tmp = t_1
	elif z <= 2.15e-13:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.9e+85:
		tmp = t_2
	elif z <= 2.8e+87:
		tmp = x
	elif z <= 4.6e+118:
		tmp = t_2
	elif (z <= 3.3e+147) or not (z <= 9.5e+257):
		tmp = t_1
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.6e+45)
		tmp = t_1;
	elseif (z <= 2.15e-13)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif (z <= 4.6e+118)
		tmp = t_2;
	elseif ((z <= 3.3e+147) || !(z <= 9.5e+257))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -3.6e+45)
		tmp = t_1;
	elseif (z <= 2.15e-13)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif (z <= 4.6e+118)
		tmp = t_2;
	elseif ((z <= 3.3e+147) || ~((z <= 9.5e+257)))
		tmp = t_1;
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+45], t$95$1, If[LessEqual[z, 2.15e-13], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+85], t$95$2, If[LessEqual[z, 2.8e+87], x, If[LessEqual[z, 4.6e+118], t$95$2, If[Or[LessEqual[z, 3.3e+147], N[Not[LessEqual[z, 9.5e+257]], $MachinePrecision]], t$95$1, N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.6e45 or 4.60000000000000032e118 < z < 3.30000000000000025e147 or 9.50000000000000022e257 < z

   1. Initial program 63.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. div-sub 68.3%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 82.4%

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

      9. distribute-rgt-out-- 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in t around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. div-sub 75.6%

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

      3. mul-1-neg 75.6%

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

      4. associate-/l* 82.5%

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

      5. distribute-lft-neg-in 82.5%

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

      6. distribute-rgt-in 82.5%

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

      7. sub-neg 82.5%

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

      8. associate-/r/ 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in t around 0 82.7%

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

       1. associate-*r/ 82.7%

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

       2. neg-mul-1 82.7%

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

   11. Simplified 82.7%

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

   12. Taylor expanded in y around inf 68.8%

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

       1. mul-1-neg 68.8%

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

       2. associate-/l* 74.1%

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

       3. distribute-rgt-neg-in 74.1%

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

       4. distribute-neg-frac2 74.1%

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

   14. Simplified 74.1%

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

   if -3.6e45 < z < 2.1499999999999999e-13

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l/ 88.9%

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

      3. associate-*r/ 94.9%

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

      4. clear-num 94.9%

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

      5. un-div-inv 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in z around 0 82.0%

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

   if 2.1499999999999999e-13 < z < 2.89999999999999997e85 or 2.80000000000000015e87 < z < 4.60000000000000032e118

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 69.6%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if 2.89999999999999997e85 < z < 2.80000000000000015e87

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.7%

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

   if 3.30000000000000025e147 < z < 9.50000000000000022e257

   1. Initial program 71.3%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. associate--l+ 76.8%

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

      2. distribute-lft-out-- 76.8%

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

      3. div-sub 76.8%

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

      4. mul-1-neg 76.8%

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

      5. unsub-neg 76.8%

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

      6. div-sub 76.8%

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

      7. associate-/l* 82.9%

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

      8. associate-/l* 89.0%

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

      9. distribute-rgt-out-- 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in y around inf 65.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+147} \lor \neg \left(z \leq 9.5 \cdot 10^{+257}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+113} \lor \neg \left(z \leq 1.5 \cdot 10^{+149}\right) \land z \leq 4.7 \cdot 10^{+257}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -6.6e+43)
     t_1
     (if (<= z 7.5e-13)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 2.9e+85)
         t_2
         (if (<= z 2.8e+87)
           x
           (if (or (<= z 5.5e+113) (and (not (<= z 1.5e+149)) (<= z 4.7e+257)))
             t_2
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.6e+43) {
		tmp = t_1;
	} else if (z <= 7.5e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if ((z <= 5.5e+113) || (!(z <= 1.5e+149) && (z <= 4.7e+257))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-6.6d+43)) then
        tmp = t_1
    else if (z <= 7.5d-13) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.9d+85) then
        tmp = t_2
    else if (z <= 2.8d+87) then
        tmp = x
    else if ((z <= 5.5d+113) .or. (.not. (z <= 1.5d+149)) .and. (z <= 4.7d+257)) then
        tmp = t_2
    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 + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.6e+43) {
		tmp = t_1;
	} else if (z <= 7.5e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if ((z <= 5.5e+113) || (!(z <= 1.5e+149) && (z <= 4.7e+257))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -6.6e+43:
		tmp = t_1
	elif z <= 7.5e-13:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.9e+85:
		tmp = t_2
	elif z <= 2.8e+87:
		tmp = x
	elif (z <= 5.5e+113) or (not (z <= 1.5e+149) and (z <= 4.7e+257)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.6e+43)
		tmp = t_1;
	elseif (z <= 7.5e-13)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif ((z <= 5.5e+113) || (!(z <= 1.5e+149) && (z <= 4.7e+257)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -6.6e+43)
		tmp = t_1;
	elseif (z <= 7.5e-13)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif ((z <= 5.5e+113) || (~((z <= 1.5e+149)) && (z <= 4.7e+257)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+43], t$95$1, If[LessEqual[z, 7.5e-13], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+85], t$95$2, If[LessEqual[z, 2.8e+87], x, If[Or[LessEqual[z, 5.5e+113], And[N[Not[LessEqual[z, 1.5e+149]], $MachinePrecision], LessEqual[z, 4.7e+257]]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.6000000000000003e43 or 5.5000000000000001e113 < z < 1.50000000000000002e149 or 4.7e257 < z

   1. Initial program 63.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. div-sub 68.3%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 82.4%

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

      9. distribute-rgt-out-- 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in t around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. div-sub 75.6%

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

      3. mul-1-neg 75.6%

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

      4. associate-/l* 82.5%

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

      5. distribute-lft-neg-in 82.5%

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

      6. distribute-rgt-in 82.5%

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

      7. sub-neg 82.5%

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

      8. associate-/r/ 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in t around 0 82.7%

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

       1. associate-*r/ 82.7%

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

       2. neg-mul-1 82.7%

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

   11. Simplified 82.7%

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

   12. Taylor expanded in y around inf 68.8%

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

       1. mul-1-neg 68.8%

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

       2. associate-/l* 74.1%

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

       3. distribute-rgt-neg-in 74.1%

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

       4. distribute-neg-frac2 74.1%

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

   14. Simplified 74.1%

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

   if -6.6000000000000003e43 < z < 7.5000000000000004e-13

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l/ 88.9%

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

      3. associate-*r/ 94.9%

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

      4. clear-num 94.9%

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

      5. un-div-inv 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in z around 0 82.0%

