Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 95.1%

Time: 30.4s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-302} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -5e-302) (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) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-302) || !(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) / (z - a)))
    if ((t_1 <= (-5d-302)) .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) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-302) || !(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) / (z - a)))
	tmp = 0
	if (t_1 <= -5e-302) 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(z - a))))
	tmp = 0.0
	if ((t_1 <= -5e-302) || !(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) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -5e-302) || ~((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[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-302], 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)))) < -5.00000000000000033e-302 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 94.7%

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

      4. clear-num 94.6%

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

      5. un-div-inv 95.1%

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

   4. Applied egg-rr 95.1%

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

   if -5.00000000000000033e-302 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in z around inf 94.4%

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

      1. associate--l+ 94.4%

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

      2. distribute-lft-out-- 94.4%

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

      3. div-sub 94.4%

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

      4. mul-1-neg 94.4%

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

      5. unsub-neg 94.4%

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

      6. div-sub 94.4%

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

      7. associate-/l* 94.3%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -5 \cdot 10^{-302} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-237}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))) (t_2 (- x (/ (* z t) a))))
   (if (<= z -1.35e+134)
     t
     (if (<= z -9.2e-61)
       t_2
       (if (<= z -2.55e-173)
         t_1
         (if (<= z -2.1e-212)
           t_2
           (if (<= z -5.1e-303)
             (* y (/ (- t x) a))
             (if (<= z 4.5e-237)
               t_2
               (if (<= z 5.5e-56) t_1 (if (<= z 3.6e+61) t_2 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (z <= -1.35e+134) {
		tmp = t;
	} else if (z <= -9.2e-61) {
		tmp = t_2;
	} else if (z <= -2.55e-173) {
		tmp = t_1;
	} else if (z <= -2.1e-212) {
		tmp = t_2;
	} else if (z <= -5.1e-303) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e-237) {
		tmp = t_2;
	} else if (z <= 5.5e-56) {
		tmp = t_1;
	} else if (z <= 3.6e+61) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - x) * (y / a)
    t_2 = x - ((z * t) / a)
    if (z <= (-1.35d+134)) then
        tmp = t
    else if (z <= (-9.2d-61)) then
        tmp = t_2
    else if (z <= (-2.55d-173)) then
        tmp = t_1
    else if (z <= (-2.1d-212)) then
        tmp = t_2
    else if (z <= (-5.1d-303)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.5d-237) then
        tmp = t_2
    else if (z <= 5.5d-56) then
        tmp = t_1
    else if (z <= 3.6d+61) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (z <= -1.35e+134) {
		tmp = t;
	} else if (z <= -9.2e-61) {
		tmp = t_2;
	} else if (z <= -2.55e-173) {
		tmp = t_1;
	} else if (z <= -2.1e-212) {
		tmp = t_2;
	} else if (z <= -5.1e-303) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.5e-237) {
		tmp = t_2;
	} else if (z <= 5.5e-56) {
		tmp = t_1;
	} else if (z <= 3.6e+61) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	t_2 = x - ((z * t) / a)
	tmp = 0
	if z <= -1.35e+134:
		tmp = t
	elif z <= -9.2e-61:
		tmp = t_2
	elif z <= -2.55e-173:
		tmp = t_1
	elif z <= -2.1e-212:
		tmp = t_2
	elif z <= -5.1e-303:
		tmp = y * ((t - x) / a)
	elif z <= 4.5e-237:
		tmp = t_2
	elif z <= 5.5e-56:
		tmp = t_1
	elif z <= 3.6e+61:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	t_2 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (z <= -1.35e+134)
		tmp = t;
	elseif (z <= -9.2e-61)
		tmp = t_2;
	elseif (z <= -2.55e-173)
		tmp = t_1;
	elseif (z <= -2.1e-212)
		tmp = t_2;
	elseif (z <= -5.1e-303)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.5e-237)
		tmp = t_2;
	elseif (z <= 5.5e-56)
		tmp = t_1;
	elseif (z <= 3.6e+61)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	t_2 = x - ((z * t) / a);
	tmp = 0.0;
	if (z <= -1.35e+134)
		tmp = t;
	elseif (z <= -9.2e-61)
		tmp = t_2;
	elseif (z <= -2.55e-173)
		tmp = t_1;
	elseif (z <= -2.1e-212)
		tmp = t_2;
	elseif (z <= -5.1e-303)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.5e-237)
		tmp = t_2;
	elseif (z <= 5.5e-56)
		tmp = t_1;
	elseif (z <= 3.6e+61)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+134], t, If[LessEqual[z, -9.2e-61], t$95$2, If[LessEqual[z, -2.55e-173], t$95$1, If[LessEqual[z, -2.1e-212], t$95$2, If[LessEqual[z, -5.1e-303], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-237], t$95$2, If[LessEqual[z, 5.5e-56], t$95$1, If[LessEqual[z, 3.6e+61], t$95$2, t]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e134 or 3.6000000000000001e61 < z

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 53.1%

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

   if -1.35e134 < z < -9.19999999999999967e-61 or -2.5499999999999999e-173 < z < -2.1e-212 or -5.1e-303 < z < 4.50000000000000009e-237 or 5.4999999999999999e-56 < z < 3.6000000000000001e61

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in z around 0 54.7%

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

   7. Taylor expanded in t around inf 56.1%

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

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

   if -9.19999999999999967e-61 < z < -2.5499999999999999e-173 or 4.50000000000000009e-237 < z < 5.4999999999999999e-56

