Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.4% → 90.5%

Time: 27.5s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.4% 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: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-301} \lor \neg \left(t_1 \leq 5 \cdot 10^{-203}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (or (<= t_1 -2e-301) (not (<= t_1 5e-203)))
     t_1
     (+ t (* (/ x z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-301) || !(t_1 <= 5e-203)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) / (a - z)) * (z - y))
    if ((t_1 <= (-2d-301)) .or. (.not. (t_1 <= 5d-203))) then
        tmp = t_1
    else
        tmp = 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 t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-301) || !(t_1 <= 5e-203)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if (t_1 <= -2e-301) or not (t_1 <= 5e-203):
		tmp = t_1
	else:
		tmp = t + ((x / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if ((t_1 <= -2e-301) || !(t_1 <= 5e-203))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if ((t_1 <= -2e-301) || ~((t_1 <= 5e-203)))
		tmp = t_1;
	else
		tmp = t + ((x / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-301], N[Not[LessEqual[t$95$1, 5e-203]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $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)))) < -2.00000000000000013e-301 or 5.0000000000000002e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.7%

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

   if -2.00000000000000013e-301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-203

   1. Initial program 6.1%

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

   3. Taylor expanded in z around inf 83.6%

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

      1. associate--l+ 83.6%

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

      2. distribute-lft-out-- 83.6%

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

      3. div-sub 83.6%

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

      4. mul-1-neg 83.6%

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

      5. unsub-neg 83.6%

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

      6. distribute-rgt-out-- 83.7%

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

      7. associate-/l* 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-/l* 95.3%

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

      3. associate-/r/ 97.7%

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

   8. Simplified 97.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-301} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 5 \cdot 10^{-203}\right):\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-286}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-109}:\\ \;\;\;\;x + z \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= y -6.2e+35)
     t_2
     (if (<= y -1e-16)
       t_1
       (if (<= y 3.3e-286)
         (- x (/ (* x y) a))
         (if (<= y 1.02e-176)
           (/ t (/ (- z) (- y z)))
           (if (<= y 2.7e-109)
             (+ x (* z (/ x a)))
             (if (<= y 8.5e-11) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -6.2e+35) {
		tmp = t_2;
	} else if (y <= -1e-16) {
		tmp = t_1;
	} else if (y <= 3.3e-286) {
		tmp = x - ((x * y) / a);
	} else if (y <= 1.02e-176) {
		tmp = t / (-z / (y - z));
	} else if (y <= 2.7e-109) {
		tmp = x + (z * (x / a));
	} else if (y <= 8.5e-11) {
		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) * (t / (a - z))
    t_2 = (t - x) * (y / (a - z))
    if (y <= (-6.2d+35)) then
        tmp = t_2
    else if (y <= (-1d-16)) then
        tmp = t_1
    else if (y <= 3.3d-286) then
        tmp = x - ((x * y) / a)
    else if (y <= 1.02d-176) then
        tmp = t / (-z / (y - z))
    else if (y <= 2.7d-109) then
        tmp = x + (z * (x / a))
    else if (y <= 8.5d-11) 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) * (t / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -6.2e+35) {
		tmp = t_2;
	} else if (y <= -1e-16) {
		tmp = t_1;
	} else if (y <= 3.3e-286) {
		tmp = x - ((x * y) / a);
	} else if (y <= 1.02e-176) {
		tmp = t / (-z / (y - z));
	} else if (y <= 2.7e-109) {
		tmp = x + (z * (x / a));
	} else if (y <= 8.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -6.2e+35:
		tmp = t_2
	elif y <= -1e-16:
		tmp = t_1
	elif y <= 3.3e-286:
		tmp = x - ((x * y) / a)
	elif y <= 1.02e-176:
		tmp = t / (-z / (y - z))
	elif y <= 2.7e-109:
		tmp = x + (z * (x / a))
	elif y <= 8.5e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -6.2e+35)
		tmp = t_2;
	elseif (y <= -1e-16)
		tmp = t_1;
	elseif (y <= 3.3e-286)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (y <= 1.02e-176)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (y <= 2.7e-109)
		tmp = Float64(x + Float64(z * Float64(x / a)));
	elseif (y <= 8.5e-11)
		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) * (t / (a - z));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -6.2e+35)
		tmp = t_2;
	elseif (y <= -1e-16)
		tmp = t_1;
	elseif (y <= 3.3e-286)
		tmp = x - ((x * y) / a);
	elseif (y <= 1.02e-176)
		tmp = t / (-z / (y - z));
	elseif (y <= 2.7e-109)
		tmp = x + (z * (x / a));
	elseif (y <= 8.5e-11)
		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[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+35], t$95$2, If[LessEqual[y, -1e-16], t$95$1, If[LessEqual[y, 3.3e-286], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-176], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-109], N[(x + N[(z * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-11], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.19999999999999973e35 or 8.50000000000000037e-11 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. div-sub 71.2%

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

      2. associate-*r/ 57.0%

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

      3. associate-/l* 71.1%

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

      4. associate-/r/ 72.3%

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

   5. Simplified 72.3%

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

   if -6.19999999999999973e35 < y < -9.9999999999999998e-17 or 2.7e-109 < y < 8.50000000000000037e-11

   1. Initial program 83.8%

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

   3. Taylor expanded in x around 0 49.4%

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

      1. associate-/l* 77.2%

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

      2. associate-/r/ 70.9%

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

   5. Simplified 70.9%

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

   if -9.9999999999999998e-17 < y < 3.2999999999999999e-286

   1. Initial program 72.3%

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

   3. Taylor expanded in a around inf 49.3%

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

      1. associate-/l* 55.7%

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

      2. associate-/r/ 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in t around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-/l* 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in z around 0 50.6%

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

   if 3.2999999999999999e-286 < y < 1.02000000000000002e-176

   1. Initial program 42.3%

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

   3. Taylor expanded in x around 0 47.8%

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

      1. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in a around 0 54.5%

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

      1. associate-*r/ 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if 1.02000000000000002e-176 < y < 2.7e-109

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf 77.4%

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

      1. associate-/l* 85.1%

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

      2. associate-/r/ 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in y around 0 62.9%