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

   if 7.5000000000000004e-13 < z < 2.89999999999999997e85 or 2.80000000000000015e87 < z < 5.5000000000000001e113 or 1.50000000000000002e149 < z < 4.7e257

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 59.7%

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

      1. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   if 2.89999999999999997e85 < z < 2.80000000000000015e87

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+43}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+113} \lor \neg \left(z \leq 1.5 \cdot 10^{+149}\right) \land z \leq 4.7 \cdot 10^{+257}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+114} \lor \neg \left(z \leq 6 \cdot 10^{+147}\right) \land z \leq 4.6 \cdot 10^{+256}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -5.5e+46)
     t_1
     (if (<= z 2.7e-19)
       (+ x (* y (/ (- t x) a)))
       (if (<= z 2.5e+85)
         t_2
         (if (<= z 2.8e+87)
           x
           (if (or (<= z 4.2e+114) (and (not (<= z 6e+147)) (<= z 4.6e+256)))
             t_2
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -5.5e+46) {
		tmp = t_1;
	} else if (z <= 2.7e-19) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2.5e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if ((z <= 4.2e+114) || (!(z <= 6e+147) && (z <= 4.6e+256))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-5.5d+46)) then
        tmp = t_1
    else if (z <= 2.7d-19) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 2.5d+85) then
        tmp = t_2
    else if (z <= 2.8d+87) then
        tmp = x
    else if ((z <= 4.2d+114) .or. (.not. (z <= 6d+147)) .and. (z <= 4.6d+256)) then
        tmp = t_2
    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 + (x * (y / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -5.5e+46) {
		tmp = t_1;
	} else if (z <= 2.7e-19) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2.5e+85) {
		tmp = t_2;
	} else if (z <= 2.8e+87) {
		tmp = x;
	} else if ((z <= 4.2e+114) || (!(z <= 6e+147) && (z <= 4.6e+256))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -5.5e+46:
		tmp = t_1
	elif z <= 2.7e-19:
		tmp = x + (y * ((t - x) / a))
	elif z <= 2.5e+85:
		tmp = t_2
	elif z <= 2.8e+87:
		tmp = x
	elif (z <= 4.2e+114) or (not (z <= 6e+147) and (z <= 4.6e+256)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -5.5e+46)
		tmp = t_1;
	elseif (z <= 2.7e-19)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 2.5e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif ((z <= 4.2e+114) || (!(z <= 6e+147) && (z <= 4.6e+256)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -5.5e+46)
		tmp = t_1;
	elseif (z <= 2.7e-19)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 2.5e+85)
		tmp = t_2;
	elseif (z <= 2.8e+87)
		tmp = x;
	elseif ((z <= 4.2e+114) || (~((z <= 6e+147)) && (z <= 4.6e+256)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+46], t$95$1, If[LessEqual[z, 2.7e-19], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+85], t$95$2, If[LessEqual[z, 2.8e+87], x, If[Or[LessEqual[z, 4.2e+114], And[N[Not[LessEqual[z, 6e+147]], $MachinePrecision], LessEqual[z, 4.6e+256]]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4999999999999998e46 or 4.2000000000000001e114 < z < 5.99999999999999987e147 or 4.5999999999999997e256 < z

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 67.8%

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

      1. associate--l+ 67.8%

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

      2. distribute-lft-out-- 67.8%

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

      3. div-sub 67.8%

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

      4. mul-1-neg 67.8%

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

      5. unsub-neg 67.8%

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

      6. div-sub 67.8%

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

      7. associate-/l* 74.6%

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

      8. associate-/l* 82.1%

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

      9. distribute-rgt-out-- 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. div-sub 75.2%

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

      3. mul-1-neg 75.2%

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

      4. associate-/l* 82.2%

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

      5. distribute-lft-neg-in 82.2%

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

      6. distribute-rgt-in 82.2%

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

      7. sub-neg 82.2%

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

      8. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in t around 0 82.5%

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

       1. associate-*r/ 82.5%

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

       2. neg-mul-1 82.5%

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

   11. Simplified 82.5%

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

   12. Taylor expanded in y around inf 68.3%

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

       1. mul-1-neg 68.3%

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

       2. associate-/l* 73.7%

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

       3. distribute-rgt-neg-in 73.7%

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

       4. distribute-neg-frac2 73.7%

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

   14. Simplified 73.7%

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

   if -5.4999999999999998e46 < z < 2.7000000000000001e-19

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 75.2%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

   if 2.7000000000000001e-19 < z < 2.5e85 or 2.80000000000000015e87 < z < 4.2000000000000001e114 or 5.99999999999999987e147 < z < 4.5999999999999997e256

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 59.7%

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

      1. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   if 2.5e85 < z < 2.80000000000000015e87

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+114} \lor \neg \left(z \leq 6 \cdot 10^{+147}\right) \land z \leq 4.6 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8600:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -190:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -2.6e+32)
     t_1
     (if (<= z -8600.0)
       (- x (* x (/ y a)))
       (if (<= z -190.0)
         t_1
         (if (<= z -3.1e-221)
           t_2
           (if (<= z -3.2e-243)
             (* (- t x) (/ y a))
             (if (<= z 4.8e+36) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -2.6e+32) {
		tmp = t_1;
	} else if (z <= -8600.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -190.0) {
		tmp = t_1;
	} else if (z <= -3.1e-221) {
		tmp = t_2;
	} else if (z <= -3.2e-243) {
		tmp = (t - x) * (y / a);
	} else if (z <= 4.8e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (z / (z - a))
    t_2 = x + ((y * t) / a)
    if (z <= (-2.6d+32)) then
        tmp = t_1
    else if (z <= (-8600.0d0)) then
        tmp = x - (x * (y / a))
    else if (z <= (-190.0d0)) then
        tmp = t_1
    else if (z <= (-3.1d-221)) then
        tmp = t_2
    else if (z <= (-3.2d-243)) then
        tmp = (t - x) * (y / a)
    else if (z <= 4.8d+36) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -2.6e+32) {
		tmp = t_1;
	} else if (z <= -8600.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -190.0) {
		tmp = t_1;
	} else if (z <= -3.1e-221) {
		tmp = t_2;
	} else if (z <= -3.2e-243) {
		tmp = (t - x) * (y / a);
	} else if (z <= 4.8e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -2.6e+32:
		tmp = t_1
	elif z <= -8600.0:
		tmp = x - (x * (y / a))
	elif z <= -190.0:
		tmp = t_1
	elif z <= -3.1e-221:
		tmp = t_2
	elif z <= -3.2e-243:
		tmp = (t - x) * (y / a)
	elif z <= 4.8e+36:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -2.6e+32)
		tmp = t_1;
	elseif (z <= -8600.0)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= -190.0)
		tmp = t_1;
	elseif (z <= -3.1e-221)
		tmp = t_2;
	elseif (z <= -3.2e-243)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 4.8e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -2.6e+32)
		tmp = t_1;
	elseif (z <= -8600.0)
		tmp = x - (x * (y / a));
	elseif (z <= -190.0)
		tmp = t_1;
	elseif (z <= -3.1e-221)
		tmp = t_2;
	elseif (z <= -3.2e-243)
		tmp = (t - x) * (y / a);
	elseif (z <= 4.8e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+32], t$95$1, If[LessEqual[z, -8600.0], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -190.0], t$95$1, If[LessEqual[z, -3.1e-221], t$95$2, If[LessEqual[z, -3.2e-243], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+36], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000002e32 or -8600 < z < -190 or 4.79999999999999985e36 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in y around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. unsub-neg 34.0%