   1. Initial program 92.1%

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

   3. Taylor expanded in y around -inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/l* 68.6%

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

   5. Applied egg-rr 68.6%

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

   6. Taylor expanded in a around inf 54.5%

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

   if -2.1e-212 < z < -5.1e-303

   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 inf 72.8%

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

      1. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around inf 72.8%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-61}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-237}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-56}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a}\\ t_3 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+133}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* z t) a)))
        (t_2 (* (- t x) (/ y a)))
        (t_3 (* t (/ z (- z a)))))
   (if (<= z -8e+133)
     t_3
     (if (<= z -5.2e-60)
       t_1
       (if (<= z -2.65e-173)
         t_2
         (if (<= z -1.7e-212)
           t_1
           (if (<= z -1.02e-297)
             (* y (/ (- t x) a))
             (if (<= z 9.2e-238)
               t_1
               (if (<= z 6.8e-46) t_2 (if (<= z 1.15e+63) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double t_2 = (t - x) * (y / a);
	double t_3 = t * (z / (z - a));
	double tmp;
	if (z <= -8e+133) {
		tmp = t_3;
	} else if (z <= -5.2e-60) {
		tmp = t_1;
	} else if (z <= -2.65e-173) {
		tmp = t_2;
	} else if (z <= -1.7e-212) {
		tmp = t_1;
	} else if (z <= -1.02e-297) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.2e-238) {
		tmp = t_1;
	} else if (z <= 6.8e-46) {
		tmp = t_2;
	} else if (z <= 1.15e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - ((z * t) / a)
    t_2 = (t - x) * (y / a)
    t_3 = t * (z / (z - a))
    if (z <= (-8d+133)) then
        tmp = t_3
    else if (z <= (-5.2d-60)) then
        tmp = t_1
    else if (z <= (-2.65d-173)) then
        tmp = t_2
    else if (z <= (-1.7d-212)) then
        tmp = t_1
    else if (z <= (-1.02d-297)) then
        tmp = y * ((t - x) / a)
    else if (z <= 9.2d-238) then
        tmp = t_1
    else if (z <= 6.8d-46) then
        tmp = t_2
    else if (z <= 1.15d+63) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double t_2 = (t - x) * (y / a);
	double t_3 = t * (z / (z - a));
	double tmp;
	if (z <= -8e+133) {
		tmp = t_3;
	} else if (z <= -5.2e-60) {
		tmp = t_1;
	} else if (z <= -2.65e-173) {
		tmp = t_2;
	} else if (z <= -1.7e-212) {
		tmp = t_1;
	} else if (z <= -1.02e-297) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.2e-238) {
		tmp = t_1;
	} else if (z <= 6.8e-46) {
		tmp = t_2;
	} else if (z <= 1.15e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z * t) / a)
	t_2 = (t - x) * (y / a)
	t_3 = t * (z / (z - a))
	tmp = 0
	if z <= -8e+133:
		tmp = t_3
	elif z <= -5.2e-60:
		tmp = t_1
	elif z <= -2.65e-173:
		tmp = t_2
	elif z <= -1.7e-212:
		tmp = t_1
	elif z <= -1.02e-297:
		tmp = y * ((t - x) / a)
	elif z <= 9.2e-238:
		tmp = t_1
	elif z <= 6.8e-46:
		tmp = t_2
	elif z <= 1.15e+63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z * t) / a))
	t_2 = Float64(Float64(t - x) * Float64(y / a))
	t_3 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -8e+133)
		tmp = t_3;
	elseif (z <= -5.2e-60)
		tmp = t_1;
	elseif (z <= -2.65e-173)
		tmp = t_2;
	elseif (z <= -1.7e-212)
		tmp = t_1;
	elseif (z <= -1.02e-297)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 9.2e-238)
		tmp = t_1;
	elseif (z <= 6.8e-46)
		tmp = t_2;
	elseif (z <= 1.15e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z * t) / a);
	t_2 = (t - x) * (y / a);
	t_3 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -8e+133)
		tmp = t_3;
	elseif (z <= -5.2e-60)
		tmp = t_1;
	elseif (z <= -2.65e-173)
		tmp = t_2;
	elseif (z <= -1.7e-212)
		tmp = t_1;
	elseif (z <= -1.02e-297)
		tmp = y * ((t - x) / a);
	elseif (z <= 9.2e-238)
		tmp = t_1;
	elseif (z <= 6.8e-46)
		tmp = t_2;
	elseif (z <= 1.15e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+133], t$95$3, If[LessEqual[z, -5.2e-60], t$95$1, If[LessEqual[z, -2.65e-173], t$95$2, If[LessEqual[z, -1.7e-212], t$95$1, If[LessEqual[z, -1.02e-297], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-238], t$95$1, If[LessEqual[z, 6.8e-46], t$95$2, If[LessEqual[z, 1.15e+63], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.0000000000000002e133 or 1.14999999999999997e63 < z

   1. Initial program 68.9%

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

   3. Taylor expanded in y around 0 25.9%

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

      1. mul-1-neg 25.9%

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

      2. unsub-neg 25.9%

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

      3. associate-/l* 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in x around 0 28.9%

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

      1. mul-1-neg 28.9%

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

      2. associate-/l* 56.0%

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

   8. Simplified 56.0%

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

   if -8.0000000000000002e133 < z < -5.1999999999999995e-60 or -2.64999999999999982e-173 < z < -1.69999999999999999e-212 or -1.0200000000000001e-297 < z < 9.20000000000000019e-238 or 6.79999999999999992e-46 < z < 1.14999999999999997e63

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in z around 0 54.7%

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

   7. Taylor expanded in t around inf 56.1%

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

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

   if -5.1999999999999995e-60 < z < -2.64999999999999982e-173 or 9.20000000000000019e-238 < z < 6.79999999999999992e-46

   1. Initial program 92.1%

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

   3. Taylor expanded in y around -inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/l* 68.6%

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

   5. Applied egg-rr 68.6%

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

   6. Taylor expanded in a around inf 54.5%

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

   if -1.69999999999999999e-212 < z < -1.0200000000000001e-297

   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 inf 72.8%

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

      1. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around inf 72.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-212}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-238}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-302} \lor \neg \left(t\_1 \leq 4 \cdot 10^{-185}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -5e-302) (not (<= t_1 4e-185)))
     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) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-302) || !(t_1 <= 4e-185)) {
		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) / (z - a)))
    if ((t_1 <= (-5d-302)) .or. (.not. (t_1 <= 4d-185))) 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) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-302) || !(t_1 <= 4e-185)) {
		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) / (z - a)))
	tmp = 0
	if (t_1 <= -5e-302) or not (t_1 <= 4e-185):
		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(z - a))))
	tmp = 0.0
	if ((t_1 <= -5e-302) || !(t_1 <= 4e-185))
		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) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -5e-302) || ~((t_1 <= 4e-185)))
		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[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-302], N[Not[LessEqual[t$95$1, 4e-185]], $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)))) < -5.00000000000000033e-302 or 4e-185 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.3%

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

   if -5.00000000000000033e-302 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4e-185

   1. Initial program 8.5%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. distribute-lft-out-- 84.5%

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

      3. div-sub 84.5%

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

      4. mul-1-neg 84.5%

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

      5. unsub-neg 84.5%

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

      6. div-sub 84.5%

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

      7. associate-/l* 82.7%

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

      8. associate-/l* 86.5%

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

      9. distribute-rgt-out-- 86.5%

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

   5. Simplified 86.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -5 \cdot 10^{-302} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 4 \cdot 10^{-185}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -1.35e+173)
     t
     (if (<= z -1.85e-37)
       (* x (/ y z))
       (if (<= z -3.8e-174)
         t_1
         (if (<= z 6.5e-237)
           x
           (if (<= z 1.3e-150)
             t_1
             (if (<= z 2.1e-105)
               x
               (if (<= z 3.1e-54) t_1 (if (<= z 1.66e+62) x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t;
	} else if (z <= -1.85e-37) {
		tmp = x * (y / z);
	} else if (z <= -3.8e-174) {
		tmp = t_1;
	} else if (z <= 6.5e-237) {
		tmp = x;
	} else if (z <= 1.3e-150) {
		tmp = t_1;
	} else if (z <= 2.1e-105) {
		tmp = x;
	} else if (z <= 3.1e-54) {
		tmp = t_1;
	} else if (z <= 1.66e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-1.35d+173)) then
        tmp = t
    else if (z <= (-1.85d-37)) then
        tmp = x * (y / z)
    else if (z <= (-3.8d-174)) then
        tmp = t_1
    else if (z <= 6.5d-237) then
        tmp = x
    else if (z <= 1.3d-150) then
        tmp = t_1
    else if (z <= 2.1d-105) then
        tmp = x
    else if (z <= 3.1d-54) then
        tmp = t_1
    else if (z <= 1.66d+62) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t;
	} else if (z <= -1.85e-37) {
		tmp = x * (y / z);
	} else if (z <= -3.8e-174) {
		tmp = t_1;
	} else if (z <= 6.5e-237) {
		tmp = x;
	} else if (z <= 1.3e-150) {
		tmp = t_1;
	} else if (z <= 2.1e-105) {
		tmp = x;
	} else if (z <= 3.1e-54) {
		tmp = t_1;
	} else if (z <= 1.66e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -1.35e+173:
		tmp = t
	elif z <= -1.85e-37:
		tmp = x * (y / z)
	elif z <= -3.8e-174:
		tmp = t_1
	elif z <= 6.5e-237:
		tmp = x
	elif z <= 1.3e-150:
		tmp = t_1
	elif z <= 2.1e-105:
		tmp = x
	elif z <= 3.1e-54:
		tmp = t_1
	elif z <= 1.66e+62:
		tmp = x
	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 (z <= -1.35e+173)
		tmp = t;
	elseif (z <= -1.85e-37)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -3.8e-174)
		tmp = t_1;
	elseif (z <= 6.5e-237)
		tmp = x;
	elseif (z <= 1.3e-150)
		tmp = t_1;
	elseif (z <= 2.1e-105)
		tmp = x;
	elseif (z <= 3.1e-54)
		tmp = t_1;
	elseif (z <= 1.66e+62)
		tmp = x;
	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 (z <= -1.35e+173)
		tmp = t;
	elseif (z <= -1.85e-37)
		tmp = x * (y / z);
	elseif (z <= -3.8e-174)
		tmp = t_1;
	elseif (z <= 6.5e-237)
		tmp = x;
	elseif (z <= 1.3e-150)
		tmp = t_1;
	elseif (z <= 2.1e-105)
		tmp = x;
	elseif (z <= 3.1e-54)
		tmp = t_1;
	elseif (z <= 1.66e+62)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+173], t, If[LessEqual[z, -1.85e-37], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-174], t$95$1, If[LessEqual[z, 6.5e-237], x, If[LessEqual[z, 1.3e-150], t$95$1, If[LessEqual[z, 2.1e-105], x, If[LessEqual[z, 3.1e-54], t$95$1, If[LessEqual[z, 1.66e+62], x, t]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3500000000000001e173 or 1.6600000000000001e62 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -1.3500000000000001e173 < z < -1.85e-37