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

       1. sub-neg 62.9%

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

       2. mul-1-neg 62.9%

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

       3. remove-double-neg 62.9%

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

       4. *-commutative 62.9%

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

       5. associate-*r/ 70.6%

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

   11. Simplified 70.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-286}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-109}:\\ \;\;\;\;x + z \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-25}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t a)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.2e+32)
     t_2
     (if (<= y 2.3e-286)
       t_1
       (if (<= y 4.5e-180)
         (/ t (/ (- z) (- y z)))
         (if (<= y 4.8e-107)
           t_1
           (if (<= y 4.8e-25)
             (* (- y z) (/ t (- a z)))
             (if (<= y 2.45e+45) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.2e+32) {
		tmp = t_2;
	} else if (y <= 2.3e-286) {
		tmp = t_1;
	} else if (y <= 4.5e-180) {
		tmp = t / (-z / (y - z));
	} else if (y <= 4.8e-107) {
		tmp = t_1;
	} else if (y <= 4.8e-25) {
		tmp = (y - z) * (t / (a - z));
	} else if (y <= 2.45e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    t_2 = (t - x) * (y / (a - z))
    if (y <= (-1.2d+32)) then
        tmp = t_2
    else if (y <= 2.3d-286) then
        tmp = t_1
    else if (y <= 4.5d-180) then
        tmp = t / (-z / (y - z))
    else if (y <= 4.8d-107) then
        tmp = t_1
    else if (y <= 4.8d-25) then
        tmp = (y - z) * (t / (a - z))
    else if (y <= 2.45d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.2e+32) {
		tmp = t_2;
	} else if (y <= 2.3e-286) {
		tmp = t_1;
	} else if (y <= 4.5e-180) {
		tmp = t / (-z / (y - z));
	} else if (y <= 4.8e-107) {
		tmp = t_1;
	} else if (y <= 4.8e-25) {
		tmp = (y - z) * (t / (a - z));
	} else if (y <= 2.45e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.2e+32:
		tmp = t_2
	elif y <= 2.3e-286:
		tmp = t_1
	elif y <= 4.5e-180:
		tmp = t / (-z / (y - z))
	elif y <= 4.8e-107:
		tmp = t_1
	elif y <= 4.8e-25:
		tmp = (y - z) * (t / (a - z))
	elif y <= 2.45e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.2e+32)
		tmp = t_2;
	elseif (y <= 2.3e-286)
		tmp = t_1;
	elseif (y <= 4.5e-180)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (y <= 4.8e-107)
		tmp = t_1;
	elseif (y <= 4.8e-25)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (y <= 2.45e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.2e+32)
		tmp = t_2;
	elseif (y <= 2.3e-286)
		tmp = t_1;
	elseif (y <= 4.5e-180)
		tmp = t / (-z / (y - z));
	elseif (y <= 4.8e-107)
		tmp = t_1;
	elseif (y <= 4.8e-25)
		tmp = (y - z) * (t / (a - z));
	elseif (y <= 2.45e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+32], t$95$2, If[LessEqual[y, 2.3e-286], t$95$1, If[LessEqual[y, 4.5e-180], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-107], t$95$1, If[LessEqual[y, 4.8e-25], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+45], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.19999999999999996e32 or 2.4500000000000001e45 < y

   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 71.8%

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

      1. div-sub 71.8%

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

      2. associate-*r/ 56.2%

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

      3. associate-/l* 71.7%

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

      4. associate-/r/ 73.1%

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

   5. Simplified 73.1%

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

   if -1.19999999999999996e32 < y < 2.3000000000000002e-286 or 4.50000000000000009e-180 < y < 4.79999999999999989e-107 or 4.80000000000000018e-25 < y < 2.4500000000000001e45

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 54.3%

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

      1. associate-/l* 62.2%

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

      2. associate-/r/ 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in t around inf 61.3%

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

   if 2.3000000000000002e-286 < y < 4.50000000000000009e-180

   1. Initial program 42.3%

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

   3. Taylor expanded in x around 0 47.8%

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

      1. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in a around 0 54.5%

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

      1. associate-*r/ 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if 4.79999999999999989e-107 < y < 4.80000000000000018e-25

   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 49.9%

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

      1. associate-/l* 76.9%

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

      2. associate-/r/ 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-286}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-25}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+45}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{a}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -920000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ a (/ z t)))))
   (if (<= z -920000000.0)
     t_1
     (if (<= z 5.9e-270)
       (* t (/ (- y z) a))
       (if (<= z 9.2e-187)
         x
         (if (<= z 1.9e-185)
           (* y (/ t a))
           (if (<= z 1.4e-34) (/ (- x) (/ a y)) (if (<= z 7e+79) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / (z / t));
	double tmp;
	if (z <= -920000000.0) {
		tmp = t_1;
	} else if (z <= 5.9e-270) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.2e-187) {
		tmp = x;
	} else if (z <= 1.9e-185) {
		tmp = y * (t / a);
	} else if (z <= 1.4e-34) {
		tmp = -x / (a / y);
	} else if (z <= 7e+79) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (a / (z / t))
    if (z <= (-920000000.0d0)) then
        tmp = t_1
    else if (z <= 5.9d-270) then
        tmp = t * ((y - z) / a)
    else if (z <= 9.2d-187) then
        tmp = x
    else if (z <= 1.9d-185) then
        tmp = y * (t / a)
    else if (z <= 1.4d-34) then
        tmp = -x / (a / y)
    else if (z <= 7d+79) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / (z / t));
	double tmp;
	if (z <= -920000000.0) {
		tmp = t_1;
	} else if (z <= 5.9e-270) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.2e-187) {
		tmp = x;
	} else if (z <= 1.9e-185) {
		tmp = y * (t / a);
	} else if (z <= 1.4e-34) {
		tmp = -x / (a / y);
	} else if (z <= 7e+79) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (a / (z / t))
	tmp = 0
	if z <= -920000000.0:
		tmp = t_1
	elif z <= 5.9e-270:
		tmp = t * ((y - z) / a)
	elif z <= 9.2e-187:
		tmp = x
	elif z <= 1.9e-185:
		tmp = y * (t / a)
	elif z <= 1.4e-34:
		tmp = -x / (a / y)
	elif z <= 7e+79:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(a / Float64(z / t)))
	tmp = 0.0
	if (z <= -920000000.0)
		tmp = t_1;
	elseif (z <= 5.9e-270)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 9.2e-187)
		tmp = x;
	elseif (z <= 1.9e-185)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.4e-34)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (z <= 7e+79)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (a / (z / t));
	tmp = 0.0;
	if (z <= -920000000.0)
		tmp = t_1;
	elseif (z <= 5.9e-270)
		tmp = t * ((y - z) / a);
	elseif (z <= 9.2e-187)
		tmp = x;
	elseif (z <= 1.9e-185)
		tmp = y * (t / a);
	elseif (z <= 1.4e-34)
		tmp = -x / (a / y);
	elseif (z <= 7e+79)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -920000000.0], t$95$1, If[LessEqual[z, 5.9e-270], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-187], x, If[LessEqual[z, 1.9e-185], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-34], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+79], x, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.2e8 or 6.99999999999999961e79 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 34.1%

