Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.5% → 87.6%

Time: 33.4s

Alternatives: 27

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.72 \cdot 10^{+103}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.4e+47) (not (<= t 1.72e+103)))
   (+ y (/ (- x y) (/ t (- z a))))
   (fma (/ (- z t) (- a t)) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.4e+47) || !(t <= 1.72e+103)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.4e+47) || !(t <= 1.72e+103))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.4e+47], N[Not[LessEqual[t, 1.72e+103]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4e47 or 1.72e103 < t

   1. Initial program 32.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. associate-*r/ 66.9%

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

      3. associate-*r/ 66.9%

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

      4. div-sub 66.9%

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

      5. distribute-lft-out-- 66.9%

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

      6. associate-*r/ 66.9%

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

      7. mul-1-neg 66.9%

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

      8. unsub-neg 66.9%

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

      9. distribute-rgt-out-- 67.1%

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

      10. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

   if -6.4e47 < t < 1.72e103

   1. Initial program 88.2%

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

      1. +-commutative 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-/l* 91.3%

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

      4. associate-/r/ 94.4%

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

      5. fma-def 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.72 \cdot 10^{+103}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (* x (/ (- z a) t))))
   (if (<= t -6.8e+66)
     y
     (if (<= t -4.8e-53)
       t_2
       (if (<= t -1.3e-53)
         (* y (/ (- t) a))
         (if (<= t 3.5e-116)
           t_1
           (if (<= t 1.4e-52)
             (* x (- 1.0 (/ z a)))
             (if (<= t 6e+38)
               t_1
               (if (<= t 1.55e+99)
                 y
                 (if (<= t 2.25e+101) x (if (<= t 6.2e+126) t_2 y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * ((z - a) / t);
	double tmp;
	if (t <= -6.8e+66) {
		tmp = y;
	} else if (t <= -4.8e-53) {
		tmp = t_2;
	} else if (t <= -1.3e-53) {
		tmp = y * (-t / a);
	} else if (t <= 3.5e-116) {
		tmp = t_1;
	} else if (t <= 1.4e-52) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6e+38) {
		tmp = t_1;
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 2.25e+101) {
		tmp = x;
	} else if (t <= 6.2e+126) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x * ((z - a) / t)
    if (t <= (-6.8d+66)) then
        tmp = y
    else if (t <= (-4.8d-53)) then
        tmp = t_2
    else if (t <= (-1.3d-53)) then
        tmp = y * (-t / a)
    else if (t <= 3.5d-116) then
        tmp = t_1
    else if (t <= 1.4d-52) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6d+38) then
        tmp = t_1
    else if (t <= 1.55d+99) then
        tmp = y
    else if (t <= 2.25d+101) then
        tmp = x
    else if (t <= 6.2d+126) then
        tmp = t_2
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * ((z - a) / t);
	double tmp;
	if (t <= -6.8e+66) {
		tmp = y;
	} else if (t <= -4.8e-53) {
		tmp = t_2;
	} else if (t <= -1.3e-53) {
		tmp = y * (-t / a);
	} else if (t <= 3.5e-116) {
		tmp = t_1;
	} else if (t <= 1.4e-52) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6e+38) {
		tmp = t_1;
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 2.25e+101) {
		tmp = x;
	} else if (t <= 6.2e+126) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x * ((z - a) / t)
	tmp = 0
	if t <= -6.8e+66:
		tmp = y
	elif t <= -4.8e-53:
		tmp = t_2
	elif t <= -1.3e-53:
		tmp = y * (-t / a)
	elif t <= 3.5e-116:
		tmp = t_1
	elif t <= 1.4e-52:
		tmp = x * (1.0 - (z / a))
	elif t <= 6e+38:
		tmp = t_1
	elif t <= 1.55e+99:
		tmp = y
	elif t <= 2.25e+101:
		tmp = x
	elif t <= 6.2e+126:
		tmp = t_2
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (t <= -6.8e+66)
		tmp = y;
	elseif (t <= -4.8e-53)
		tmp = t_2;
	elseif (t <= -1.3e-53)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (t <= 3.5e-116)
		tmp = t_1;
	elseif (t <= 1.4e-52)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6e+38)
		tmp = t_1;
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 2.25e+101)
		tmp = x;
	elseif (t <= 6.2e+126)
		tmp = t_2;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x * ((z - a) / t);
	tmp = 0.0;
	if (t <= -6.8e+66)
		tmp = y;
	elseif (t <= -4.8e-53)
		tmp = t_2;
	elseif (t <= -1.3e-53)
		tmp = y * (-t / a);
	elseif (t <= 3.5e-116)
		tmp = t_1;
	elseif (t <= 1.4e-52)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6e+38)
		tmp = t_1;
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 2.25e+101)
		tmp = x;
	elseif (t <= 6.2e+126)
		tmp = t_2;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+66], y, If[LessEqual[t, -4.8e-53], t$95$2, If[LessEqual[t, -1.3e-53], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-116], t$95$1, If[LessEqual[t, 1.4e-52], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+38], t$95$1, If[LessEqual[t, 1.55e+99], y, If[LessEqual[t, 2.25e+101], x, If[LessEqual[t, 6.2e+126], t$95$2, y]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.8000000000000006e66 or 6.0000000000000002e38 < t < 1.55e99 or 6.2e126 < t