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 41.6%

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

      1. div-sub 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 31.4%

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

      1. neg-mul-1 31.4%

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

      2. distribute-neg-frac 31.4%

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

   8. Simplified 31.4%

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

   9. Taylor expanded in a around 0 25.1%

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

       1. associate-/l* 31.2%

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

   11. Simplified 31.2%

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

   if -1.85e-37 < z < -3.80000000000000021e-174 or 6.5000000000000001e-237 < z < 1.2999999999999999e-150 or 2.1e-105 < z < 3.10000000000000004e-54

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in t around inf 53.8%

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

      1. associate-/l* 58.8%

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

   8. Simplified 58.8%

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

   if -3.80000000000000021e-174 < z < 6.5000000000000001e-237 or 1.2999999999999999e-150 < z < 2.1e-105 or 3.10000000000000004e-54 < z < 1.6600000000000001e62

   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 54.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -3.1e+173)
     t
     (if (<= z -2.1e-37)
       (* x (/ y z))
       (if (<= z -2.3e-173)
         t_1
         (if (<= z 2.9e-236)
           x
           (if (<= z 1.02e-150)
             t_1
             (if (<= z 2.15e-105)
               x
               (if (<= z 7.6e-52)
                 (* y (/ t (- a z)))
                 (if (<= z 1.12e+62) x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -3.1e+173) {
		tmp = t;
	} else if (z <= -2.1e-37) {
		tmp = x * (y / z);
	} else if (z <= -2.3e-173) {
		tmp = t_1;
	} else if (z <= 2.9e-236) {
		tmp = x;
	} else if (z <= 1.02e-150) {
		tmp = t_1;
	} else if (z <= 2.15e-105) {
		tmp = x;
	} else if (z <= 7.6e-52) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.12e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-3.1d+173)) then
        tmp = t
    else if (z <= (-2.1d-37)) then
        tmp = x * (y / z)
    else if (z <= (-2.3d-173)) then
        tmp = t_1
    else if (z <= 2.9d-236) then
        tmp = x
    else if (z <= 1.02d-150) then
        tmp = t_1
    else if (z <= 2.15d-105) then
        tmp = x
    else if (z <= 7.6d-52) then
        tmp = y * (t / (a - z))
    else if (z <= 1.12d+62) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -3.1e+173) {
		tmp = t;
	} else if (z <= -2.1e-37) {
		tmp = x * (y / z);
	} else if (z <= -2.3e-173) {
		tmp = t_1;
	} else if (z <= 2.9e-236) {
		tmp = x;
	} else if (z <= 1.02e-150) {
		tmp = t_1;
	} else if (z <= 2.15e-105) {
		tmp = x;
	} else if (z <= 7.6e-52) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.12e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -3.1e+173:
		tmp = t
	elif z <= -2.1e-37:
		tmp = x * (y / z)
	elif z <= -2.3e-173:
		tmp = t_1
	elif z <= 2.9e-236:
		tmp = x
	elif z <= 1.02e-150:
		tmp = t_1
	elif z <= 2.15e-105:
		tmp = x
	elif z <= 7.6e-52:
		tmp = y * (t / (a - z))
	elif z <= 1.12e+62:
		tmp = x
	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 (z <= -3.1e+173)
		tmp = t;
	elseif (z <= -2.1e-37)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.3e-173)
		tmp = t_1;
	elseif (z <= 2.9e-236)
		tmp = x;
	elseif (z <= 1.02e-150)
		tmp = t_1;
	elseif (z <= 2.15e-105)
		tmp = x;
	elseif (z <= 7.6e-52)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 1.12e+62)
		tmp = x;
	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 (z <= -3.1e+173)
		tmp = t;
	elseif (z <= -2.1e-37)
		tmp = x * (y / z);
	elseif (z <= -2.3e-173)
		tmp = t_1;
	elseif (z <= 2.9e-236)
		tmp = x;
	elseif (z <= 1.02e-150)
		tmp = t_1;
	elseif (z <= 2.15e-105)
		tmp = x;
	elseif (z <= 7.6e-52)
		tmp = y * (t / (a - z));
	elseif (z <= 1.12e+62)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+173], t, If[LessEqual[z, -2.1e-37], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-173], t$95$1, If[LessEqual[z, 2.9e-236], x, If[LessEqual[z, 1.02e-150], t$95$1, If[LessEqual[z, 2.15e-105], x, If[LessEqual[z, 7.6e-52], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+62], x, t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1e173 or 1.1200000000000001e62 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -3.1e173 < z < -2.1000000000000001e-37

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 41.6%

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

      1. div-sub 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 31.4%

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

      1. neg-mul-1 31.4%

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

      2. distribute-neg-frac 31.4%

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

   8. Simplified 31.4%

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

   9. Taylor expanded in a around 0 25.1%

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

       1. associate-/l* 31.2%

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

   11. Simplified 31.2%

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

   if -2.1000000000000001e-37 < z < -2.29999999999999988e-173 or 2.9e-236 < z < 1.0199999999999999e-150

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 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 t around inf 49.6%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -2.29999999999999988e-173 < z < 2.9e-236 or 1.0199999999999999e-150 < z < 2.14999999999999982e-105 or 7.6000000000000007e-52 < z < 1.1200000000000001e62