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

      3. associate-/l* 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   if -2.6000000000000002e32 < z < -8600

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 83.9%

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

      1. neg-mul-1 83.9%

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

      2. distribute-neg-frac 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. associate-/l* 83.5%

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

   8. Simplified 83.5%

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

   if -190 < z < -3.0999999999999999e-221 or -3.1999999999999998e-243 < z < 4.79999999999999985e36

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 96.2%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 78.9%

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

   6. Taylor expanded in t around inf 62.7%

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

   if -3.0999999999999999e-221 < z < -3.1999999999999998e-243

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. div-sub 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in a around inf 99.2%

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

   7. Taylor expanded in y around 0 68.3%

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

   8. Taylor expanded in t around 0 68.3%

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

      1. neg-mul-1 68.3%

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

      2. associate-*r/ 84.1%

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

      3. +-commutative 84.1%

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

      4. associate-*r/ 99.7%

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

      5. distribute-lft-neg-out 99.7%

         \[\leadsto t \cdot \frac{y}{a} + \color{blue}{\left(-x\right) \cdot \frac{y}{a}} \]

      6. distribute-rgt-in 99.7%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t + \left(-x\right)\right)} \]

      7. sub-neg 99.7%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(t - x\right)} \]

      8. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a}} \]

   10. Simplified 99.7%

       \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -8600:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -190:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8500:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.2e+36)
     t
     (if (<= z -8500.0)
       (- x (* x (/ y a)))
       (if (<= z -8000.0)
         t
         (if (<= z -4.4e-122)
           t_1
           (if (<= z -1.2e-260)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.38e+19) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.2e+36) {
		tmp = t;
	} else if (z <= -8500.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -8000.0) {
		tmp = t;
	} else if (z <= -4.4e-122) {
		tmp = t_1;
	} else if (z <= -1.2e-260) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.38e+19) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.2d+36)) then
        tmp = t
    else if (z <= (-8500.0d0)) then
        tmp = x - (x * (y / a))
    else if (z <= (-8000.0d0)) then
        tmp = t
    else if (z <= (-4.4d-122)) then
        tmp = t_1
    else if (z <= (-1.2d-260)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.38d+19) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.2e+36) {
		tmp = t;
	} else if (z <= -8500.0) {
		tmp = x - (x * (y / a));
	} else if (z <= -8000.0) {
		tmp = t;
	} else if (z <= -4.4e-122) {
		tmp = t_1;
	} else if (z <= -1.2e-260) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.38e+19) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.2e+36:
		tmp = t
	elif z <= -8500.0:
		tmp = x - (x * (y / a))
	elif z <= -8000.0:
		tmp = t
	elif z <= -4.4e-122:
		tmp = t_1
	elif z <= -1.2e-260:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.38e+19:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.2e+36)
		tmp = t;
	elseif (z <= -8500.0)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= -8000.0)
		tmp = t;
	elseif (z <= -4.4e-122)
		tmp = t_1;
	elseif (z <= -1.2e-260)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.38e+19)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.2e+36)
		tmp = t;
	elseif (z <= -8500.0)
		tmp = x - (x * (y / a));
	elseif (z <= -8000.0)
		tmp = t;
	elseif (z <= -4.4e-122)
		tmp = t_1;
	elseif (z <= -1.2e-260)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.38e+19)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+36], t, If[LessEqual[z, -8500.0], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8000.0], t, If[LessEqual[z, -4.4e-122], t$95$1, If[LessEqual[z, -1.2e-260], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e+19], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.19999999999999996e36 or -8500 < z < -8e3 or 1.38e19 < z

   1. Initial program 69.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.3%

      \[\leadsto \color{blue}{t} \]

   if -1.19999999999999996e36 < z < -8500

   1. Initial program 83.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.9%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(-1 \cdot \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. neg-mul-1 83.9%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(-\frac{x}{a - z}\right)} \]

      2. distribute-neg-frac 83.9%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{-x}{a - z}} \]

   5. Simplified 83.9%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{-x}{a - z}} \]

   6. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 68.1%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 68.1%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 83.5%

         \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   8. Simplified 83.5%

      \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -8e3 < z < -4.4e-122 or -1.2e-260 < z < 1.38e19

   1. Initial program 95.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 95.3%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 91.7%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 96.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 96.9%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 97.3%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 97.3%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 79.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   6. Taylor expanded in t around inf 61.0%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