   1. Initial program 38.2%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   5. Taylor expanded in t around inf 57.5%

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

   if -6.8000000000000006e66 < t < -4.80000000000000015e-53 or 2.2500000000000001e101 < t < 6.2e126

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-*l/ 75.4%

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

      3. fma-def 75.6%

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

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 75.4%

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

      2. associate-/r/ 78.3%

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

      3. div-inv 78.3%

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

      4. clear-num 78.4%

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

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in y around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. unsub-neg 35.7%

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

      3. associate-/l* 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in t around inf 42.5%

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

       1. distribute-lft-out-- 42.5%

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

       2. mul-1-neg 42.5%

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

       3. *-commutative 42.5%

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

       4. distribute-lft-out-- 42.5%

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

   12. Simplified 42.5%

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

   13. Taylor expanded in x around inf 42.5%

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

       1. associate-*r/ 52.5%

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

   15. Simplified 52.5%

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

   if -4.80000000000000015e-53 < t < -1.29999999999999998e-53

   1. Initial program 100.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in z around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-/l* 53.0%

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

   10. Simplified 53.0%

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

   11. Taylor expanded in x around 0 53.0%

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

       1. mul-1-neg 53.0%

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

       2. associate-*l/ 53.0%

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

       3. *-commutative 53.0%

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

       4. distribute-rgt-neg-in 53.0%

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

       5. distribute-frac-neg 53.0%

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

   13. Simplified 53.0%

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

   if -1.29999999999999998e-53 < t < 3.49999999999999984e-116 or 1.39999999999999997e-52 < t < 6.0000000000000002e38