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

      1. associate-/l* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y around 0 48.3%

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

      1. mul-1-neg 48.3%

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

      2. div-sub 48.3%

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

      3. sub-neg 48.3%

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

      4. *-inverses 48.3%

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

      5. metadata-eval 48.3%

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

   8. Simplified 48.3%

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

   9. Taylor expanded in a around 0 40.2%

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

       1. associate-/l* 46.2%

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

   11. Simplified 46.2%

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

   if -9.2e8 < z < 5.9e-270

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 36.0%

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

      1. associate-/l* 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in a around inf 33.1%

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

      1. associate-/l* 41.2%

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

      2. div-inv 41.2%

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

      3. clear-num 41.2%

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

   8. Applied egg-rr 41.2%

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

   if 5.9e-270 < z < 9.19999999999999991e-187 or 1.39999999999999998e-34 < z < 6.99999999999999961e79

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 54.3%

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

   if 9.19999999999999991e-187 < z < 1.9e-185

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. associate-/l* 99.2%

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

   8. Simplified 99.2%

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

      1. associate-/r/ 100.0%

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

   10. Applied egg-rr 100.0%

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

   if 1.9e-185 < z < 1.39999999999999998e-34

   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 63.0%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in y around inf 35.7%

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

       1. mul-1-neg 35.7%

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

       2. associate-/l* 38.0%

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

       3. distribute-neg-frac 38.0%

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

   11. Simplified 38.0%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -920000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+20)
   t
   (if (<= z -3.3e-229)
     x
     (if (<= z 9.5e-267)
       (/ t (/ a y))
       (if (<= z 8.5e-187)
         x
         (if (<= z 8.6e-186)
           (* y (/ t a))
           (if (<= z 7.5e-38) (/ (- x) (/ a y)) (if (<= z 4.2e+83) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+20) {
		tmp = t;
	} else if (z <= -3.3e-229) {
		tmp = x;
	} else if (z <= 9.5e-267) {
		tmp = t / (a / y);
	} else if (z <= 8.5e-187) {
		tmp = x;
	} else if (z <= 8.6e-186) {
		tmp = y * (t / a);
	} else if (z <= 7.5e-38) {
		tmp = -x / (a / y);
	} else if (z <= 4.2e+83) {
		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 <= (-6.2d+20)) then
        tmp = t
    else if (z <= (-3.3d-229)) then
        tmp = x
    else if (z <= 9.5d-267) then
        tmp = t / (a / y)
    else if (z <= 8.5d-187) then
        tmp = x
    else if (z <= 8.6d-186) then
        tmp = y * (t / a)
    else if (z <= 7.5d-38) then
        tmp = -x / (a / y)
    else if (z <= 4.2d+83) 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 <= -6.2e+20) {
		tmp = t;
	} else if (z <= -3.3e-229) {
		tmp = x;
	} else if (z <= 9.5e-267) {
		tmp = t / (a / y);
	} else if (z <= 8.5e-187) {
		tmp = x;
	} else if (z <= 8.6e-186) {
		tmp = y * (t / a);
	} else if (z <= 7.5e-38) {
		tmp = -x / (a / y);
	} else if (z <= 4.2e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+20:
		tmp = t
	elif z <= -3.3e-229:
		tmp = x
	elif z <= 9.5e-267:
		tmp = t / (a / y)
	elif z <= 8.5e-187:
		tmp = x
	elif z <= 8.6e-186:
		tmp = y * (t / a)
	elif z <= 7.5e-38:
		tmp = -x / (a / y)
	elif z <= 4.2e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+20)
		tmp = t;
	elseif (z <= -3.3e-229)
		tmp = x;
	elseif (z <= 9.5e-267)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 8.5e-187)
		tmp = x;
	elseif (z <= 8.6e-186)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 7.5e-38)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (z <= 4.2e+83)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+20)
		tmp = t;
	elseif (z <= -3.3e-229)
		tmp = x;
	elseif (z <= 9.5e-267)
		tmp = t / (a / y);
	elseif (z <= 8.5e-187)
		tmp = x;
	elseif (z <= 8.6e-186)
		tmp = y * (t / a);
	elseif (z <= 7.5e-38)
		tmp = -x / (a / y);
	elseif (z <= 4.2e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+20], t, If[LessEqual[z, -3.3e-229], x, If[LessEqual[z, 9.5e-267], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-187], x, If[LessEqual[z, 8.6e-186], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-38], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+83], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2e20 or 4.20000000000000005e83 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 45.9%

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

   if -6.2e20 < z < -3.30000000000000021e-229 or 9.49999999999999985e-267 < z < 8.4999999999999999e-187 or 7.5e-38 < z < 4.20000000000000005e83

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 44.6%

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

   if -3.30000000000000021e-229 < z < 9.49999999999999985e-267

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 50.1%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

   if 8.4999999999999999e-187 < z < 8.5999999999999998e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. associate-/l* 99.2%

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

   8. Simplified 99.2%

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

      1. associate-/r/ 100.0%

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

   10. Applied egg-rr 100.0%

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

   if 8.5999999999999998e-186 < z < 7.5e-38

   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 63.0%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in y around inf 35.7%

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

       1. mul-1-neg 35.7%

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

       2. associate-/l* 38.0%

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

       3. distribute-neg-frac 38.0%

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

   11. Simplified 38.0%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+64} \lor \neg \left(t \leq -8.5 \cdot 10^{-19}\right) \land \left(t \leq -3.8 \cdot 10^{-117} \lor \neg \left(t \leq 4.7 \cdot 10^{-6}\right)\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+64)
         (and (not (<= t -8.5e-19)) (or (<= t -3.8e-117) (not (<= t 4.7e-6)))))
   (* (- y z) (/ t (- a z)))
   (- x (/ x (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+64) || (!(t <= -8.5e-19) && ((t <= -3.8e-117) || !(t <= 4.7e-6)))) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x - (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 ((t <= (-1.4d+64)) .or. (.not. (t <= (-8.5d-19))) .and. (t <= (-3.8d-117)) .or. (.not. (t <= 4.7d-6))) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = x - (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 ((t <= -1.4e+64) || (!(t <= -8.5e-19) && ((t <= -3.8e-117) || !(t <= 4.7e-6)))) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+64) or (not (t <= -8.5e-19) and ((t <= -3.8e-117) or not (t <= 4.7e-6))):
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+64) || (!(t <= -8.5e-19) && ((t <= -3.8e-117) || !(t <= 4.7e-6))))
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+64) || (~((t <= -8.5e-19)) && ((t <= -3.8e-117) || ~((t <= 4.7e-6)))))
		tmp = (y - z) * (t / (a - z));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+64], And[N[Not[LessEqual[t, -8.5e-19]], $MachinePrecision], Or[LessEqual[t, -3.8e-117], N[Not[LessEqual[t, 4.7e-6]], $MachinePrecision]]]], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000012e64 or -8.50000000000000003e-19 < t < -3.79999999999999972e-117 or 4.69999999999999989e-6 < t