   if -4.4e-122 < z < -1.2e-260

   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 inf 75.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 75.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   5. Simplified 75.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   6. Taylor expanded in z around 0 74.2%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8500:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -31000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-259}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.75e+35)
     t
     (if (<= z -31000.0)
       t_2
       (if (<= z -1300.0)
         t
         (if (<= z -9e-127)
           t_1
           (if (<= z -1.85e-259) t_2 (if (<= z 1.38e+19) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.75e+35) {
		tmp = t;
	} else if (z <= -31000.0) {
		tmp = t_2;
	} else if (z <= -1300.0) {
		tmp = t;
	} else if (z <= -9e-127) {
		tmp = t_1;
	} else if (z <= -1.85e-259) {
		tmp = t_2;
	} else if (z <= 1.38e+19) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.75d+35)) then
        tmp = t
    else if (z <= (-31000.0d0)) then
        tmp = t_2
    else if (z <= (-1300.0d0)) then
        tmp = t
    else if (z <= (-9d-127)) then
        tmp = t_1
    else if (z <= (-1.85d-259)) then
        tmp = t_2
    else if (z <= 1.38d+19) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.75e+35) {
		tmp = t;
	} else if (z <= -31000.0) {
		tmp = t_2;
	} else if (z <= -1300.0) {
		tmp = t;
	} else if (z <= -9e-127) {
		tmp = t_1;
	} else if (z <= -1.85e-259) {
		tmp = t_2;
	} else if (z <= 1.38e+19) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.75e+35:
		tmp = t
	elif z <= -31000.0:
		tmp = t_2
	elif z <= -1300.0:
		tmp = t
	elif z <= -9e-127:
		tmp = t_1
	elif z <= -1.85e-259:
		tmp = t_2
	elif z <= 1.38e+19:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.75e+35)
		tmp = t;
	elseif (z <= -31000.0)
		tmp = t_2;
	elseif (z <= -1300.0)
		tmp = t;
	elseif (z <= -9e-127)
		tmp = t_1;
	elseif (z <= -1.85e-259)
		tmp = t_2;
	elseif (z <= 1.38e+19)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.75e+35)
		tmp = t;
	elseif (z <= -31000.0)
		tmp = t_2;
	elseif (z <= -1300.0)
		tmp = t;
	elseif (z <= -9e-127)
		tmp = t_1;
	elseif (z <= -1.85e-259)
		tmp = t_2;
	elseif (z <= 1.38e+19)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+35], t, If[LessEqual[z, -31000.0], t$95$2, If[LessEqual[z, -1300.0], t, If[LessEqual[z, -9e-127], t$95$1, If[LessEqual[z, -1.85e-259], t$95$2, If[LessEqual[z, 1.38e+19], t$95$1, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e35 or -31000 < z < -1300 or 1.38e19 < z

   1. Initial program 69.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.3%

      \[\leadsto \color{blue}{t} \]

   if -1.75e35 < z < -31000 or -8.9999999999999998e-127 < z < -1.84999999999999996e-259

   1. Initial program 92.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 76.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   6. Taylor expanded in z around 0 75.6%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   if -1300 < z < -8.9999999999999998e-127 or -1.84999999999999996e-259 < z < 1.38e19

   1. Initial program 95.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 95.3%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 91.7%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 96.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 96.9%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 97.3%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 97.3%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 79.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   6. Taylor expanded in t around inf 61.0%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -31000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y (- a)))))
   (if (<= z -4.5e-198)
     (+ x t)
     (if (<= z -2.2e-243)
       t_1
       (if (<= z -7.4e-252)
         x
         (if (<= z -2.6e-262)
           t_1
           (if (<= z 5e-77) x (if (<= z 4.5e+32) (/ t (/ a y)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / -a);
	double tmp;
	if (z <= -4.5e-198) {
		tmp = x + t;
	} else if (z <= -2.2e-243) {
		tmp = t_1;
	} else if (z <= -7.4e-252) {
		tmp = x;
	} else if (z <= -2.6e-262) {
		tmp = t_1;
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 4.5e+32) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / -a)
    if (z <= (-4.5d-198)) then
        tmp = x + t
    else if (z <= (-2.2d-243)) then
        tmp = t_1
    else if (z <= (-7.4d-252)) then
        tmp = x
    else if (z <= (-2.6d-262)) then
        tmp = t_1
    else if (z <= 5d-77) then
        tmp = x
    else if (z <= 4.5d+32) then
        tmp = t / (a / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / -a);
	double tmp;
	if (z <= -4.5e-198) {
		tmp = x + t;
	} else if (z <= -2.2e-243) {
		tmp = t_1;
	} else if (z <= -7.4e-252) {
		tmp = x;
	} else if (z <= -2.6e-262) {
		tmp = t_1;
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 4.5e+32) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / -a)
	tmp = 0
	if z <= -4.5e-198:
		tmp = x + t
	elif z <= -2.2e-243:
		tmp = t_1
	elif z <= -7.4e-252:
		tmp = x
	elif z <= -2.6e-262:
		tmp = t_1
	elif z <= 5e-77:
		tmp = x
	elif z <= 4.5e+32:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -4.5e-198)
		tmp = Float64(x + t);
	elseif (z <= -2.2e-243)
		tmp = t_1;
	elseif (z <= -7.4e-252)
		tmp = x;
	elseif (z <= -2.6e-262)
		tmp = t_1;
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 4.5e+32)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / -a);
	tmp = 0.0;
	if (z <= -4.5e-198)
		tmp = x + t;
	elseif (z <= -2.2e-243)
		tmp = t_1;
	elseif (z <= -7.4e-252)
		tmp = x;
	elseif (z <= -2.6e-262)
		tmp = t_1;
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 4.5e+32)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e-198], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.2e-243], t$95$1, If[LessEqual[z, -7.4e-252], x, If[LessEqual[z, -2.6e-262], t$95$1, If[LessEqual[z, 5e-77], x, If[LessEqual[z, 4.5e+32], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4999999999999998e-198

   1. Initial program 78.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 44.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.8%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. unsub-neg 44.8%

         \[\leadsto \color{blue}{x - \frac{z \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 53.9%

         \[\leadsto x - \color{blue}{z \cdot \frac{t - x}{a - z}} \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{x - z \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in t around inf 51.8%

      \[\leadsto x - z \cdot \color{blue}{\frac{t}{a - z}} \]

   7. Taylor expanded in z around inf 45.6%

      \[\leadsto \color{blue}{x - -1 \cdot t} \]
   8. Step-by-step derivation

      1. sub-neg 45.6%

         \[\leadsto \color{blue}{x + \left(--1 \cdot t\right)} \]

      2. neg-mul-1 45.6%

         \[\leadsto x + \left(-\color{blue}{\left(-t\right)}\right) \]

      3. remove-double-neg 45.6%

         \[\leadsto x + \color{blue}{t} \]

   9. Simplified 45.6%

      \[\leadsto \color{blue}{x + t} \]

   if -4.4999999999999998e-198 < z < -2.1999999999999999e-243 or -7.4000000000000002e-252 < z < -2.5999999999999999e-262

   1. Initial program 99.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 85.9%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 85.9%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around 0 58.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a}} \]

      2. associate-/l* 65.2%

         \[\leadsto -\color{blue}{x \cdot \frac{y}{a}} \]

   9. Simplified 65.2%

      \[\leadsto \color{blue}{-x \cdot \frac{y}{a}} \]

   if -2.1999999999999999e-243 < z < -7.4000000000000002e-252 or -2.5999999999999999e-262 < z < 4.99999999999999963e-77

   1. Initial program 95.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{x} \]

   if 4.99999999999999963e-77 < z < 4.5000000000000003e32

   1. Initial program 91.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 67.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 48.1%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 36.1%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 47.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 47.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num 48.0%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv 48.0%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr 48.0%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 4.5000000000000003e32 < z