   1. Initial program 91.4%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 71.9%

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

   6. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   8. Simplified 62.0%

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

      1. div-inv 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*l* 66.5%

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

      4. div-inv 66.5%

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

   10. Applied egg-rr 66.5%

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

   if 3.49999999999999984e-116 < t < 1.39999999999999997e-52

   1. Initial program 85.4%

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

      1. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 35.5%

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

   6. Taylor expanded in x around inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. unsub-neg 44.1%

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

   8. Simplified 44.1%

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

   if 1.55e99 < t < 2.2500000000000001e101

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-116}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.7 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= t -1.9e+66)
     y
     (if (<= t -4.8e-53)
       t_1
       (if (<= t -1.3e-53)
         (* y (/ (- t) a))
         (if (<= t 3.1e-116)
           (+ x (/ y (/ a z)))
           (if (<= t 6.8e-53)
             (* x (- 1.0 (/ z a)))
             (if (<= t 5.8e+38)
               (+ x (* y (/ z a)))
               (if (<= t 1.55e+99)
                 y
                 (if (<= t 8.7e+102) x (if (<= t 1.08e+126) t_1 y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -1.9e+66) {
		tmp = y;
	} else if (t <= -4.8e-53) {
		tmp = t_1;
	} else if (t <= -1.3e-53) {
		tmp = y * (-t / a);
	} else if (t <= 3.1e-116) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.8e-53) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.8e+38) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 8.7e+102) {
		tmp = x;
	} else if (t <= 1.08e+126) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (t <= (-1.9d+66)) then
        tmp = y
    else if (t <= (-4.8d-53)) then
        tmp = t_1
    else if (t <= (-1.3d-53)) then
        tmp = y * (-t / a)
    else if (t <= 3.1d-116) then
        tmp = x + (y / (a / z))
    else if (t <= 6.8d-53) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5.8d+38) then
        tmp = x + (y * (z / a))
    else if (t <= 1.55d+99) then
        tmp = y
    else if (t <= 8.7d+102) then
        tmp = x
    else if (t <= 1.08d+126) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -1.9e+66) {
		tmp = y;
	} else if (t <= -4.8e-53) {
		tmp = t_1;
	} else if (t <= -1.3e-53) {
		tmp = y * (-t / a);
	} else if (t <= 3.1e-116) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.8e-53) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.8e+38) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 8.7e+102) {
		tmp = x;
	} else if (t <= 1.08e+126) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if t <= -1.9e+66:
		tmp = y
	elif t <= -4.8e-53:
		tmp = t_1
	elif t <= -1.3e-53:
		tmp = y * (-t / a)
	elif t <= 3.1e-116:
		tmp = x + (y / (a / z))
	elif t <= 6.8e-53:
		tmp = x * (1.0 - (z / a))
	elif t <= 5.8e+38:
		tmp = x + (y * (z / a))
	elif t <= 1.55e+99:
		tmp = y
	elif t <= 8.7e+102:
		tmp = x
	elif t <= 1.08e+126:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (t <= -1.9e+66)
		tmp = y;
	elseif (t <= -4.8e-53)
		tmp = t_1;
	elseif (t <= -1.3e-53)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (t <= 3.1e-116)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 6.8e-53)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5.8e+38)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 8.7e+102)
		tmp = x;
	elseif (t <= 1.08e+126)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (t <= -1.9e+66)
		tmp = y;
	elseif (t <= -4.8e-53)
		tmp = t_1;
	elseif (t <= -1.3e-53)
		tmp = y * (-t / a);
	elseif (t <= 3.1e-116)
		tmp = x + (y / (a / z));
	elseif (t <= 6.8e-53)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5.8e+38)
		tmp = x + (y * (z / a));
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 8.7e+102)
		tmp = x;
	elseif (t <= 1.08e+126)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+66], y, If[LessEqual[t, -4.8e-53], t$95$1, If[LessEqual[t, -1.3e-53], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-116], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-53], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+38], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+99], y, If[LessEqual[t, 8.7e+102], x, If[LessEqual[t, 1.08e+126], t$95$1, y]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.9000000000000001e66 or 5.80000000000000013e38 < t < 1.55e99 or 1.0799999999999999e126 < t

   1. Initial program 38.2%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   5. Taylor expanded in t around inf 57.5%

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

   if -1.9000000000000001e66 < t < -4.80000000000000015e-53 or 8.69999999999999974e102 < t < 1.0799999999999999e126

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-*l/ 75.4%

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

      3. fma-def 75.6%

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

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 75.4%

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

      2. associate-/r/ 78.3%

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

      3. div-inv 78.3%

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

      4. clear-num 78.4%

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

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in y around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. unsub-neg 35.7%

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

      3. associate-/l* 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in t around inf 42.5%

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

       1. distribute-lft-out-- 42.5%

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

       2. mul-1-neg 42.5%

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

       3. *-commutative 42.5%

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

       4. distribute-lft-out-- 42.5%

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

   12. Simplified 42.5%

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

   13. Taylor expanded in x around inf 42.5%

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

       1. associate-*r/ 52.5%

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

   15. Simplified 52.5%

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

   if -4.80000000000000015e-53 < t < -1.29999999999999998e-53

   1. Initial program 100.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in z around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-/l* 53.0%