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0 50.6%

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

      1. associate-/l* 78.0%

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

      2. associate-/r/ 73.3%

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

   5. Simplified 73.3%

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

   if -1.40000000000000012e64 < t < -8.50000000000000003e-19 or -3.79999999999999972e-117 < t < 4.69999999999999989e-6

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 44.8%

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

      1. associate-/l* 53.3%

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

      2. associate-/r/ 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in y around inf 51.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+64} \lor \neg \left(t \leq -8.5 \cdot 10^{-19}\right) \land \left(t \leq -3.8 \cdot 10^{-117} \lor \neg \left(t \leq 4.7 \cdot 10^{-6}\right)\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{-z}{y - z}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z) (- y z)))))
   (if (<= z -5.2e+120)
     t_1
     (if (<= z -4.5e+62)
       (* (- t x) (/ y (- a z)))
       (if (<= z -6.5e-27)
         (* (- y z) (/ t (- a z)))
         (if (<= z 1.5e+60) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (-z / (y - z));
	double tmp;
	if (z <= -5.2e+120) {
		tmp = t_1;
	} else if (z <= -4.5e+62) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -6.5e-27) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 1.5e+60) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (-z / (y - z))
    if (z <= (-5.2d+120)) then
        tmp = t_1
    else if (z <= (-4.5d+62)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= (-6.5d-27)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 1.5d+60) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (-z / (y - z));
	double tmp;
	if (z <= -5.2e+120) {
		tmp = t_1;
	} else if (z <= -4.5e+62) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -6.5e-27) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 1.5e+60) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (-z / (y - z))
	tmp = 0
	if z <= -5.2e+120:
		tmp = t_1
	elif z <= -4.5e+62:
		tmp = (t - x) * (y / (a - z))
	elif z <= -6.5e-27:
		tmp = (y - z) * (t / (a - z))
	elif z <= 1.5e+60:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(-z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -5.2e+120)
		tmp = t_1;
	elseif (z <= -4.5e+62)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= -6.5e-27)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 1.5e+60)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (-z / (y - z));
	tmp = 0.0;
	if (z <= -5.2e+120)
		tmp = t_1;
	elseif (z <= -4.5e+62)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= -6.5e-27)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 1.5e+60)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+120], t$95$1, If[LessEqual[z, -4.5e+62], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-27], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+60], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999998e120 or 1.4999999999999999e60 < z

   1. Initial program 61.2%

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

   3. Taylor expanded in x around 0 32.3%

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

      1. associate-/l* 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in a around 0 56.5%

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

      1. associate-*r/ 56.5%

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

      2. neg-mul-1 56.5%

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

   8. Simplified 56.5%

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

   if -5.1999999999999998e120 < z < -4.49999999999999999e62

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. div-sub 55.7%

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

      2. associate-*r/ 49.2%

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

      3. associate-/l* 55.7%

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

      4. associate-/r/ 55.8%

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

   5. Simplified 55.8%

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

   if -4.49999999999999999e62 < z < -6.50000000000000025e-27

   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 0 52.6%

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

      1. associate-/l* 63.4%

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

      2. associate-/r/ 63.3%

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

   5. Simplified 63.3%

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

   if -6.50000000000000025e-27 < z < 1.4999999999999999e60

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+120}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(a - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+63}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+58}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- a y) (/ t z)))))
   (if (<= z -3.3e+118)
     t_1
     (if (<= z -2.65e+63)
       (* (- t x) (/ y (- a z)))
       (if (<= z -5.5e-20)
         (* (- y z) (/ t (- a z)))
         (if (<= z 3.85e+58) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((a - y) * (t / z));
	double tmp;
	if (z <= -3.3e+118) {
		tmp = t_1;
	} else if (z <= -2.65e+63) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -5.5e-20) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 3.85e+58) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((a - y) * (t / z))
    if (z <= (-3.3d+118)) then
        tmp = t_1
    else if (z <= (-2.65d+63)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= (-5.5d-20)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 3.85d+58) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((a - y) * (t / z));
	double tmp;
	if (z <= -3.3e+118) {
		tmp = t_1;
	} else if (z <= -2.65e+63) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -5.5e-20) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 3.85e+58) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((a - y) * (t / z))
	tmp = 0
	if z <= -3.3e+118:
		tmp = t_1
	elif z <= -2.65e+63:
		tmp = (t - x) * (y / (a - z))
	elif z <= -5.5e-20:
		tmp = (y - z) * (t / (a - z))
	elif z <= 3.85e+58:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(a - y) * Float64(t / z)))
	tmp = 0.0
	if (z <= -3.3e+118)
		tmp = t_1;
	elseif (z <= -2.65e+63)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= -5.5e-20)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 3.85e+58)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((a - y) * (t / z));
	tmp = 0.0;
	if (z <= -3.3e+118)
		tmp = t_1;
	elseif (z <= -2.65e+63)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= -5.5e-20)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 3.85e+58)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(a - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+118], t$95$1, If[LessEqual[z, -2.65e+63], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-20], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.85e+58], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3e118 or 3.85000000000000026e58 < z

   1. Initial program 61.2%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. distribute-lft-out-- 67.0%

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

      3. div-sub 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. distribute-rgt-out-- 68.3%