   1. Initial program 71.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- y a) (/ z x)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2e+44)
     t_1
     (if (<= z 1.15e-13)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 9.2e+83)
         t_2
         (if (<= z 4.5e+88)
           (* x (+ (/ (- y z) (- z a)) 1.0))
           (if (<= z 6.2e+107) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y - a) / (z / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2e+44) {
		tmp = t_1;
	} else if (z <= 1.15e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 9.2e+83) {
		tmp = t_2;
	} else if (z <= 4.5e+88) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 6.2e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((y - a) / (z / x))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2d+44)) then
        tmp = t_1
    else if (z <= 1.15d-13) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 9.2d+83) then
        tmp = t_2
    else if (z <= 4.5d+88) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (z <= 6.2d+107) then
        tmp = t_2
    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 - a) / (z / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2e+44) {
		tmp = t_1;
	} else if (z <= 1.15e-13) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 9.2e+83) {
		tmp = t_2;
	} else if (z <= 4.5e+88) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 6.2e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y - a) / (z / x))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2e+44:
		tmp = t_1
	elif z <= 1.15e-13:
		tmp = x + ((t - x) / (a / y))
	elif z <= 9.2e+83:
		tmp = t_2
	elif z <= 4.5e+88:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif z <= 6.2e+107:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y - a) / Float64(z / x)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2e+44)
		tmp = t_1;
	elseif (z <= 1.15e-13)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 9.2e+83)
		tmp = t_2;
	elseif (z <= 4.5e+88)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (z <= 6.2e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y - a) / (z / x));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2e+44)
		tmp = t_1;
	elseif (z <= 1.15e-13)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 9.2e+83)
		tmp = t_2;
	elseif (z <= 4.5e+88)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (z <= 6.2e+107)
		tmp = t_2;
	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 - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+44], t$95$1, If[LessEqual[z, 1.15e-13], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+83], t$95$2, If[LessEqual[z, 4.5e+88], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+107], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0000000000000002e44 or 6.20000000000000052e107 < z

   1. Initial program 65.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. div-sub 70.6%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 77.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 84.1%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 85.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in t around 0 76.5%

      \[\leadsto t - \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z} + t \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 76.5%

         \[\leadsto t - \color{blue}{\left(t \cdot \left(\frac{y}{z} - \frac{a}{z}\right) + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. div-sub 76.5%

         \[\leadsto t - \left(t \cdot \color{blue}{\frac{y - a}{z}} + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right) \]

      3. mul-1-neg 76.5%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]

      4. associate-/l* 83.0%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right)\right) \]

      5. distribute-lft-neg-in 83.0%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-x\right) \cdot \frac{y - a}{z}}\right) \]

      6. distribute-rgt-in 83.0%

         \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(t + \left(-x\right)\right)} \]

      7. sub-neg 83.0%

         \[\leadsto t - \frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)} \]

      8. associate-/r/ 85.2%

         \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   8. Simplified 85.2%

      \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   9. Taylor expanded in t around 0 80.1%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   10. Step-by-step derivation

       1. associate-*r/ 80.1%

          \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

       2. neg-mul-1 80.1%

          \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   11. Simplified 80.1%

       \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   if -2.0000000000000002e44 < z < 1.1499999999999999e-13

   1. Initial program 93.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 93.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 88.9%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 94.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 94.9%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 95.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 95.1%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 82.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   if 1.1499999999999999e-13 < z < 9.1999999999999998e83 or 4.5e88 < z < 6.20000000000000052e107

   1. Initial program 88.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 67.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 71.0%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 9.1999999999999998e83 < z < 4.5e88

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 100.0%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- y a) (/ z x)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+45)
     t_1
     (if (<= z 8.2e-14)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 2.8e+85)
         t_2
         (if (<= z 5.5e+87) x (if (<= z 2.3e+108) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y - a) / (z / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+45) {
		tmp = t_1;
	} else if (z <= 8.2e-14) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.8e+85) {
		tmp = t_2;
	} else if (z <= 5.5e+87) {
		tmp = x;
	} else if (z <= 2.3e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((y - a) / (z / x))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-1.35d+45)) then
        tmp = t_1
    else if (z <= 8.2d-14) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.8d+85) then
        tmp = t_2
    else if (z <= 5.5d+87) then
        tmp = x
    else if (z <= 2.3d+108) then
        tmp = t_2
    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 - a) / (z / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+45) {
		tmp = t_1;
	} else if (z <= 8.2e-14) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.8e+85) {
		tmp = t_2;
	} else if (z <= 5.5e+87) {
		tmp = x;
	} else if (z <= 2.3e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y - a) / (z / x))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+45:
		tmp = t_1
	elif z <= 8.2e-14:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.8e+85:
		tmp = t_2
	elif z <= 5.5e+87:
		tmp = x
	elif z <= 2.3e+108:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y - a) / Float64(z / x)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.35e+45)
		tmp = t_1;
	elseif (z <= 8.2e-14)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.8e+85)
		tmp = t_2;
	elseif (z <= 5.5e+87)
		tmp = x;
	elseif (z <= 2.3e+108)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y - a) / (z / x));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+45)
		tmp = t_1;
	elseif (z <= 8.2e-14)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.8e+85)
		tmp = t_2;
	elseif (z <= 5.5e+87)
		tmp = x;
	elseif (z <= 2.3e+108)
		tmp = t_2;
	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 - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+45], t$95$1, If[LessEqual[z, 8.2e-14], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+85], t$95$2, If[LessEqual[z, 5.5e+87], x, If[LessEqual[z, 2.3e+108], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999992e45 or 2.2999999999999999e108 < z

   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 70.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 70.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 70.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 70.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 70.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 70.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 70.3%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 76.8%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 83.9%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 85.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 85.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in t around 0 76.2%

      \[\leadsto t - \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z} + t \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto t - \color{blue}{\left(t \cdot \left(\frac{y}{z} - \frac{a}{z}\right) + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. div-sub 76.2%

         \[\leadsto t - \left(t \cdot \color{blue}{\frac{y - a}{z}} + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right) \]

      3. mul-1-neg 76.2%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]

      4. associate-/l* 82.8%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right)\right) \]

      5. distribute-lft-neg-in 82.8%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-x\right) \cdot \frac{y - a}{z}}\right) \]

      6. distribute-rgt-in 82.8%

         \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(t + \left(-x\right)\right)} \]

      7. sub-neg 82.8%

         \[\leadsto t - \frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)} \]

      8. associate-/r/ 85.0%

         \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   8. Simplified 85.0%

      \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   9. Taylor expanded in t around 0 79.8%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   10. Step-by-step derivation