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

   10. Simplified 53.0%

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

   11. Taylor expanded in x around 0 53.0%

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

       1. mul-1-neg 53.0%

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

       2. associate-*l/ 53.0%

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

       3. *-commutative 53.0%

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

       4. distribute-rgt-neg-in 53.0%

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

       5. distribute-frac-neg 53.0%

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

   13. Simplified 53.0%

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

   if -1.29999999999999998e-53 < t < 3.10000000000000018e-116

   1. Initial program 93.4%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around 0 76.0%

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

   6. Taylor expanded in y around inf 65.1%

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

      1. associate-/l* 67.8%

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

   8. Simplified 67.8%

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

   if 3.10000000000000018e-116 < t < 6.8e-53

   1. Initial program 85.4%

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

      1. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 35.5%

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

   6. Taylor expanded in x around inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. unsub-neg 44.1%

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

   8. Simplified 44.1%

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

   if 6.8e-53 < t < 5.80000000000000013e38

   1. Initial program 81.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

   8. Simplified 45.3%

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

      1. div-inv 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*l* 59.5%

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

      4. div-inv 59.4%

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

   10. Applied egg-rr 59.4%

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

   if 1.55e99 < t < 8.69999999999999974e102

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.7 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+39}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.03 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= t -2.2e+69)
     y
     (if (<= t -8.5e-23)
       t_1
       (if (<= t 7e-117)
         (+ x (/ y (/ a z)))
         (if (<= t 4.8e-69)
           t_1
           (if (<= t 1.08e+39)
             (+ x (* y (/ z a)))
             (if (<= t 2.7e+97)
               y
               (if (<= t 1.03e+102)
                 x
                 (if (<= t 5.1e+127) (* x (/ (- z a) t)) y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -2.2e+69) {
		tmp = y;
	} else if (t <= -8.5e-23) {
		tmp = t_1;
	} else if (t <= 7e-117) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-69) {
		tmp = t_1;
	} else if (t <= 1.08e+39) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e+97) {
		tmp = y;
	} else if (t <= 1.03e+102) {
		tmp = x;
	} else if (t <= 5.1e+127) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (t <= (-2.2d+69)) then
        tmp = y
    else if (t <= (-8.5d-23)) then
        tmp = t_1
    else if (t <= 7d-117) then
        tmp = x + (y / (a / z))
    else if (t <= 4.8d-69) then
        tmp = t_1
    else if (t <= 1.08d+39) then
        tmp = x + (y * (z / a))
    else if (t <= 2.7d+97) then
        tmp = y
    else if (t <= 1.03d+102) then
        tmp = x
    else if (t <= 5.1d+127) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -2.2e+69) {
		tmp = y;
	} else if (t <= -8.5e-23) {
		tmp = t_1;
	} else if (t <= 7e-117) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-69) {
		tmp = t_1;
	} else if (t <= 1.08e+39) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e+97) {
		tmp = y;
	} else if (t <= 1.03e+102) {
		tmp = x;
	} else if (t <= 5.1e+127) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if t <= -2.2e+69:
		tmp = y
	elif t <= -8.5e-23:
		tmp = t_1
	elif t <= 7e-117:
		tmp = x + (y / (a / z))
	elif t <= 4.8e-69:
		tmp = t_1
	elif t <= 1.08e+39:
		tmp = x + (y * (z / a))
	elif t <= 2.7e+97:
		tmp = y
	elif t <= 1.03e+102:
		tmp = x
	elif t <= 5.1e+127:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -2.2e+69)
		tmp = y;
	elseif (t <= -8.5e-23)
		tmp = t_1;
	elseif (t <= 7e-117)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.8e-69)
		tmp = t_1;
	elseif (t <= 1.08e+39)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.7e+97)
		tmp = y;
	elseif (t <= 1.03e+102)
		tmp = x;
	elseif (t <= 5.1e+127)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -2.2e+69)
		tmp = y;
	elseif (t <= -8.5e-23)
		tmp = t_1;
	elseif (t <= 7e-117)
		tmp = x + (y / (a / z));
	elseif (t <= 4.8e-69)
		tmp = t_1;
	elseif (t <= 1.08e+39)
		tmp = x + (y * (z / a));
	elseif (t <= 2.7e+97)
		tmp = y;
	elseif (t <= 1.03e+102)
		tmp = x;
	elseif (t <= 5.1e+127)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+69], y, If[LessEqual[t, -8.5e-23], t$95$1, If[LessEqual[t, 7e-117], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-69], t$95$1, If[LessEqual[t, 1.08e+39], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+97], y, If[LessEqual[t, 1.03e+102], x, If[LessEqual[t, 5.1e+127], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.2000000000000002e69 or 1.07999999999999998e39 < t < 2.69999999999999993e97 or 5.10000000000000038e127 < t