   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 54.6%

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

   if 2.14999999999999982e-105 < z < 7.6000000000000007e-52

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 91.6%

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

      1. div-sub 91.6%

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

   5. Simplified 91.6%

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

   6. Taylor expanded in t around inf 68.3%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -1.35e+173)
     t
     (if (<= z -2.1e-37)
       (* x (/ y z))
       (if (<= z -2.4e-173)
         (* t (/ y (- a z)))
         (if (<= z -2.5e-212)
           x
           (if (<= z -8.5e-303)
             t_1
             (if (<= z 4.7e-238)
               x
               (if (<= z 5.6e-54) t_1 (if (<= z 6.8e+61) x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t;
	} else if (z <= -2.1e-37) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-173) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.5e-212) {
		tmp = x;
	} else if (z <= -8.5e-303) {
		tmp = t_1;
	} else if (z <= 4.7e-238) {
		tmp = x;
	} else if (z <= 5.6e-54) {
		tmp = t_1;
	} else if (z <= 6.8e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-1.35d+173)) then
        tmp = t
    else if (z <= (-2.1d-37)) then
        tmp = x * (y / z)
    else if (z <= (-2.4d-173)) then
        tmp = t * (y / (a - z))
    else if (z <= (-2.5d-212)) then
        tmp = x
    else if (z <= (-8.5d-303)) then
        tmp = t_1
    else if (z <= 4.7d-238) then
        tmp = x
    else if (z <= 5.6d-54) then
        tmp = t_1
    else if (z <= 6.8d+61) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t;
	} else if (z <= -2.1e-37) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-173) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.5e-212) {
		tmp = x;
	} else if (z <= -8.5e-303) {
		tmp = t_1;
	} else if (z <= 4.7e-238) {
		tmp = x;
	} else if (z <= 5.6e-54) {
		tmp = t_1;
	} else if (z <= 6.8e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -1.35e+173:
		tmp = t
	elif z <= -2.1e-37:
		tmp = x * (y / z)
	elif z <= -2.4e-173:
		tmp = t * (y / (a - z))
	elif z <= -2.5e-212:
		tmp = x
	elif z <= -8.5e-303:
		tmp = t_1
	elif z <= 4.7e-238:
		tmp = x
	elif z <= 5.6e-54:
		tmp = t_1
	elif z <= 6.8e+61:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -1.35e+173)
		tmp = t;
	elseif (z <= -2.1e-37)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.4e-173)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -2.5e-212)
		tmp = x;
	elseif (z <= -8.5e-303)
		tmp = t_1;
	elseif (z <= 4.7e-238)
		tmp = x;
	elseif (z <= 5.6e-54)
		tmp = t_1;
	elseif (z <= 6.8e+61)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -1.35e+173)
		tmp = t;
	elseif (z <= -2.1e-37)
		tmp = x * (y / z);
	elseif (z <= -2.4e-173)
		tmp = t * (y / (a - z));
	elseif (z <= -2.5e-212)
		tmp = x;
	elseif (z <= -8.5e-303)
		tmp = t_1;
	elseif (z <= 4.7e-238)
		tmp = x;
	elseif (z <= 5.6e-54)
		tmp = t_1;
	elseif (z <= 6.8e+61)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+173], t, If[LessEqual[z, -2.1e-37], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-173], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-212], x, If[LessEqual[z, -8.5e-303], t$95$1, If[LessEqual[z, 4.7e-238], x, If[LessEqual[z, 5.6e-54], t$95$1, If[LessEqual[z, 6.8e+61], x, t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3500000000000001e173 or 6.80000000000000051e61 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -1.3500000000000001e173 < z < -2.1000000000000001e-37

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 41.6%

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

      1. div-sub 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 31.4%

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

      1. neg-mul-1 31.4%

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

      2. distribute-neg-frac 31.4%

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

   8. Simplified 31.4%

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

   9. Taylor expanded in a around 0 25.1%

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

       1. associate-/l* 31.2%

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

   11. Simplified 31.2%

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

   if -2.1000000000000001e-37 < z < -2.40000000000000017e-173

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   if -2.40000000000000017e-173 < z < -2.50000000000000022e-212 or -8.5e-303 < z < 4.70000000000000023e-238 or 5.6000000000000004e-54 < z < 6.80000000000000051e61

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf 61.1%

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

   if -2.50000000000000022e-212 < z < -8.5e-303 or 4.70000000000000023e-238 < z < 5.6000000000000004e-54

   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 66.1%

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

      1. div-sub 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around inf 55.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+173)
   t
   (if (<= z -7.9e-38)
     (* x (/ y z))
     (if (<= z -2.4e-173)
       (* t (/ y (- a z)))
       (if (<= z -2.1e-212)
         x
         (if (<= z -2.6e-301)
           (* y (/ (- t x) a))
           (if (<= z 3.6e-239)
             x
             (if (<= z 3.8e-57)
               (* (- t x) (/ y a))
               (if (<= z 7.8e+60) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+173) {
		tmp = t;
	} else if (z <= -7.9e-38) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-173) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.1e-212) {
		tmp = x;
	} else if (z <= -2.6e-301) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.6e-239) {
		tmp = x;
	} else if (z <= 3.8e-57) {
		tmp = (t - x) * (y / a);
	} else if (z <= 7.8e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+173)) then
        tmp = t
    else if (z <= (-7.9d-38)) then
        tmp = x * (y / z)
    else if (z <= (-2.4d-173)) then
        tmp = t * (y / (a - z))
    else if (z <= (-2.1d-212)) then
        tmp = x
    else if (z <= (-2.6d-301)) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.6d-239) then
        tmp = x
    else if (z <= 3.8d-57) then
        tmp = (t - x) * (y / a)
    else if (z <= 7.8d+60) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+173) {
		tmp = t;
	} else if (z <= -7.9e-38) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-173) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.1e-212) {
		tmp = x;
	} else if (z <= -2.6e-301) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.6e-239) {
		tmp = x;
	} else if (z <= 3.8e-57) {
		tmp = (t - x) * (y / a);
	} else if (z <= 7.8e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+173:
		tmp = t
	elif z <= -7.9e-38:
		tmp = x * (y / z)
	elif z <= -2.4e-173:
		tmp = t * (y / (a - z))
	elif z <= -2.1e-212:
		tmp = x
	elif z <= -2.6e-301:
		tmp = y * ((t - x) / a)
	elif z <= 3.6e-239:
		tmp = x
	elif z <= 3.8e-57:
		tmp = (t - x) * (y / a)
	elif z <= 7.8e+60:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+173)
		tmp = t;
	elseif (z <= -7.9e-38)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.4e-173)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -2.1e-212)
		tmp = x;
	elseif (z <= -2.6e-301)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.6e-239)
		tmp = x;
	elseif (z <= 3.8e-57)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 7.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+173)
		tmp = t;
	elseif (z <= -7.9e-38)
		tmp = x * (y / z);
	elseif (z <= -2.4e-173)
		tmp = t * (y / (a - z));
	elseif (z <= -2.1e-212)
		tmp = x;
	elseif (z <= -2.6e-301)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.6e-239)
		tmp = x;
	elseif (z <= 3.8e-57)
		tmp = (t - x) * (y / a);
	elseif (z <= 7.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+173], t, If[LessEqual[z, -7.9e-38], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-173], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-212], x, If[LessEqual[z, -2.6e-301], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-239], x, If[LessEqual[z, 3.8e-57], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+60], x, t]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.39999999999999991e173 or 7.8000000000000006e60 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -1.39999999999999991e173 < z < -7.8999999999999998e-38

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 41.6%

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

      1. div-sub 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 31.4%

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

      1. neg-mul-1 31.4%

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

      2. distribute-neg-frac 31.4%

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

   8. Simplified 31.4%

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

   9. Taylor expanded in a around 0 25.1%

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

       1. associate-/l* 31.2%

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

   11. Simplified 31.2%

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

   if -7.8999999999999998e-38 < z < -2.40000000000000017e-173

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   if -2.40000000000000017e-173 < z < -2.1e-212 or -2.5999999999999998e-301 < z < 3.6000000000000001e-239 or 3.7999999999999997e-57 < z < 7.8000000000000006e60