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

      7. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in t around inf 44.8%

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

      1. associate-/l* 57.3%

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

      2. associate-/r/ 57.3%

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

   8. Simplified 57.3%

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

   if -3.3e118 < z < -2.65e63

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. div-sub 55.7%

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

      2. associate-*r/ 49.2%

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

      3. associate-/l* 55.7%

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

      4. associate-/r/ 55.8%

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

   5. Simplified 55.8%

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

   if -2.65e63 < z < -5.4999999999999996e-20

   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 0 52.6%

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

      1. associate-/l* 63.4%

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

      2. associate-/r/ 63.3%

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

   5. Simplified 63.3%

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

   if -5.4999999999999996e-20 < z < 3.85000000000000026e58

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;t + \left(a - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+63}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+58}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(a - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-36}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -14000000000.0)
   t
   (if (<= z 1.3e-268)
     (* t (/ (- y z) a))
     (if (<= z 9e-187)
       x
       (if (<= z 6.5e-186)
         (* y (/ t a))
         (if (<= z 8e-36) (/ (- x) (/ a y)) (if (<= z 3.7e+81) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -14000000000.0) {
		tmp = t;
	} else if (z <= 1.3e-268) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9e-187) {
		tmp = x;
	} else if (z <= 6.5e-186) {
		tmp = y * (t / a);
	} else if (z <= 8e-36) {
		tmp = -x / (a / y);
	} else if (z <= 3.7e+81) {
		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 <= (-14000000000.0d0)) then
        tmp = t
    else if (z <= 1.3d-268) then
        tmp = t * ((y - z) / a)
    else if (z <= 9d-187) then
        tmp = x
    else if (z <= 6.5d-186) then
        tmp = y * (t / a)
    else if (z <= 8d-36) then
        tmp = -x / (a / y)
    else if (z <= 3.7d+81) 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 <= -14000000000.0) {
		tmp = t;
	} else if (z <= 1.3e-268) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9e-187) {
		tmp = x;
	} else if (z <= 6.5e-186) {
		tmp = y * (t / a);
	} else if (z <= 8e-36) {
		tmp = -x / (a / y);
	} else if (z <= 3.7e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -14000000000.0:
		tmp = t
	elif z <= 1.3e-268:
		tmp = t * ((y - z) / a)
	elif z <= 9e-187:
		tmp = x
	elif z <= 6.5e-186:
		tmp = y * (t / a)
	elif z <= 8e-36:
		tmp = -x / (a / y)
	elif z <= 3.7e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -14000000000.0)
		tmp = t;
	elseif (z <= 1.3e-268)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 9e-187)
		tmp = x;
	elseif (z <= 6.5e-186)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 8e-36)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (z <= 3.7e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -14000000000.0)
		tmp = t;
	elseif (z <= 1.3e-268)
		tmp = t * ((y - z) / a);
	elseif (z <= 9e-187)
		tmp = x;
	elseif (z <= 6.5e-186)
		tmp = y * (t / a);
	elseif (z <= 8e-36)
		tmp = -x / (a / y);
	elseif (z <= 3.7e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -14000000000.0], t, If[LessEqual[z, 1.3e-268], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-187], x, If[LessEqual[z, 6.5e-186], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-36], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+81], x, t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.4e10 or 3.7000000000000001e81 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 45.6%

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

   if -1.4e10 < z < 1.30000000000000001e-268

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 36.0%

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

      1. associate-/l* 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in a around inf 33.1%

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

      1. associate-/l* 41.2%

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

      2. div-inv 41.2%

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

      3. clear-num 41.2%

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

   8. Applied egg-rr 41.2%

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

   if 1.30000000000000001e-268 < z < 8.9999999999999996e-187 or 7.9999999999999995e-36 < z < 3.7000000000000001e81

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 54.3%

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

   if 8.9999999999999996e-187 < z < 6.49999999999999962e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. associate-/l* 99.2%

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

   8. Simplified 99.2%

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

      1. associate-/r/ 100.0%

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

   10. Applied egg-rr 100.0%

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

   if 6.49999999999999962e-186 < z < 7.9999999999999995e-36

   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 63.0%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in y around inf 35.7%

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

       1. mul-1-neg 35.7%

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

       2. associate-/l* 38.0%

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

       3. distribute-neg-frac 38.0%

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

   11. Simplified 38.0%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-36}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x z) (- y a)))))
   (if (<= z -9e+87)
     t_1
     (if (<= z -1.1e-28)
       (- t (/ y (/ z (- t x))))
       (if (<= z 7.4e+56) (+ x (* (- t x) (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -9e+87) {
		tmp = t_1;
	} else if (z <= -1.1e-28) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 7.4e+56) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / z) * (y - a))
    if (z <= (-9d+87)) then
        tmp = t_1
    else if (z <= (-1.1d-28)) then
        tmp = t - (y / (z / (t - x)))
    else if (z <= 7.4d+56) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -9e+87) {
		tmp = t_1;
	} else if (z <= -1.1e-28) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 7.4e+56) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x / z) * (y - a))
	tmp = 0
	if z <= -9e+87:
		tmp = t_1
	elif z <= -1.1e-28:
		tmp = t - (y / (z / (t - x)))
	elif z <= 7.4e+56:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -9e+87)
		tmp = t_1;
	elseif (z <= -1.1e-28)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (z <= 7.4e+56)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x / z) * (y - a));
	tmp = 0.0;
	if (z <= -9e+87)
		tmp = t_1;
	elseif (z <= -1.1e-28)
		tmp = t - (y / (z / (t - x)));
	elseif (z <= 7.4e+56)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+87], t$95$1, If[LessEqual[z, -1.1e-28], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+56], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000005e87 or 7.39999999999999994e56 < z

   1. Initial program 59.6%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. distribute-lft-out-- 68.9%

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

      3. div-sub 68.9%

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

      4. mul-1-neg 68.9%

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

      5. unsub-neg 68.9%

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

      6. distribute-rgt-out-- 70.2%

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

      7. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in t around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 84.1%

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

      3. associate-/r/ 84.2%

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

   8. Simplified 84.2%

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

   if -9.0000000000000005e87 < z < -1.09999999999999998e-28

   1. Initial program 81.6%

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

   3. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 56.3%

         \[\leadsto \color{blue}{t + \left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. +-commutative 56.3%

         \[\leadsto t + \left(\color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate--l+ 56.3%

         \[\leadsto t + \color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)\right)} \]

   5. Simplified 56.4%

      \[\leadsto \color{blue}{\left(t - \frac{a}{{z}^{2}} \cdot \left(\left(t - x\right) \cdot \left(y - a\right)\right)\right) - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in a around 0 63.3%

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

      1. associate-/l* 68.7%

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

   8. Simplified 68.7%

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

   if -1.09999999999999998e-28 < z < 7.39999999999999994e56

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+87}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-31} \lor \neg \left(z \leq 3.85 \cdot 10^{+55}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-31) (not (<= z 3.85e+55)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-31) || !(z <= 3.85e+55)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d-31)) .or. (.not. (z <= 3.85d+55))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-31) || !(z <= 3.85e+55)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-31) or not (z <= 3.85e+55):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-31) || !(z <= 3.85e+55))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-31) || ~((z <= 3.85e+55)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-31], N[Not[LessEqual[z, 3.85e+55]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-31 or 3.84999999999999984e55 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 68.8%