   1. Initial program 38.2%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   5. Taylor expanded in t around inf 57.5%

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

   if -2.2000000000000002e69 < t < -8.4999999999999996e-23 or 6.9999999999999997e-117 < t < 4.8000000000000002e-69

   1. Initial program 80.1%

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

      1. associate-*l/ 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in z around inf 60.0%

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

      1. div-sub 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   10. Simplified 56.8%

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

   if -8.4999999999999996e-23 < t < 6.9999999999999997e-117

   1. Initial program 92.8%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 74.2%

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

   6. Taylor expanded in y around inf 63.8%

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

      1. associate-/l* 66.4%

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

   8. Simplified 66.4%

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

   if 4.8000000000000002e-69 < t < 1.07999999999999998e39

   1. Initial program 80.1%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 47.9%

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

   6. Taylor expanded in y around inf 40.0%

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

      1. *-commutative 40.0%

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

   8. Simplified 40.0%

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

      1. div-inv 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*l* 51.9%

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

      4. div-inv 51.8%

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

   10. Applied egg-rr 51.8%

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

   if 2.69999999999999993e97 < t < 1.03e102

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if 1.03e102 < t < 5.10000000000000038e127

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+39}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.03 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a} + 1\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+69)
   y
   (if (<= t -5.8e-30)
     (* z (/ (- x y) t))
     (if (<= t 1.2e-115)
       (+ x (/ y (/ a z)))
       (if (<= t 1.85e-52)
         (* x (+ (/ (- t z) a) 1.0))
         (if (<= t 2.5e+39)
           (+ x (* y (/ z a)))
           (if (<= t 1.55e+99)
             y
             (if (<= t 1.55e+100)
               x
               (if (<= t 9.2e+125) (* x (/ (- z a) t)) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+69) {
		tmp = y;
	} else if (t <= -5.8e-30) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.2e-115) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.85e-52) {
		tmp = x * (((t - z) / a) + 1.0);
	} else if (t <= 2.5e+39) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 1.55e+100) {
		tmp = x;
	} else if (t <= 9.2e+125) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = 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 <= (-1.45d+69)) then
        tmp = y
    else if (t <= (-5.8d-30)) then
        tmp = z * ((x - y) / t)
    else if (t <= 1.2d-115) then
        tmp = x + (y / (a / z))
    else if (t <= 1.85d-52) then
        tmp = x * (((t - z) / a) + 1.0d0)
    else if (t <= 2.5d+39) then
        tmp = x + (y * (z / a))
    else if (t <= 1.55d+99) then
        tmp = y
    else if (t <= 1.55d+100) then
        tmp = x
    else if (t <= 9.2d+125) then
        tmp = x * ((z - a) / t)
    else
        tmp = 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 <= -1.45e+69) {
		tmp = y;
	} else if (t <= -5.8e-30) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.2e-115) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.85e-52) {
		tmp = x * (((t - z) / a) + 1.0);
	} else if (t <= 2.5e+39) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.55e+99) {
		tmp = y;
	} else if (t <= 1.55e+100) {
		tmp = x;
	} else if (t <= 9.2e+125) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+69:
		tmp = y
	elif t <= -5.8e-30:
		tmp = z * ((x - y) / t)
	elif t <= 1.2e-115:
		tmp = x + (y / (a / z))
	elif t <= 1.85e-52:
		tmp = x * (((t - z) / a) + 1.0)
	elif t <= 2.5e+39:
		tmp = x + (y * (z / a))
	elif t <= 1.55e+99:
		tmp = y
	elif t <= 1.55e+100:
		tmp = x
	elif t <= 9.2e+125:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+69)
		tmp = y;
	elseif (t <= -5.8e-30)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 1.2e-115)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.85e-52)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / a) + 1.0));
	elseif (t <= 2.5e+39)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 1.55e+100)
		tmp = x;
	elseif (t <= 9.2e+125)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+69)
		tmp = y;
	elseif (t <= -5.8e-30)
		tmp = z * ((x - y) / t);
	elseif (t <= 1.2e-115)
		tmp = x + (y / (a / z));
	elseif (t <= 1.85e-52)
		tmp = x * (((t - z) / a) + 1.0);
	elseif (t <= 2.5e+39)
		tmp = x + (y * (z / a));
	elseif (t <= 1.55e+99)
		tmp = y;
	elseif (t <= 1.55e+100)
		tmp = x;
	elseif (t <= 9.2e+125)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+69], y, If[LessEqual[t, -5.8e-30], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-115], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-52], N[(x * N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+39], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+99], y, If[LessEqual[t, 1.55e+100], x, If[LessEqual[t, 9.2e+125], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.4499999999999999e69 or 2.50000000000000008e39 < t < 1.55e99 or 9.20000000000000051e125 < t