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf 61.1%

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

   if -2.1e-212 < z < -2.5999999999999998e-301

   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 inf 72.8%

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

      1. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around inf 72.8%

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

   if 3.6000000000000001e-239 < z < 3.7999999999999997e-57

   1. Initial program 93.2%

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

   3. Taylor expanded in y around -inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 66.0%

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

   5. Applied egg-rr 66.0%

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

   6. Taylor expanded in a around inf 52.3%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-212}:\\ \;\;\;\;x + x \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-51}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+173)
   t
   (if (<= z -1.1e-38)
     (* x (/ y z))
     (if (<= z -2e-174)
       (* t (/ y (- a z)))
       (if (<= z -1.2e-212)
         (+ x (* x (/ z a)))
         (if (<= z -1.2e-299)
           (* y (/ (- t x) a))
           (if (<= z 1.28e-238)
             x
             (if (<= z 1.1e-51)
               (* (- t x) (/ y a))
               (if (<= z 5.2e+62) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+173) {
		tmp = t;
	} else if (z <= -1.1e-38) {
		tmp = x * (y / z);
	} else if (z <= -2e-174) {
		tmp = t * (y / (a - z));
	} else if (z <= -1.2e-212) {
		tmp = x + (x * (z / a));
	} else if (z <= -1.2e-299) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.28e-238) {
		tmp = x;
	} else if (z <= 1.1e-51) {
		tmp = (t - x) * (y / a);
	} else if (z <= 5.2e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.1d+173)) then
        tmp = t
    else if (z <= (-1.1d-38)) then
        tmp = x * (y / z)
    else if (z <= (-2d-174)) then
        tmp = t * (y / (a - z))
    else if (z <= (-1.2d-212)) then
        tmp = x + (x * (z / a))
    else if (z <= (-1.2d-299)) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.28d-238) then
        tmp = x
    else if (z <= 1.1d-51) then
        tmp = (t - x) * (y / a)
    else if (z <= 5.2d+62) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+173) {
		tmp = t;
	} else if (z <= -1.1e-38) {
		tmp = x * (y / z);
	} else if (z <= -2e-174) {
		tmp = t * (y / (a - z));
	} else if (z <= -1.2e-212) {
		tmp = x + (x * (z / a));
	} else if (z <= -1.2e-299) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.28e-238) {
		tmp = x;
	} else if (z <= 1.1e-51) {
		tmp = (t - x) * (y / a);
	} else if (z <= 5.2e+62) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+173:
		tmp = t
	elif z <= -1.1e-38:
		tmp = x * (y / z)
	elif z <= -2e-174:
		tmp = t * (y / (a - z))
	elif z <= -1.2e-212:
		tmp = x + (x * (z / a))
	elif z <= -1.2e-299:
		tmp = y * ((t - x) / a)
	elif z <= 1.28e-238:
		tmp = x
	elif z <= 1.1e-51:
		tmp = (t - x) * (y / a)
	elif z <= 5.2e+62:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+173)
		tmp = t;
	elseif (z <= -1.1e-38)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2e-174)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -1.2e-212)
		tmp = Float64(x + Float64(x * Float64(z / a)));
	elseif (z <= -1.2e-299)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.28e-238)
		tmp = x;
	elseif (z <= 1.1e-51)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 5.2e+62)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+173)
		tmp = t;
	elseif (z <= -1.1e-38)
		tmp = x * (y / z);
	elseif (z <= -2e-174)
		tmp = t * (y / (a - z));
	elseif (z <= -1.2e-212)
		tmp = x + (x * (z / a));
	elseif (z <= -1.2e-299)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.28e-238)
		tmp = x;
	elseif (z <= 1.1e-51)
		tmp = (t - x) * (y / a);
	elseif (z <= 5.2e+62)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+173], t, If[LessEqual[z, -1.1e-38], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-174], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-212], N[(x + N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-299], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.28e-238], x, If[LessEqual[z, 1.1e-51], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+62], x, t]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -3.1e173 or 5.19999999999999968e62 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -3.1e173 < z < -1.10000000000000004e-38

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 41.6%

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

      1. div-sub 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 31.4%

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

      1. neg-mul-1 31.4%

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

      2. distribute-neg-frac 31.4%

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

   8. Simplified 31.4%

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

   9. Taylor expanded in a around 0 25.1%

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

       1. associate-/l* 31.2%

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

   11. Simplified 31.2%

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

   if -1.10000000000000004e-38 < z < -2e-174

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   if -2e-174 < z < -1.19999999999999995e-212

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

      3. associate-/l* 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in t around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. associate-/l* 63.1%

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

      3. distribute-lft-neg-in 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in z around 0 72.0%

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

       1. associate-/l* 72.0%

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

   11. Simplified 72.0%

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

   if -1.19999999999999995e-212 < z < -1.2000000000000001e-299

   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 inf 72.8%

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

      1. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around inf 72.8%

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

   if -1.2000000000000001e-299 < z < 1.28e-238 or 1.1e-51 < z < 5.19999999999999968e62

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 60.4%

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

   if 1.28e-238 < z < 1.1e-51

   1. Initial program 93.2%

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

   3. Taylor expanded in y around -inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 66.0%

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

   5. Applied egg-rr 66.0%

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

   6. Taylor expanded in a around inf 52.3%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-212}:\\ \;\;\;\;x + x \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-51}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t))) (t_2 (- x (/ (* z t) a))))
   (if (<= a -1.75e+19)
     t_2
     (if (<= a -1.2e-142)
       (* t (/ z (- z a)))
       (if (<= a -9.5e-208)
         t_1
         (if (<= a -3e-216) t (if (<= a 3.7e-60) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -1.75e+19) {
		tmp = t_2;
	} else if (a <= -1.2e-142) {
		tmp = t * (z / (z - a));
	} else if (a <= -9.5e-208) {
		tmp = t_1;
	} else if (a <= -3e-216) {
		tmp = t;
	} else if (a <= 3.7e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    t_2 = x - ((z * t) / a)
    if (a <= (-1.75d+19)) then
        tmp = t_2
    else if (a <= (-1.2d-142)) then
        tmp = t * (z / (z - a))
    else if (a <= (-9.5d-208)) then
        tmp = t_1
    else if (a <= (-3d-216)) then
        tmp = t
    else if (a <= 3.7d-60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -1.75e+19) {
		tmp = t_2;
	} else if (a <= -1.2e-142) {
		tmp = t * (z / (z - a));
	} else if (a <= -9.5e-208) {
		tmp = t_1;
	} else if (a <= -3e-216) {
		tmp = t;
	} else if (a <= 3.7e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	t_2 = x - ((z * t) / a)
	tmp = 0
	if a <= -1.75e+19:
		tmp = t_2
	elif a <= -1.2e-142:
		tmp = t * (z / (z - a))
	elif a <= -9.5e-208:
		tmp = t_1
	elif a <= -3e-216:
		tmp = t
	elif a <= 3.7e-60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	t_2 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (a <= -1.75e+19)
		tmp = t_2;
	elseif (a <= -1.2e-142)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (a <= -9.5e-208)
		tmp = t_1;
	elseif (a <= -3e-216)
		tmp = t;
	elseif (a <= 3.7e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	t_2 = x - ((z * t) / a);
	tmp = 0.0;
	if (a <= -1.75e+19)
		tmp = t_2;
	elseif (a <= -1.2e-142)
		tmp = t * (z / (z - a));
	elseif (a <= -9.5e-208)
		tmp = t_1;
	elseif (a <= -3e-216)
		tmp = t;
	elseif (a <= 3.7e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+19], t$95$2, If[LessEqual[a, -1.2e-142], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-208], t$95$1, If[LessEqual[a, -3e-216], t, If[LessEqual[a, 3.7e-60], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.75e19 or 3.70000000000000025e-60 < a

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      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 z around 0 52.5%

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

   7. Taylor expanded in t around inf 56.1%

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

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

   if -1.75e19 < a < -1.19999999999999994e-142

   1. Initial program 73.7%

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

   3. Taylor expanded in y around 0 23.9%

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

      1. mul-1-neg 23.9%

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

      2. unsub-neg 23.9%

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

      3. associate-/l* 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in x around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. associate-/l* 42.8%

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

   8. Simplified 42.8%

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

   if -1.19999999999999994e-142 < a < -9.5000000000000001e-208 or -3.00000000000000013e-216 < a < 3.70000000000000025e-60