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

      7. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   if -2.5e-31 < z < 3.84999999999999984e55

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-31} \lor \neg \left(z \leq 3.85 \cdot 10^{+55}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e-20)
   (- t (* (- y a) (/ (- t x) z)))
   (if (<= z 5.4e+55)
     (+ x (* (- t x) (/ y a)))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e-20) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else if (z <= 5.4e+55) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d-20)) then
        tmp = t - ((y - a) * ((t - x) / z))
    else if (z <= 5.4d+55) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e-20) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else if (z <= 5.4e+55) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e-20:
		tmp = t - ((y - a) * ((t - x) / z))
	elif z <= 5.4e+55:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e-20)
		tmp = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)));
	elseif (z <= 5.4e+55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e-20)
		tmp = t - ((y - a) * ((t - x) / z));
	elseif (z <= 5.4e+55)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e-20], N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999998e-20

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 55.8%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 55.8%

         \[\leadsto \color{blue}{t + \left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. +-commutative 55.8%

         \[\leadsto t + \left(\color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate--l+ 55.8%

         \[\leadsto t + \color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)\right)} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{\left(t - \frac{a}{{z}^{2}} \cdot \left(\left(t - x\right) \cdot \left(y - a\right)\right)\right) - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-*l/ 84.8%

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

      3. *-commutative 84.8%

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

      4. distribute-lft-neg-in 84.8%

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

   8. Simplified 84.8%

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

   if -4.5999999999999998e-20 < z < 5.39999999999999954e55

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

   if 5.39999999999999954e55 < z

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. distribute-lft-out-- 66.5%

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

      3. div-sub 66.5%

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

      4. mul-1-neg 66.5%

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

      5. unsub-neg 66.5%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{a}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -2600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;x + z \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ a (/ z t)))))
   (if (<= z -2600000000000.0)
     t_1
     (if (<= z 8.2e-263)
       (* t (/ (- y z) a))
       (if (<= z 5.5e+65) (+ x (* z (/ x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / (z / t));
	double tmp;
	if (z <= -2600000000000.0) {
		tmp = t_1;
	} else if (z <= 8.2e-263) {
		tmp = t * ((y - z) / a);
	} else if (z <= 5.5e+65) {
		tmp = x + (z * (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 + (a / (z / t))
    if (z <= (-2600000000000.0d0)) then
        tmp = t_1
    else if (z <= 8.2d-263) then
        tmp = t * ((y - z) / a)
    else if (z <= 5.5d+65) then
        tmp = x + (z * (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 + (a / (z / t));
	double tmp;
	if (z <= -2600000000000.0) {
		tmp = t_1;
	} else if (z <= 8.2e-263) {
		tmp = t * ((y - z) / a);
	} else if (z <= 5.5e+65) {
		tmp = x + (z * (x / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (a / (z / t))
	tmp = 0
	if z <= -2600000000000.0:
		tmp = t_1
	elif z <= 8.2e-263:
		tmp = t * ((y - z) / a)
	elif z <= 5.5e+65:
		tmp = x + (z * (x / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(a / Float64(z / t)))
	tmp = 0.0
	if (z <= -2600000000000.0)
		tmp = t_1;
	elseif (z <= 8.2e-263)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 5.5e+65)
		tmp = Float64(x + Float64(z * Float64(x / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (a / (z / t));
	tmp = 0.0;
	if (z <= -2600000000000.0)
		tmp = t_1;
	elseif (z <= 8.2e-263)
		tmp = t * ((y - z) / a);
	elseif (z <= 5.5e+65)
		tmp = x + (z * (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[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2600000000000.0], t$95$1, If[LessEqual[z, 8.2e-263], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+65], N[(x + N[(z * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e12 or 5.4999999999999996e65 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in x around 0 33.6%

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

      1. associate-/l* 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in y around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. div-sub 47.6%

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

      3. sub-neg 47.6%

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

      4. *-inverses 47.6%

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

      5. metadata-eval 47.6%

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

   8. Simplified 47.6%

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

   9. Taylor expanded in a around 0 39.6%

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

       1. associate-/l* 45.5%

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

   11. Simplified 45.5%

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

   if -2.6e12 < z < 8.1999999999999994e-263

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 36.0%

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

      1. associate-/l* 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in a around inf 33.1%

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

      1. associate-/l* 41.2%

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

      2. div-inv 41.2%

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

      3. clear-num 41.2%

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

   8. Applied egg-rr 41.2%

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

   if 8.1999999999999994e-263 < z < 5.4999999999999996e65

   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 71.5%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in y around 0 45.1%

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

       1. sub-neg 45.1%

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

       2. mul-1-neg 45.1%

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

       3. remove-double-neg 45.1%

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

       4. *-commutative 45.1%

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

       5. associate-*r/ 48.2%

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

   11. Simplified 48.2%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2600000000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;x + z \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-24} \lor \neg \left(z \leq 7.8 \cdot 10^{+55}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e-24) (not (<= z 7.8e+55)))
   (- t (/ y (/ z (- t x))))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-24) || !(z <= 7.8e+55)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.4d-24)) .or. (.not. (z <= 7.8d+55))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-24) || !(z <= 7.8e+55)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e-24) or not (z <= 7.8e+55):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e-24) || !(z <= 7.8e+55))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e-24) || ~((z <= 7.8e+55)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e-24], N[Not[LessEqual[z, 7.8e+55]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000003e-24 or 7.80000000000000054e55 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 58.3%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 58.3%

         \[\leadsto \color{blue}{t + \left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. +-commutative 58.3%

         \[\leadsto t + \left(\color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate--l+ 58.3%

         \[\leadsto t + \color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)\right)} \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{\left(t - \frac{a}{{z}^{2}} \cdot \left(\left(t - x\right) \cdot \left(y - a\right)\right)\right) - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in a around 0 62.0%

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

      1. associate-/l* 75.1%

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

   8. Simplified 75.1%

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

   if -4.40000000000000003e-24 < z < 7.80000000000000054e55

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-24} \lor \neg \left(z \leq 7.8 \cdot 10^{+55}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e-27)
   (- t (/ y (/ z (- t x))))
   (if (<= z 3.75e+56) (+ x (* (- t x) (/ y a))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e-27) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 3.75e+56) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.4d-27)) then
        tmp = t - (y / (z / (t - x)))
    else if (z <= 3.75d+56) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e-27) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 3.75e+56) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e-27:
		tmp = t - (y / (z / (t - x)))
	elif z <= 3.75e+56:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e-27)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (z <= 3.75e+56)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e-27)
		tmp = t - (y / (z / (t - x)));
	elseif (z <= 3.75e+56)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e-27], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.75e+56], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.39999999999999982e-27