   1. Initial program 38.2%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   5. Taylor expanded in t around inf 57.5%

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

   if -1.4499999999999999e69 < t < -5.79999999999999978e-30

   1. Initial program 74.6%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around inf 58.5%

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

      1. div-sub 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in a around 0 59.1%

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

      1. associate-*r/ 59.1%

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

      2. neg-mul-1 59.1%

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

   10. Simplified 59.1%

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

   if -5.79999999999999978e-30 < t < 1.20000000000000011e-115

   1. Initial program 92.8%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around 0 73.6%

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

   6. Taylor expanded in y around inf 63.2%

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

      1. associate-/l* 65.8%

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

   8. Simplified 65.8%

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

   if 1.20000000000000011e-115 < t < 1.8499999999999999e-52

   1. Initial program 85.4%

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

      1. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 43.8%

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

   7. Simplified 43.8%

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

   8. Taylor expanded in x around inf 45.2%

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

      1. mul-1-neg 45.2%

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

      2. unsub-neg 45.2%

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

   10. Simplified 45.2%

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

   if 1.8499999999999999e-52 < t < 2.50000000000000008e39

   1. Initial program 81.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

   8. Simplified 45.3%

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

      1. div-inv 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*l* 59.5%

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

      4. div-inv 59.4%

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

   10. Applied egg-rr 59.4%

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

   if 1.55e99 < t < 1.55000000000000003e100

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if 1.55000000000000003e100 < t < 9.20000000000000051e125