   1. Initial program 79.4%

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

   3. Taylor expanded in y around -inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 66.2%

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

   5. Applied egg-rr 66.2%

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

   6. Taylor expanded in a around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. neg-mul-1 59.4%

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

   8. Simplified 59.4%

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

   if -9.5000000000000001e-208 < a < -3.00000000000000013e-216

   1. Initial program 42.6%

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

   3. Taylor expanded in z around inf 91.4%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+19}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-208}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.2e+89)
     t
     (if (<= z -9.2e-61)
       x
       (if (<= z -1.3e-154)
         t_1
         (if (<= z 1.7e-239)
           x
           (if (<= z 2.75e-58) t_1 (if (<= z 4.4e+61) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.2e+89) {
		tmp = t;
	} else if (z <= -9.2e-61) {
		tmp = x;
	} else if (z <= -1.3e-154) {
		tmp = t_1;
	} else if (z <= 1.7e-239) {
		tmp = x;
	} else if (z <= 2.75e-58) {
		tmp = t_1;
	} else if (z <= 4.4e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.2d+89)) then
        tmp = t
    else if (z <= (-9.2d-61)) then
        tmp = x
    else if (z <= (-1.3d-154)) then
        tmp = t_1
    else if (z <= 1.7d-239) then
        tmp = x
    else if (z <= 2.75d-58) then
        tmp = t_1
    else if (z <= 4.4d+61) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.2e+89) {
		tmp = t;
	} else if (z <= -9.2e-61) {
		tmp = x;
	} else if (z <= -1.3e-154) {
		tmp = t_1;
	} else if (z <= 1.7e-239) {
		tmp = x;
	} else if (z <= 2.75e-58) {
		tmp = t_1;
	} else if (z <= 4.4e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.2e+89:
		tmp = t
	elif z <= -9.2e-61:
		tmp = x
	elif z <= -1.3e-154:
		tmp = t_1
	elif z <= 1.7e-239:
		tmp = x
	elif z <= 2.75e-58:
		tmp = t_1
	elif z <= 4.4e+61:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.2e+89)
		tmp = t;
	elseif (z <= -9.2e-61)
		tmp = x;
	elseif (z <= -1.3e-154)
		tmp = t_1;
	elseif (z <= 1.7e-239)
		tmp = x;
	elseif (z <= 2.75e-58)
		tmp = t_1;
	elseif (z <= 4.4e+61)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.2e+89)
		tmp = t;
	elseif (z <= -9.2e-61)
		tmp = x;
	elseif (z <= -1.3e-154)
		tmp = t_1;
	elseif (z <= 1.7e-239)
		tmp = x;
	elseif (z <= 2.75e-58)
		tmp = t_1;
	elseif (z <= 4.4e+61)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+89], t, If[LessEqual[z, -9.2e-61], x, If[LessEqual[z, -1.3e-154], t$95$1, If[LessEqual[z, 1.7e-239], x, If[LessEqual[z, 2.75e-58], t$95$1, If[LessEqual[z, 4.4e+61], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000002e89 or 4.4000000000000001e61 < z

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 48.9%

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

   if -1.20000000000000002e89 < z < -9.19999999999999967e-61 or -1.3e-154 < z < 1.7e-239 or 2.74999999999999998e-58 < z < 4.4000000000000001e61

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 47.3%

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

   if -9.19999999999999967e-61 < z < -1.3e-154 or 1.7e-239 < z < 2.74999999999999998e-58

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 49.4%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in a around inf 40.5%

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

       1. associate-/l* 48.6%

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

   11. Simplified 48.6%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.45e+173)
     t
     (if (<= z -8.8e-60)
       (* x (/ y z))
       (if (<= z -7.6e-155)
         t_1
         (if (<= z 1.75e-236)
           x
           (if (<= z 4e-53) t_1 (if (<= z 3.3e+61) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.45e+173) {
		tmp = t;
	} else if (z <= -8.8e-60) {
		tmp = x * (y / z);
	} else if (z <= -7.6e-155) {
		tmp = t_1;
	} else if (z <= 1.75e-236) {
		tmp = x;
	} else if (z <= 4e-53) {
		tmp = t_1;
	} else if (z <= 3.3e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.45d+173)) then
        tmp = t
    else if (z <= (-8.8d-60)) then
        tmp = x * (y / z)
    else if (z <= (-7.6d-155)) then
        tmp = t_1
    else if (z <= 1.75d-236) then
        tmp = x
    else if (z <= 4d-53) then
        tmp = t_1
    else if (z <= 3.3d+61) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.45e+173) {
		tmp = t;
	} else if (z <= -8.8e-60) {
		tmp = x * (y / z);
	} else if (z <= -7.6e-155) {
		tmp = t_1;
	} else if (z <= 1.75e-236) {
		tmp = x;
	} else if (z <= 4e-53) {
		tmp = t_1;
	} else if (z <= 3.3e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.45e+173:
		tmp = t
	elif z <= -8.8e-60:
		tmp = x * (y / z)
	elif z <= -7.6e-155:
		tmp = t_1
	elif z <= 1.75e-236:
		tmp = x
	elif z <= 4e-53:
		tmp = t_1
	elif z <= 3.3e+61:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.45e+173)
		tmp = t;
	elseif (z <= -8.8e-60)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -7.6e-155)
		tmp = t_1;
	elseif (z <= 1.75e-236)
		tmp = x;
	elseif (z <= 4e-53)
		tmp = t_1;
	elseif (z <= 3.3e+61)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.45e+173)
		tmp = t;
	elseif (z <= -8.8e-60)
		tmp = x * (y / z);
	elseif (z <= -7.6e-155)
		tmp = t_1;
	elseif (z <= 1.75e-236)
		tmp = x;
	elseif (z <= 4e-53)
		tmp = t_1;
	elseif (z <= 3.3e+61)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+173], t, If[LessEqual[z, -8.8e-60], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-155], t$95$1, If[LessEqual[z, 1.75e-236], x, If[LessEqual[z, 4e-53], t$95$1, If[LessEqual[z, 3.3e+61], x, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000003e173 or 3.2999999999999998e61 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -1.45000000000000003e173 < z < -8.7999999999999995e-60

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 42.3%

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

      1. div-sub 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in t around 0 29.0%

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

      1. neg-mul-1 29.0%

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

      2. distribute-neg-frac 29.0%

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

   8. Simplified 29.0%

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

   9. Taylor expanded in a around 0 23.4%

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

       1. associate-/l* 30.9%

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

   11. Simplified 30.9%

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

   if -8.7999999999999995e-60 < z < -7.5999999999999995e-155 or 1.74999999999999997e-236 < z < 4.00000000000000012e-53

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 49.4%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in a around inf 40.5%

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

       1. associate-/l* 48.6%

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

   11. Simplified 48.6%

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

   if -7.5999999999999995e-155 < z < 1.74999999999999997e-236 or 4.00000000000000012e-53 < z < 3.2999999999999998e61

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+173}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+222}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (/ (* z t) a))))
   (if (<= a -3.6e+222)
     t_2
     (if (<= a -3.3e-143)
       t_1
       (if (<= a -5.5e-206)
         (* (/ y z) (- x t))
         (if (<= a 9.4e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -3.6e+222) {
		tmp = t_2;
	} else if (a <= -3.3e-143) {
		tmp = t_1;
	} else if (a <= -5.5e-206) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - ((z * t) / a)
    if (a <= (-3.6d+222)) then
        tmp = t_2
    else if (a <= (-3.3d-143)) then
        tmp = t_1
    else if (a <= (-5.5d-206)) then
        tmp = (y / z) * (x - t)
    else if (a <= 9.4d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -3.6e+222) {
		tmp = t_2;
	} else if (a <= -3.3e-143) {
		tmp = t_1;
	} else if (a <= -5.5e-206) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - ((z * t) / a)
	tmp = 0
	if a <= -3.6e+222:
		tmp = t_2
	elif a <= -3.3e-143:
		tmp = t_1
	elif a <= -5.5e-206:
		tmp = (y / z) * (x - t)
	elif a <= 9.4e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (a <= -3.6e+222)
		tmp = t_2;
	elseif (a <= -3.3e-143)
		tmp = t_1;
	elseif (a <= -5.5e-206)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 9.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - ((z * t) / a);
	tmp = 0.0;
	if (a <= -3.6e+222)
		tmp = t_2;
	elseif (a <= -3.3e-143)
		tmp = t_1;
	elseif (a <= -5.5e-206)
		tmp = (y / z) * (x - t);
	elseif (a <= 9.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+222], t$95$2, If[LessEqual[a, -3.3e-143], t$95$1, If[LessEqual[a, -5.5e-206], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6000000000000002e222 or 9.3999999999999999e52 < a