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 55.8%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 55.8%

         \[\leadsto \color{blue}{t + \left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. +-commutative 55.8%

         \[\leadsto t + \left(\color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate--l+ 55.8%

         \[\leadsto t + \color{blue}{\left(\frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)\right)} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{\left(t - \frac{a}{{z}^{2}} \cdot \left(\left(t - x\right) \cdot \left(y - a\right)\right)\right) - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in a around 0 61.7%

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

      1. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if -6.39999999999999982e-27 < z < 3.75e56

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

   if 3.75e56 < z

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. distribute-lft-out-- 66.5%

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

      3. div-sub 66.5%

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

      4. mul-1-neg 66.5%

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

      5. unsub-neg 66.5%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in y around inf 81.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-20} \lor \neg \left(z \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e-20) (not (<= z 9.5e+59)))
   (/ t (/ (- z) (- y z)))
   (- x (/ x (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e-20) || !(z <= 9.5e+59)) {
		tmp = t / (-z / (y - z));
	} else {
		tmp = x - (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 <= (-1.6d-20)) .or. (.not. (z <= 9.5d+59))) then
        tmp = t / (-z / (y - z))
    else
        tmp = x - (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 <= -1.6e-20) || !(z <= 9.5e+59)) {
		tmp = t / (-z / (y - z));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e-20) or not (z <= 9.5e+59):
		tmp = t / (-z / (y - z))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e-20) || !(z <= 9.5e+59))
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e-20) || ~((z <= 9.5e+59)))
		tmp = t / (-z / (y - z));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e-20], N[Not[LessEqual[z, 9.5e+59]], $MachinePrecision]], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999985e-20 or 9.50000000000000023e59 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in x around 0 35.4%

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

      1. associate-/l* 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in a around 0 52.8%

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

      1. associate-*r/ 52.8%

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

      2. neg-mul-1 52.8%

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

   8. Simplified 52.8%

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

   if -1.59999999999999985e-20 < z < 9.50000000000000023e59

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 73.3%

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

      1. associate-/l* 84.0%

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

      2. associate-/r/ 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-/l* 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in y around inf 62.5%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-20} \lor \neg \left(z \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-231}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+21)
   t
   (if (<= z -8.5e-231)
     x
     (if (<= z 2.3e-273) (* y (/ t a)) (if (<= z 6.5e+81) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+21) {
		tmp = t;
	} else if (z <= -8.5e-231) {
		tmp = x;
	} else if (z <= 2.3e-273) {
		tmp = y * (t / a);
	} else if (z <= 6.5e+81) {
		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 <= (-1.25d+21)) then
        tmp = t
    else if (z <= (-8.5d-231)) then
        tmp = x
    else if (z <= 2.3d-273) then
        tmp = y * (t / a)
    else if (z <= 6.5d+81) 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 <= -1.25e+21) {
		tmp = t;
	} else if (z <= -8.5e-231) {
		tmp = x;
	} else if (z <= 2.3e-273) {
		tmp = y * (t / a);
	} else if (z <= 6.5e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+21:
		tmp = t
	elif z <= -8.5e-231:
		tmp = x
	elif z <= 2.3e-273:
		tmp = y * (t / a)
	elif z <= 6.5e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+21)
		tmp = t;
	elseif (z <= -8.5e-231)
		tmp = x;
	elseif (z <= 2.3e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 6.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+21)
		tmp = t;
	elseif (z <= -8.5e-231)
		tmp = x;
	elseif (z <= 2.3e-273)
		tmp = y * (t / a);
	elseif (z <= 6.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+21], t, If[LessEqual[z, -8.5e-231], x, If[LessEqual[z, 2.3e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+81], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e21 or 6.4999999999999996e81 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 45.9%

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

   if -1.25e21 < z < -8.5e-231 or 2.29999999999999981e-273 < z < 6.4999999999999996e81

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 40.2%

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

   if -8.5e-231 < z < 2.29999999999999981e-273

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 50.1%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

      1. associate-/r/ 54.1%

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

   10. Applied egg-rr 54.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-231}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+21)
   t
   (if (<= z -8.2e-225)
     x
     (if (<= z 3.9e-267) (* t (/ y a)) (if (<= z 6e+83) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+21) {
		tmp = t;
	} else if (z <= -8.2e-225) {
		tmp = x;
	} else if (z <= 3.9e-267) {
		tmp = t * (y / a);
	} else if (z <= 6e+83) {
		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 <= (-1.05d+21)) then
        tmp = t
    else if (z <= (-8.2d-225)) then
        tmp = x
    else if (z <= 3.9d-267) then
        tmp = t * (y / a)
    else if (z <= 6d+83) 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 <= -1.05e+21) {
		tmp = t;
	} else if (z <= -8.2e-225) {
		tmp = x;
	} else if (z <= 3.9e-267) {
		tmp = t * (y / a);
	} else if (z <= 6e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+21:
		tmp = t
	elif z <= -8.2e-225:
		tmp = x
	elif z <= 3.9e-267:
		tmp = t * (y / a)
	elif z <= 6e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+21)
		tmp = t;
	elseif (z <= -8.2e-225)
		tmp = x;
	elseif (z <= 3.9e-267)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 6e+83)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+21)
		tmp = t;
	elseif (z <= -8.2e-225)
		tmp = x;
	elseif (z <= 3.9e-267)
		tmp = t * (y / a);
	elseif (z <= 6e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+21], t, If[LessEqual[z, -8.2e-225], x, If[LessEqual[z, 3.9e-267], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+83], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e21 or 5.9999999999999999e83 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 45.9%

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

   if -1.05e21 < z < -8.20000000000000044e-225 or 3.89999999999999977e-267 < z < 5.9999999999999999e83

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 40.2%

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

   if -8.20000000000000044e-225 < z < 3.89999999999999977e-267

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 50.1%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