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a} + 1\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - y \cdot \frac{t - z}{a}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+100}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (- x (* y (/ (- t z) a))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -7.5e-10)
     t_2
     (if (<= a -2.5e-164)
       t_1
       (if (<= a -3.1e-193)
         t_3
         (if (<= a 2.6e-285)
           t_1
           (if (<= a 1.3e-210)
             t_3
             (if (<= a 1.25e-35) t_1 (if (<= a 1.4e+100) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (y * ((t - z) / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -7.5e-10) {
		tmp = t_2;
	} else if (a <= -2.5e-164) {
		tmp = t_1;
	} else if (a <= -3.1e-193) {
		tmp = t_3;
	} else if (a <= 2.6e-285) {
		tmp = t_1;
	} else if (a <= 1.3e-210) {
		tmp = t_3;
	} else if (a <= 1.25e-35) {
		tmp = t_1;
	} else if (a <= 1.4e+100) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - (y * ((t - z) / a))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-7.5d-10)) then
        tmp = t_2
    else if (a <= (-2.5d-164)) then
        tmp = t_1
    else if (a <= (-3.1d-193)) then
        tmp = t_3
    else if (a <= 2.6d-285) then
        tmp = t_1
    else if (a <= 1.3d-210) then
        tmp = t_3
    else if (a <= 1.25d-35) then
        tmp = t_1
    else if (a <= 1.4d+100) then
        tmp = t_3
    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 - t));
	double t_2 = x - (y * ((t - z) / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -7.5e-10) {
		tmp = t_2;
	} else if (a <= -2.5e-164) {
		tmp = t_1;
	} else if (a <= -3.1e-193) {
		tmp = t_3;
	} else if (a <= 2.6e-285) {
		tmp = t_1;
	} else if (a <= 1.3e-210) {
		tmp = t_3;
	} else if (a <= 1.25e-35) {
		tmp = t_1;
	} else if (a <= 1.4e+100) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (y * ((t - z) / a))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -7.5e-10:
		tmp = t_2
	elif a <= -2.5e-164:
		tmp = t_1
	elif a <= -3.1e-193:
		tmp = t_3
	elif a <= 2.6e-285:
		tmp = t_1
	elif a <= 1.3e-210:
		tmp = t_3
	elif a <= 1.25e-35:
		tmp = t_1
	elif a <= 1.4e+100:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(y * Float64(Float64(t - z) / a)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -7.5e-10)
		tmp = t_2;
	elseif (a <= -2.5e-164)
		tmp = t_1;
	elseif (a <= -3.1e-193)
		tmp = t_3;
	elseif (a <= 2.6e-285)
		tmp = t_1;
	elseif (a <= 1.3e-210)
		tmp = t_3;
	elseif (a <= 1.25e-35)
		tmp = t_1;
	elseif (a <= 1.4e+100)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (y * ((t - z) / a));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -7.5e-10)
		tmp = t_2;
	elseif (a <= -2.5e-164)
		tmp = t_1;
	elseif (a <= -3.1e-193)
		tmp = t_3;
	elseif (a <= 2.6e-285)
		tmp = t_1;
	elseif (a <= 1.3e-210)
		tmp = t_3;
	elseif (a <= 1.25e-35)
		tmp = t_1;
	elseif (a <= 1.4e+100)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e-10], t$95$2, If[LessEqual[a, -2.5e-164], t$95$1, If[LessEqual[a, -3.1e-193], t$95$3, If[LessEqual[a, 2.6e-285], t$95$1, If[LessEqual[a, 1.3e-210], t$95$3, If[LessEqual[a, 1.25e-35], t$95$1, If[LessEqual[a, 1.4e+100], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999995e-10 or 1.3999999999999999e100 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 63.3%

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

      1. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around inf 62.0%

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

      1. associate-*r/ 69.7%

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

   10. Simplified 69.7%

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

   if -7.49999999999999995e-10 < a < -2.49999999999999981e-164 or -3.1000000000000002e-193 < a < 2.6000000000000002e-285 or 1.2999999999999999e-210 < a < 1.24999999999999991e-35

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-*l/ 69.7%

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

      3. fma-def 69.6%

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

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 69.7%

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

      2. associate-/r/ 76.6%

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

      3. div-inv 76.5%

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

      4. clear-num 76.6%

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

   6. Applied egg-rr 76.6%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. div-sub 73.8%

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

   9. Simplified 73.8%

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

   if -2.49999999999999981e-164 < a < -3.1000000000000002e-193 or 2.6000000000000002e-285 < a < 1.2999999999999999e-210 or 1.24999999999999991e-35 < a < 1.3999999999999999e100