       1. associate-*r/ 79.8%

          \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

       2. neg-mul-1 79.8%

          \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   11. Simplified 79.8%

       \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   if -1.34999999999999992e45 < z < 8.2000000000000004e-14

   1. Initial program 93.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 93.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 88.9%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 94.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 94.9%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 95.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 95.1%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 82.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   if 8.2000000000000004e-14 < z < 2.7999999999999999e85 or 5.50000000000000022e87 < z < 2.2999999999999999e108

   1. Initial program 86.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 2.7999999999999999e85 < z < 5.50000000000000022e87

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (<= z -1.1e+30)
     t_1
     (if (<= z 1.2e-19)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 2.9e+85)
         t_2
         (if (<= z 1.1e+88) x (if (<= z 8e+111) t_2 t_1)))))))

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 (z <= -1.1e+30) {
		tmp = t_1;
	} else if (z <= 1.2e-19) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 1.1e+88) {
		tmp = x;
	} else if (z <= 8e+111) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-1.1d+30)) then
        tmp = t_1
    else if (z <= 1.2d-19) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.9d+85) then
        tmp = t_2
    else if (z <= 1.1d+88) then
        tmp = x
    else if (z <= 8d+111) then
        tmp = t_2
    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 + (x * ((y - a) / z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.1e+30) {
		tmp = t_1;
	} else if (z <= 1.2e-19) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.9e+85) {
		tmp = t_2;
	} else if (z <= 1.1e+88) {
		tmp = x;
	} else if (z <= 8e+111) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 z <= -1.1e+30:
		tmp = t_1
	elif z <= 1.2e-19:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.9e+85:
		tmp = t_2
	elif z <= 1.1e+88:
		tmp = x
	elif z <= 8e+111:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.1e+30)
		tmp = t_1;
	elseif (z <= 1.2e-19)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 1.1e+88)
		tmp = x;
	elseif (z <= 8e+111)
		tmp = t_2;
	else
		tmp = t_1;
	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 (z <= -1.1e+30)
		tmp = t_1;
	elseif (z <= 1.2e-19)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.9e+85)
		tmp = t_2;
	elseif (z <= 1.1e+88)
		tmp = x;
	elseif (z <= 8e+111)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+30], t$95$1, If[LessEqual[z, 1.2e-19], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+85], t$95$2, If[LessEqual[z, 1.1e+88], x, If[LessEqual[z, 8e+111], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e30 or 7.99999999999999965e111 < z

   1. Initial program 64.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. div-sub 70.6%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 77.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 84.1%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 85.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in t around 0 71.3%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 71.3%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 77.8%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 77.8%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 77.8%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   8. Simplified 77.8%

      \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -1.1e30 < z < 1.20000000000000011e-19

   1. Initial program 94.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 89.5%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 95.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 95.5%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 95.8%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Applied egg-rr 95.8%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in z around 0 82.5%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   if 1.20000000000000011e-19 < z < 2.89999999999999997e85 or 1.10000000000000004e88 < z < 7.99999999999999965e111

   1. Initial program 86.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 2.89999999999999997e85 < z < 1.10000000000000004e88

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+30}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+45)
   t
   (if (<= z 5.4e-297)
     x
     (if (<= z 3.5e-142)
       (* t (/ y a))
       (if (<= z 5e-77) x (if (<= z 2.1e-39) (/ t (/ a y)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+45) {
		tmp = t;
	} else if (z <= 5.4e-297) {
		tmp = x;
	} else if (z <= 3.5e-142) {
		tmp = t * (y / a);
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 2.1e-39) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+45)) then
        tmp = t
    else if (z <= 5.4d-297) then
        tmp = x
    else if (z <= 3.5d-142) then
        tmp = t * (y / a)
    else if (z <= 5d-77) then
        tmp = x
    else if (z <= 2.1d-39) then
        tmp = t / (a / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+45) {
		tmp = t;
	} else if (z <= 5.4e-297) {
		tmp = x;
	} else if (z <= 3.5e-142) {
		tmp = t * (y / a);
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 2.1e-39) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+45:
		tmp = t
	elif z <= 5.4e-297:
		tmp = x
	elif z <= 3.5e-142:
		tmp = t * (y / a)
	elif z <= 5e-77:
		tmp = x
	elif z <= 2.1e-39:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+45)
		tmp = t;
	elseif (z <= 5.4e-297)
		tmp = x;
	elseif (z <= 3.5e-142)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 2.1e-39)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+45)
		tmp = t;
	elseif (z <= 5.4e-297)
		tmp = x;
	elseif (z <= 3.5e-142)
		tmp = t * (y / a);
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 2.1e-39)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+45], t, If[LessEqual[z, 5.4e-297], x, If[LessEqual[z, 3.5e-142], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-77], x, If[LessEqual[z, 2.1e-39], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8e45 or 2.09999999999999993e-39 < z

   1. Initial program 71.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.1%

      \[\leadsto \color{blue}{t} \]

   if -6.8e45 < z < 5.4000000000000002e-297 or 3.50000000000000015e-142 < z < 4.99999999999999963e-77

   1. Initial program 94.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{x} \]

   if 5.4000000000000002e-297 < z < 3.50000000000000015e-142

   1. Initial program 94.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 59.2%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 55.2%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 40.1%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 40.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 40.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if 4.99999999999999963e-77 < z < 2.09999999999999993e-39

   1. Initial program 99.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 99.5%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 99.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 84.8%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 52.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 83.1%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 83.1%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num 83.3%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv 83.6%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr 83.6%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+43)
   t
   (if (<= z 7.5e-297)
     x
     (if (<= z 2.7e-143)
       (* t (/ y a))
       (if (<= z 4.2e-77) x (if (<= z 1.35e-37) (* y (/ t a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+43) {
		tmp = t;
	} else if (z <= 7.5e-297) {
		tmp = x;
	} else if (z <= 2.7e-143) {
		tmp = t * (y / a);
	} else if (z <= 4.2e-77) {
		tmp = x;
	} else if (z <= 1.35e-37) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+43)) then
        tmp = t
    else if (z <= 7.5d-297) then
        tmp = x
    else if (z <= 2.7d-143) then
        tmp = t * (y / a)
    else if (z <= 4.2d-77) then
        tmp = x
    else if (z <= 1.35d-37) then
        tmp = y * (t / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+43) {
		tmp = t;
	} else if (z <= 7.5e-297) {
		tmp = x;
	} else if (z <= 2.7e-143) {
		tmp = t * (y / a);
	} else if (z <= 4.2e-77) {
		tmp = x;
	} else if (z <= 1.35e-37) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+43:
		tmp = t
	elif z <= 7.5e-297:
		tmp = x
	elif z <= 2.7e-143:
		tmp = t * (y / a)
	elif z <= 4.2e-77:
		tmp = x
	elif z <= 1.35e-37:
		tmp = y * (t / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+43)
		tmp = t;
	elseif (z <= 7.5e-297)
		tmp = x;
	elseif (z <= 2.7e-143)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 4.2e-77)
		tmp = x;
	elseif (z <= 1.35e-37)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+43)
		tmp = t;
	elseif (z <= 7.5e-297)
		tmp = x;
	elseif (z <= 2.7e-143)
		tmp = t * (y / a);
	elseif (z <= 4.2e-77)
		tmp = x;
	elseif (z <= 1.35e-37)
		tmp = y * (t / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+43], t, If[LessEqual[z, 7.5e-297], x, If[LessEqual[z, 2.7e-143], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-77], x, If[LessEqual[z, 1.35e-37], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5e43 or 1.35000000000000008e-37 < z