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unsub-neg 63.4%

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

      3. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in z around 0 61.9%

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

   7. Taylor expanded in t around inf 69.7%

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

      1. *-commutative 69.7%

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

   9. Simplified 69.7%

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

   if -3.6000000000000002e222 < a < -3.3000000000000001e-143 or -5.50000000000000023e-206 < a < 9.3999999999999999e52

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 58.6%

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

   5. Simplified 58.6%

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

   if -3.3000000000000001e-143 < a < -5.50000000000000023e-206

   1. Initial program 84.4%

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

   3. Taylor expanded in y around -inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 74.5%

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

   5. Applied egg-rr 74.5%

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

   6. Taylor expanded in a around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   8. Simplified 68.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+222}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{z - a}\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-206}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -3.8e+222)
     (* x (- 1.0 (/ z (- z a))))
     (if (<= a -3e-143)
       t_1
       (if (<= a -3.4e-206)
         (* (/ y z) (- x t))
         (if (<= a 9e+52) t_1 (- x (/ (* z t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -3.8e+222) {
		tmp = x * (1.0 - (z / (z - a)));
	} else if (a <= -3e-143) {
		tmp = t_1;
	} else if (a <= -3.4e-206) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9e+52) {
		tmp = t_1;
	} else {
		tmp = x - ((z * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-3.8d+222)) then
        tmp = x * (1.0d0 - (z / (z - a)))
    else if (a <= (-3d-143)) then
        tmp = t_1
    else if (a <= (-3.4d-206)) then
        tmp = (y / z) * (x - t)
    else if (a <= 9d+52) then
        tmp = t_1
    else
        tmp = x - ((z * t) / 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 tmp;
	if (a <= -3.8e+222) {
		tmp = x * (1.0 - (z / (z - a)));
	} else if (a <= -3e-143) {
		tmp = t_1;
	} else if (a <= -3.4e-206) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9e+52) {
		tmp = t_1;
	} else {
		tmp = x - ((z * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -3.8e+222:
		tmp = x * (1.0 - (z / (z - a)))
	elif a <= -3e-143:
		tmp = t_1
	elif a <= -3.4e-206:
		tmp = (y / z) * (x - t)
	elif a <= 9e+52:
		tmp = t_1
	else:
		tmp = x - ((z * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -3.8e+222)
		tmp = Float64(x * Float64(1.0 - Float64(z / Float64(z - a))));
	elseif (a <= -3e-143)
		tmp = t_1;
	elseif (a <= -3.4e-206)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 9e+52)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -3.8e+222)
		tmp = x * (1.0 - (z / (z - a)));
	elseif (a <= -3e-143)
		tmp = t_1;
	elseif (a <= -3.4e-206)
		tmp = (y / z) * (x - t);
	elseif (a <= 9e+52)
		tmp = t_1;
	else
		tmp = x - ((z * t) / 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]}, If[LessEqual[a, -3.8e+222], N[(x * N[(1.0 - N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-143], t$95$1, If[LessEqual[a, -3.4e-206], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+52], t$95$1, N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.80000000000000018e222

   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 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. associate-/l* 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in x around inf 82.8%

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

      1. sub-neg 82.8%

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

      2. mul-1-neg 82.8%

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

      3. remove-double-neg 82.8%

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

   8. Simplified 82.8%

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

   if -3.80000000000000018e222 < a < -2.99999999999999985e-143 or -3.39999999999999985e-206 < a < 8.9999999999999999e52

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 58.6%

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

   5. Simplified 58.6%

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

   if -2.99999999999999985e-143 < a < -3.39999999999999985e-206

   1. Initial program 84.4%

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

   3. Taylor expanded in y around -inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 74.5%

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

   5. Applied egg-rr 74.5%

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

   6. Taylor expanded in a around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   8. Simplified 68.4%

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

   if 8.9999999999999999e52 < a

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

      3. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in z around 0 60.5%

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

   7. Taylor expanded in t around inf 66.1%

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

      1. *-commutative 66.1%

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

   9. Simplified 66.1%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{z - a}\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-206}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-176}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-191}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -9e+73)
     t_1
     (if (<= z -6.2e-176)
       (* (- x t) (/ y (- z a)))
       (if (<= z -4.8e-191)
         (- x (/ (* z t) a))
         (if (<= z 5.6e+60) (+ x (* y (/ (- t x) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+73) {
		tmp = t_1;
	} else if (z <= -6.2e-176) {
		tmp = (x - t) * (y / (z - a));
	} else if (z <= -4.8e-191) {
		tmp = x - ((z * t) / a);
	} else if (z <= 5.6e+60) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-9d+73)) then
        tmp = t_1
    else if (z <= (-6.2d-176)) then
        tmp = (x - t) * (y / (z - a))
    else if (z <= (-4.8d-191)) then
        tmp = x - ((z * t) / a)
    else if (z <= 5.6d+60) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+73) {
		tmp = t_1;
	} else if (z <= -6.2e-176) {
		tmp = (x - t) * (y / (z - a));
	} else if (z <= -4.8e-191) {
		tmp = x - ((z * t) / a);
	} else if (z <= 5.6e+60) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9e+73:
		tmp = t_1
	elif z <= -6.2e-176:
		tmp = (x - t) * (y / (z - a))
	elif z <= -4.8e-191:
		tmp = x - ((z * t) / a)
	elif z <= 5.6e+60:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -9e+73)
		tmp = t_1;
	elseif (z <= -6.2e-176)
		tmp = Float64(Float64(x - t) * Float64(y / Float64(z - a)));
	elseif (z <= -4.8e-191)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= 5.6e+60)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9e+73)
		tmp = t_1;
	elseif (z <= -6.2e-176)
		tmp = (x - t) * (y / (z - a));
	elseif (z <= -4.8e-191)
		tmp = x - ((z * t) / a);
	elseif (z <= 5.6e+60)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+73], t$95$1, If[LessEqual[z, -6.2e-176], N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-191], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+60], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999969e73 or 5.6e60 < z

   1. Initial program 71.9%

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

   3. Taylor expanded in x around 0 34.9%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

   if -8.99999999999999969e73 < z < -6.19999999999999983e-176

   1. Initial program 93.2%

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

   3. Taylor expanded in y around -inf 56.2%

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

      1. *-commutative 56.2%

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

      2. associate-/l* 62.4%

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

   5. Applied egg-rr 62.4%

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

   if -6.19999999999999983e-176 < z < -4.7999999999999998e-191

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in z around 0 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -4.7999999999999998e-191 < z < 5.6e60