      1. clear-num 62.0%

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

      2. associate-/r/ 62.0%

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

      3. clear-num 62.0%

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

   10. Applied egg-rr 62.0%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+21)
   t
   (if (<= z -1.95e-227)
     x
     (if (<= z 1.5e-263) (/ t (/ a y)) (if (<= z 2.6e+79) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+21) {
		tmp = t;
	} else if (z <= -1.95e-227) {
		tmp = x;
	} else if (z <= 1.5e-263) {
		tmp = t / (a / y);
	} else if (z <= 2.6e+79) {
		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 <= (-1.25d+21)) then
        tmp = t
    else if (z <= (-1.95d-227)) then
        tmp = x
    else if (z <= 1.5d-263) then
        tmp = t / (a / y)
    else if (z <= 2.6d+79) 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 <= -1.25e+21) {
		tmp = t;
	} else if (z <= -1.95e-227) {
		tmp = x;
	} else if (z <= 1.5e-263) {
		tmp = t / (a / y);
	} else if (z <= 2.6e+79) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+21:
		tmp = t
	elif z <= -1.95e-227:
		tmp = x
	elif z <= 1.5e-263:
		tmp = t / (a / y)
	elif z <= 2.6e+79:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+21)
		tmp = t;
	elseif (z <= -1.95e-227)
		tmp = x;
	elseif (z <= 1.5e-263)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 2.6e+79)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+21)
		tmp = t;
	elseif (z <= -1.95e-227)
		tmp = x;
	elseif (z <= 1.5e-263)
		tmp = t / (a / y);
	elseif (z <= 2.6e+79)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+21], t, If[LessEqual[z, -1.95e-227], x, If[LessEqual[z, 1.5e-263], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+79], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e21 or 2.60000000000000015e79 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 45.9%

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

   if -1.25e21 < z < -1.95e-227 or 1.5e-263 < z < 2.60000000000000015e79

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 40.2%

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

   if -1.95e-227 < z < 1.5e-263

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 50.1%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{+80}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+21) (not (<= z 3.5e+80)))
   (+ t (/ a (/ z t)))
   (- x (* y (/ x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+21) || !(z <= 3.5e+80)) {
		tmp = t + (a / (z / t));
	} else {
		tmp = x - (y * (x / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.25d+21)) .or. (.not. (z <= 3.5d+80))) then
        tmp = t + (a / (z / t))
    else
        tmp = x - (y * (x / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+21) || !(z <= 3.5e+80)) {
		tmp = t + (a / (z / t));
	} else {
		tmp = x - (y * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+21) or not (z <= 3.5e+80):
		tmp = t + (a / (z / t))
	else:
		tmp = x - (y * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+21) || !(z <= 3.5e+80))
		tmp = Float64(t + Float64(a / Float64(z / t)));
	else
		tmp = Float64(x - Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+21) || ~((z <= 3.5e+80)))
		tmp = t + (a / (z / t));
	else
		tmp = x - (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+21], N[Not[LessEqual[z, 3.5e+80]], $MachinePrecision]], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e21 or 3.49999999999999994e80 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in x around 0 34.3%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. div-sub 48.7%

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

      3. sub-neg 48.7%

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

      4. *-inverses 48.7%

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

      5. metadata-eval 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in a around 0 40.4%

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

       1. associate-/l* 46.5%

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

   11. Simplified 46.5%

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

   if -1.25e21 < z < 3.49999999999999994e80

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 52.3%

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

       1. associate-*l/ 57.0%

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

       2. *-commutative 57.0%

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

   11. Simplified 57.0%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{+80}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+21} \lor \neg \left(z \leq 3.3 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+21) (not (<= z 3.3e+80)))
   (/ t (- 1.0 (/ a z)))
   (- x (* y (/ x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+21) || !(z <= 3.3e+80)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x - (y * (x / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d+21)) .or. (.not. (z <= 3.3d+80))) then
        tmp = t / (1.0d0 - (a / z))
    else
        tmp = x - (y * (x / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+21) || !(z <= 3.3e+80)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x - (y * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+21) or not (z <= 3.3e+80):
		tmp = t / (1.0 - (a / z))
	else:
		tmp = x - (y * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+21) || !(z <= 3.3e+80))
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	else
		tmp = Float64(x - Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+21) || ~((z <= 3.3e+80)))
		tmp = t / (1.0 - (a / z));
	else
		tmp = x - (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+21], N[Not[LessEqual[z, 3.3e+80]], $MachinePrecision]], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e21 or 3.29999999999999991e80 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in x around 0 34.3%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. div-sub 48.7%

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

      3. sub-neg 48.7%

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

      4. *-inverses 48.7%

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

      5. metadata-eval 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in t around 0 48.7%

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

   if -1.3e21 < z < 3.29999999999999991e80

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 52.3%

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

       1. associate-*l/ 57.0%

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

       2. *-commutative 57.0%

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

   11. Simplified 57.0%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+21} \lor \neg \left(z \leq 3.3 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 9.5 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+20) (not (<= z 9.5e+82)))
   (/ t (- 1.0 (/ a z)))
   (- x (/ x (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+20) || !(z <= 9.5e+82)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x - (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 <= (-1.85d+20)) .or. (.not. (z <= 9.5d+82))) then
        tmp = t / (1.0d0 - (a / z))
    else
        tmp = x - (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 <= -1.85e+20) || !(z <= 9.5e+82)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+20) or not (z <= 9.5e+82):
		tmp = t / (1.0 - (a / z))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+20) || !(z <= 9.5e+82))
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+20) || ~((z <= 9.5e+82)))
		tmp = t / (1.0 - (a / z));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+20], N[Not[LessEqual[z, 9.5e+82]], $MachinePrecision]], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e20 or 9.50000000000000049e82 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in x around 0 34.3%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. div-sub 48.7%

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

      3. sub-neg 48.7%

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

      4. *-inverses 48.7%

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

      5. metadata-eval 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in t around 0 48.7%

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

   if -1.85e20 < z < 9.50000000000000049e82

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in y around inf 58.4%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 9.5 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+21) t (if (<= z 4.7e+79) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+21) {
		tmp = t;
	} else if (z <= 4.7e+79) {
		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 <= (-1.15d+21)) then
        tmp = t
    else if (z <= 4.7d+79) 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 <= -1.15e+21) {
		tmp = t;
	} else if (z <= 4.7e+79) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+21:
		tmp = t
	elif z <= 4.7e+79:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+21)
		tmp = t;
	elseif (z <= 4.7e+79)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+21)
		tmp = t;
	elseif (z <= 4.7e+79)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+21], t, If[LessEqual[z, 4.7e+79], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e21 or 4.70000000000000023e79 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 45.9%

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

   if -1.15e21 < z < 4.70000000000000023e79

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 37.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 78.5%

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

3. Taylor expanded in z around inf 25.1%

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

4. Final simplification 25.1%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024013 
(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)))))