   1. Initial program 71.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.1%

      \[\leadsto \color{blue}{t} \]

   if -4.5e43 < z < 7.4999999999999994e-297 or 2.70000000000000009e-143 < z < 4.20000000000000031e-77

   1. Initial program 94.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{x} \]

   if 7.4999999999999994e-297 < z < 2.70000000000000009e-143

   1. Initial program 94.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 59.2%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 55.2%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 40.1%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 40.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 40.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if 4.20000000000000031e-77 < z < 1.35000000000000008e-37

   1. Initial program 99.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 99.5%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 99.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 84.8%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 83.3%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 24: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -3.1e+44)
     t
     (if (<= z 5.7e-297)
       x
       (if (<= z 1.25e-143)
         t_1
         (if (<= z 4.5e-77) x (if (<= z 6.8e-38) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -3.1e+44) {
		tmp = t;
	} else if (z <= 5.7e-297) {
		tmp = x;
	} else if (z <= 1.25e-143) {
		tmp = t_1;
	} else if (z <= 4.5e-77) {
		tmp = x;
	} else if (z <= 6.8e-38) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-3.1d+44)) then
        tmp = t
    else if (z <= 5.7d-297) then
        tmp = x
    else if (z <= 1.25d-143) then
        tmp = t_1
    else if (z <= 4.5d-77) then
        tmp = x
    else if (z <= 6.8d-38) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -3.1e+44) {
		tmp = t;
	} else if (z <= 5.7e-297) {
		tmp = x;
	} else if (z <= 1.25e-143) {
		tmp = t_1;
	} else if (z <= 4.5e-77) {
		tmp = x;
	} else if (z <= 6.8e-38) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -3.1e+44:
		tmp = t
	elif z <= 5.7e-297:
		tmp = x
	elif z <= 1.25e-143:
		tmp = t_1
	elif z <= 4.5e-77:
		tmp = x
	elif z <= 6.8e-38:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -3.1e+44)
		tmp = t;
	elseif (z <= 5.7e-297)
		tmp = x;
	elseif (z <= 1.25e-143)
		tmp = t_1;
	elseif (z <= 4.5e-77)
		tmp = x;
	elseif (z <= 6.8e-38)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -3.1e+44)
		tmp = t;
	elseif (z <= 5.7e-297)
		tmp = x;
	elseif (z <= 1.25e-143)
		tmp = t_1;
	elseif (z <= 4.5e-77)
		tmp = x;
	elseif (z <= 6.8e-38)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+44], t, If[LessEqual[z, 5.7e-297], x, If[LessEqual[z, 1.25e-143], t$95$1, If[LessEqual[z, 4.5e-77], x, If[LessEqual[z, 6.8e-38], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999996e44 or 6.8000000000000004e-38 < z

   1. Initial program 71.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.1%

      \[\leadsto \color{blue}{t} \]

   if -3.09999999999999996e44 < z < 5.6999999999999997e-297 or 1.2500000000000001e-143 < z < 4.5000000000000001e-77

   1. Initial program 94.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{x} \]

   if 5.6999999999999997e-297 < z < 1.2500000000000001e-143 or 4.5000000000000001e-77 < z < 6.8000000000000004e-38

   1. Initial program 95.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 66.7%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in a around inf 60.7%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   7. Taylor expanded in t around inf 42.4%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 48.2%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 48.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-9}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -3.3e+44)
     t_1
     (if (<= z 7.8e-9)
       (- x (* (- t x) (/ (- z y) a)))
       (if (<= z 1.22e+106) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -3.3e+44) {
		tmp = t_1;
	} else if (z <= 7.8e-9) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else if (z <= 1.22e+106) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    if (z <= (-3.3d+44)) then
        tmp = t_1
    else if (z <= 7.8d-9) then
        tmp = x - ((t - x) * ((z - y) / a))
    else if (z <= 1.22d+106) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -3.3e+44) {
		tmp = t_1;
	} else if (z <= 7.8e-9) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else if (z <= 1.22e+106) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -3.3e+44:
		tmp = t_1
	elif z <= 7.8e-9:
		tmp = x - ((t - x) * ((z - y) / a))
	elif z <= 1.22e+106:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -3.3e+44)
		tmp = t_1;
	elseif (z <= 7.8e-9)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	elseif (z <= 1.22e+106)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -3.3e+44)
		tmp = t_1;
	elseif (z <= 7.8e-9)
		tmp = x - ((t - x) * ((z - y) / a));
	elseif (z <= 1.22e+106)
		tmp = t * ((y - z) / (a - 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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+44], t$95$1, If[LessEqual[z, 7.8e-9], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+106], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000013e44 or 1.2199999999999999e106 < z

   1. Initial program 65.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. div-sub 70.6%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 77.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 84.1%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 85.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   if -3.30000000000000013e44 < z < 7.8000000000000004e-9