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-176}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-191}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-224}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 0.042:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.6e-37)
     t_1
     (if (<= y 1.4e-224)
       (- x (/ (* z t) a))
       (if (<= y 0.042) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.6e-37) {
		tmp = t_1;
	} else if (y <= 1.4e-224) {
		tmp = x - ((z * t) / a);
	} else if (y <= 0.042) {
		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 = y * ((t - x) / (a - z))
    if (y <= (-2.6d-37)) then
        tmp = t_1
    else if (y <= 1.4d-224) then
        tmp = x - ((z * t) / a)
    else if (y <= 0.042d0) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.6e-37) {
		tmp = t_1;
	} else if (y <= 1.4e-224) {
		tmp = x - ((z * t) / a);
	} else if (y <= 0.042) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.6e-37:
		tmp = t_1
	elif y <= 1.4e-224:
		tmp = x - ((z * t) / a)
	elif y <= 0.042:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.6e-37)
		tmp = t_1;
	elseif (y <= 1.4e-224)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (y <= 0.042)
		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 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.6e-37)
		tmp = t_1;
	elseif (y <= 1.4e-224)
		tmp = x - ((z * t) / a);
	elseif (y <= 0.042)
		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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-37], t$95$1, If[LessEqual[y, 1.4e-224], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.042], 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 y < -2.5999999999999998e-37 or 0.0420000000000000026 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. div-sub 68.8%

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

   5. Simplified 68.8%

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

   if -2.5999999999999998e-37 < y < 1.3999999999999999e-224

   1. Initial program 77.0%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

      3. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around 0 52.8%

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

   7. Taylor expanded in t around inf 56.8%

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

      1. *-commutative 56.8%

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

   9. Simplified 56.8%

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

   if 1.3999999999999999e-224 < y < 0.0420000000000000026

   1. Initial program 77.2%

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

   3. Taylor expanded in x around 0 37.6%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-224}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 0.042:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-220}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 0.024:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x t) (/ y (- z a)))))
   (if (<= y -1.75e-39)
     t_1
     (if (<= y 4.6e-220)
       (- x (/ (* z t) a))
       (if (<= y 0.024) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - t) * (y / (z - a));
	double tmp;
	if (y <= -1.75e-39) {
		tmp = t_1;
	} else if (y <= 4.6e-220) {
		tmp = x - ((z * t) / a);
	} else if (y <= 0.024) {
		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 = (x - t) * (y / (z - a))
    if (y <= (-1.75d-39)) then
        tmp = t_1
    else if (y <= 4.6d-220) then
        tmp = x - ((z * t) / a)
    else if (y <= 0.024d0) 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 = (x - t) * (y / (z - a));
	double tmp;
	if (y <= -1.75e-39) {
		tmp = t_1;
	} else if (y <= 4.6e-220) {
		tmp = x - ((z * t) / a);
	} else if (y <= 0.024) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - t) * (y / (z - a))
	tmp = 0
	if y <= -1.75e-39:
		tmp = t_1
	elif y <= 4.6e-220:
		tmp = x - ((z * t) / a)
	elif y <= 0.024:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - t) * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (y <= -1.75e-39)
		tmp = t_1;
	elseif (y <= 4.6e-220)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (y <= 0.024)
		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 = (x - t) * (y / (z - a));
	tmp = 0.0;
	if (y <= -1.75e-39)
		tmp = t_1;
	elseif (y <= 4.6e-220)
		tmp = x - ((z * t) / a);
	elseif (y <= 0.024)
		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[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-39], t$95$1, If[LessEqual[y, 4.6e-220], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.024], 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 y < -1.75e-39 or 0.024 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around -inf 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 69.8%

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

   5. Applied egg-rr 69.8%

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

   if -1.75e-39 < y < 4.59999999999999961e-220

   1. Initial program 77.0%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

      3. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around 0 52.8%

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

   7. Taylor expanded in t around inf 56.8%

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

      1. *-commutative 56.8%

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

   9. Simplified 56.8%

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

   if 4.59999999999999961e-220 < y < 0.024

   1. Initial program 77.2%

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

   3. Taylor expanded in x around 0 37.6%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-220}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 0.024:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-48} \lor \neg \left(x \leq 1950\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.15e-48) (not (<= x 1950.0)))
   (* x (+ (/ (- y z) (- z a)) 1.0))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.15e-48) || !(x <= 1950.0)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.15d-48)) .or. (.not. (x <= 1950.0d0))) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.15e-48) || !(x <= 1950.0)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.15e-48) or not (x <= 1950.0):
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.15e-48) || !(x <= 1950.0))
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.15e-48) || ~((x <= 1950.0)))
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.15e-48], N[Not[LessEqual[x, 1950.0]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-48 or 1950 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. unsub-neg 68.9%

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

   5. Simplified 68.9%

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

   if -1.15e-48 < x < 1950

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 59.0%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-48} \lor \neg \left(x \leq 1950\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x - t}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+21)
   (- x (/ (- y z) (/ a (- x t))))
   (if (<= a 2.2e-62)
     (+ t (* (/ (- t x) z) (- a y)))
     (- x (* (- t x) (/ (- z y) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+21) {
		tmp = x - ((y - z) / (a / (x - t)));
	} else if (a <= 2.2e-62) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x - ((t - x) * ((z - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.8d+21)) then
        tmp = x - ((y - z) / (a / (x - t)))
    else if (a <= 2.2d-62) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x - ((t - x) * ((z - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+21) {
		tmp = x - ((y - z) / (a / (x - t)));
	} else if (a <= 2.2e-62) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x - ((t - x) * ((z - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+21:
		tmp = x - ((y - z) / (a / (x - t)))
	elif a <= 2.2e-62:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x - ((t - x) * ((z - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+21)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(a / Float64(x - t))));
	elseif (a <= 2.2e-62)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+21)
		tmp = x - ((y - z) / (a / (x - t)));
	elseif (a <= 2.2e-62)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x - ((t - x) * ((z - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+21], N[(x - N[(N[(y - z), $MachinePrecision] / N[(a / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-62], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.8e21

   1. Initial program 95.9%

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

      1. clear-num 95.6%

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

      2. un-div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in a around inf 80.4%

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

   if -8.8e21 < a < 2.20000000000000017e-62

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. div-sub 81.2%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 72.7%

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

      9. distribute-rgt-out-- 81.4%

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

   5. Simplified 81.4%

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

   if 2.20000000000000017e-62 < a

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf 69.7%

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

      1. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x - t}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+59} \lor \neg \left(z \leq 1.5 \cdot 10^{+60}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.55e+59) (not (<= z 1.5e+60)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+59) || !(z <= 1.5e+60)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (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) :: tmp
    if ((z <= (-2.55d+59)) .or. (.not. (z <= 1.5d+60))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+59) || !(z <= 1.5e+60)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.55e+59) or not (z <= 1.5e+60):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.55e+59) || !(z <= 1.5e+60))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.55e+59) || ~((z <= 1.5e+60)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.55e+59], N[Not[LessEqual[z, 1.5e+60]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5500000000000002e59 or 1.4999999999999999e60 < z

   1. Initial program 72.1%

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

   3. Taylor expanded in x around 0 34.7%

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

      1. associate-/l* 60.6%

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

   5. Simplified 60.6%

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

   if -2.5500000000000002e59 < z < 1.4999999999999999e60

   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/ 88.6%

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

      3. associate-*r/ 94.2%

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

      4. clear-num 94.2%

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

      5. un-div-inv 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in z around 0 74.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+59} \lor \neg \left(z \leq 1.5 \cdot 10^{+60}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+80) t (if (<= z 5.8e+60) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+80) {
		tmp = t;
	} else if (z <= 5.8e+60) {
		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 <= (-2d+80)) then
        tmp = t
    else if (z <= 5.8d+60) 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 <= -2e+80) {
		tmp = t;
	} else if (z <= 5.8e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+80:
		tmp = t
	elif z <= 5.8e+60:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+80)
		tmp = t;
	elseif (z <= 5.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+80)
		tmp = t;
	elseif (z <= 5.8e+60)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+80], t, If[LessEqual[z, 5.8e+60], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2e80 or 5.79999999999999999e60 < z

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 48.9%

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

   if -2e80 < z < 5.79999999999999999e60

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf 38.5%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.3% 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 85.0%

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

3. Taylor expanded in z around inf 22.5%

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

4. Final simplification 22.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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)))))