   1. Initial program 93.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 78.7%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 84.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   5. Simplified 84.6%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]

   if 7.8000000000000004e-9 < z < 1.2199999999999999e106

   1. Initial program 88.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-9}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-9}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- y a) (/ z x)))))
   (if (<= z -4e+35)
     t_1
     (if (<= z 4.8e-9)
       (- x (* (- t x) (/ (- z y) a)))
       (if (<= z 2.1e+108) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y - a) / (z / x));
	double tmp;
	if (z <= -4e+35) {
		tmp = t_1;
	} else if (z <= 4.8e-9) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else if (z <= 2.1e+108) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y - a) / (z / x))
    if (z <= (-4d+35)) then
        tmp = t_1
    else if (z <= 4.8d-9) then
        tmp = x - ((t - x) * ((z - y) / a))
    else if (z <= 2.1d+108) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y - a) / (z / x));
	double tmp;
	if (z <= -4e+35) {
		tmp = t_1;
	} else if (z <= 4.8e-9) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else if (z <= 2.1e+108) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y - a) / (z / x))
	tmp = 0
	if z <= -4e+35:
		tmp = t_1
	elif z <= 4.8e-9:
		tmp = x - ((t - x) * ((z - y) / a))
	elif z <= 2.1e+108:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y - a) / Float64(z / x)))
	tmp = 0.0
	if (z <= -4e+35)
		tmp = t_1;
	elseif (z <= 4.8e-9)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	elseif (z <= 2.1e+108)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y - a) / (z / x));
	tmp = 0.0;
	if (z <= -4e+35)
		tmp = t_1;
	elseif (z <= 4.8e-9)
		tmp = x - ((t - x) * ((z - y) / a));
	elseif (z <= 2.1e+108)
		tmp = t * ((y - z) / (a - 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 - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+35], t$95$1, If[LessEqual[z, 4.8e-9], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+108], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999999e35 or 2.1000000000000001e108 < z

   1. Initial program 64.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 71.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 71.0%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 71.0%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 71.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 71.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 71.0%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 77.3%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 84.3%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 85.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   5. Simplified 85.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   6. Taylor expanded in t around 0 76.7%

      \[\leadsto t - \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z} + t \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto t - \color{blue}{\left(t \cdot \left(\frac{y}{z} - \frac{a}{z}\right) + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. div-sub 76.7%

         \[\leadsto t - \left(t \cdot \color{blue}{\frac{y - a}{z}} + -1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right) \]

      3. mul-1-neg 76.7%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]

      4. associate-/l* 83.2%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right)\right) \]

      5. distribute-lft-neg-in 83.2%

         \[\leadsto t - \left(t \cdot \frac{y - a}{z} + \color{blue}{\left(-x\right) \cdot \frac{y - a}{z}}\right) \]

      6. distribute-rgt-in 83.2%

         \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(t + \left(-x\right)\right)} \]

      7. sub-neg 83.2%

         \[\leadsto t - \frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)} \]

      8. associate-/r/ 85.4%

         \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   8. Simplified 85.4%

      \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   9. Taylor expanded in t around 0 80.3%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   10. Step-by-step derivation

       1. associate-*r/ 80.3%

          \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

       2. neg-mul-1 80.3%

          \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   11. Simplified 80.3%

       \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   if -3.9999999999999999e35 < z < 4.8e-9

   1. Initial program 94.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 79.2%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.2%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]

   if 4.8e-9 < z < 2.1000000000000001e108

   1. Initial program 88.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+35}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-9}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.85e+37)
   t
   (if (<= z 4.8e-77)
     (* x (- 1.0 (/ y a)))
     (if (<= z 4.2e+35) (* t (/ (- y z) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.85e+37) {
		tmp = t;
	} else if (z <= 4.8e-77) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.85d+37)) then
        tmp = t
    else if (z <= 4.8d-77) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.2d+35) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.85e+37) {
		tmp = t;
	} else if (z <= 4.8e-77) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e+35) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.85e+37:
		tmp = t
	elif z <= 4.8e-77:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.2e+35:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.85e+37)
		tmp = t;
	elseif (z <= 4.8e-77)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.2e+35)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.85e+37)
		tmp = t;
	elseif (z <= 4.8e-77)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.2e+35)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.85e+37], t, If[LessEqual[z, 4.8e-77], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+35], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.85000000000000011e37 or 4.1999999999999998e35 < z

   1. Initial program 66.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.9%

      \[\leadsto \color{blue}{t} \]

   if -3.85000000000000011e37 < z < 4.7999999999999998e-77

   1. Initial program 95.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 66.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 66.0%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   5. Simplified 66.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   6. Taylor expanded in z around 0 62.7%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   if 4.7999999999999998e-77 < z < 4.1999999999999998e35

   1. Initial program 92.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   4. Taylor expanded in a around inf 43.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 53.8%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]

   6. Simplified 53.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 28: 38.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.28e+42) t (if (<= z 3.8e-135) x (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.28e+42) {
		tmp = t;
	} else if (z <= 3.8e-135) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.28d+42)) then
        tmp = t
    else if (z <= 3.8d-135) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.28e+42) {
		tmp = t;
	} else if (z <= 3.8e-135) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.28e+42:
		tmp = t
	elif z <= 3.8e-135:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.28e+42)
		tmp = t;
	elseif (z <= 3.8e-135)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.28e+42)
		tmp = t;
	elseif (z <= 3.8e-135)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.28e+42], t, If[LessEqual[z, 3.8e-135], x, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.28000000000000004e42

   1. Initial program 63.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{t} \]

   if -1.28000000000000004e42 < z < 3.8000000000000003e-135

   1. Initial program 95.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{x} \]

   if 3.8000000000000003e-135 < z

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 32.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. unsub-neg 32.0%

         \[\leadsto \color{blue}{x - \frac{z \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 42.9%

         \[\leadsto x - \color{blue}{z \cdot \frac{t - x}{a - z}} \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{x - z \cdot \frac{t - x}{a - z}} \]

   6. Taylor expanded in t around inf 41.1%

      \[\leadsto x - z \cdot \color{blue}{\frac{t}{a - z}} \]

   7. Taylor expanded in z around inf 34.1%

      \[\leadsto \color{blue}{x - -1 \cdot t} \]
   8. Step-by-step derivation

      1. sub-neg 34.1%

         \[\leadsto \color{blue}{x + \left(--1 \cdot t\right)} \]

      2. neg-mul-1 34.1%

         \[\leadsto x + \left(-\color{blue}{\left(-t\right)}\right) \]

      3. remove-double-neg 34.1%

         \[\leadsto x + \color{blue}{t} \]

   9. Simplified 34.1%

      \[\leadsto \color{blue}{x + t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 29: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+81) t (if (<= z 4e-20) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+81) {
		tmp = t;
	} else if (z <= 4e-20) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+81)) then
        tmp = t
    else if (z <= 4d-20) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+81) {
		tmp = t;
	} else if (z <= 4e-20) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+81:
		tmp = t
	elif z <= 4e-20:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+81)
		tmp = t;
	elseif (z <= 4e-20)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+81)
		tmp = t;
	elseif (z <= 4e-20)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+81], t, If[LessEqual[z, 4e-20], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000017e81 or 3.99999999999999978e-20 < z

   1. Initial program 71.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 45.7%

      \[\leadsto \color{blue}{t} \]

   if -4.50000000000000017e81 < z < 3.99999999999999978e-20

   1. Initial program 92.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 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 83.3%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 24.4%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024105 
(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)))))