   1. Initial program 79.4%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. div-sub 80.7%

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

   7. Simplified 80.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.5e-11)
     y
     (if (<= t -2.3e-238)
       t_1
       (if (<= t -1.55e-298)
         (* z (/ y (- a t)))
         (if (<= t 2.7e+39)
           t_1
           (if (<= t 2.55e+97)
             y
             (if (<= t 7.5e+101)
               x
               (if (<= t 6.2e+126) (* x (/ (- z a) t)) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.5e-11) {
		tmp = y;
	} else if (t <= -2.3e-238) {
		tmp = t_1;
	} else if (t <= -1.55e-298) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.7e+39) {
		tmp = t_1;
	} else if (t <= 2.55e+97) {
		tmp = y;
	} else if (t <= 7.5e+101) {
		tmp = x;
	} else if (t <= 6.2e+126) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.5d-11)) then
        tmp = y
    else if (t <= (-2.3d-238)) then
        tmp = t_1
    else if (t <= (-1.55d-298)) then
        tmp = z * (y / (a - t))
    else if (t <= 2.7d+39) then
        tmp = t_1
    else if (t <= 2.55d+97) then
        tmp = y
    else if (t <= 7.5d+101) then
        tmp = x
    else if (t <= 6.2d+126) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.5e-11) {
		tmp = y;
	} else if (t <= -2.3e-238) {
		tmp = t_1;
	} else if (t <= -1.55e-298) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.7e+39) {
		tmp = t_1;
	} else if (t <= 2.55e+97) {
		tmp = y;
	} else if (t <= 7.5e+101) {
		tmp = x;
	} else if (t <= 6.2e+126) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.5e-11:
		tmp = y
	elif t <= -2.3e-238:
		tmp = t_1
	elif t <= -1.55e-298:
		tmp = z * (y / (a - t))
	elif t <= 2.7e+39:
		tmp = t_1
	elif t <= 2.55e+97:
		tmp = y
	elif t <= 7.5e+101:
		tmp = x
	elif t <= 6.2e+126:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.5e-11)
		tmp = y;
	elseif (t <= -2.3e-238)
		tmp = t_1;
	elseif (t <= -1.55e-298)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= 2.7e+39)
		tmp = t_1;
	elseif (t <= 2.55e+97)
		tmp = y;
	elseif (t <= 7.5e+101)
		tmp = x;
	elseif (t <= 6.2e+126)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.5e-11)
		tmp = y;
	elseif (t <= -2.3e-238)
		tmp = t_1;
	elseif (t <= -1.55e-298)
		tmp = z * (y / (a - t));
	elseif (t <= 2.7e+39)
		tmp = t_1;
	elseif (t <= 2.55e+97)
		tmp = y;
	elseif (t <= 7.5e+101)
		tmp = x;
	elseif (t <= 6.2e+126)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-11], y, If[LessEqual[t, -2.3e-238], t$95$1, If[LessEqual[t, -1.55e-298], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+39], t$95$1, If[LessEqual[t, 2.55e+97], y, If[LessEqual[t, 7.5e+101], x, If[LessEqual[t, 6.2e+126], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.5e-11 or 2.70000000000000003e39 < t < 2.55000000000000017e97 or 6.2e126 < t

   1. Initial program 44.3%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around inf 51.7%

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

   if -1.5e-11 < t < -2.30000000000000005e-238 or -1.5500000000000001e-298 < t < 2.70000000000000003e39

   1. Initial program 89.8%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around 0 64.3%

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

   6. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   8. Simplified 53.0%

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

   if -2.30000000000000005e-238 < t < -1.5500000000000001e-298

   1. Initial program 99.9%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around inf 67.7%

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

      1. div-sub 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in y around inf 67.8%

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

   if 2.55000000000000017e97 < t < 7.4999999999999995e101

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if 7.4999999999999995e101 < t < 6.2e126

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -4.5e-11)
     y
     (if (<= t -1.75e-223)
       t_1
       (if (<= t 3.4e-276)
         (* z (/ (- y x) a))
         (if (<= t 2.55e+39)
           t_1
           (if (<= t 1.35e+97)
             y
             (if (<= t 3.4e+103)
               x
               (if (<= t 6e+129) (* x (/ (- z a) t)) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -4.5e-11) {
		tmp = y;
	} else if (t <= -1.75e-223) {
		tmp = t_1;
	} else if (t <= 3.4e-276) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.55e+39) {
		tmp = t_1;
	} else if (t <= 1.35e+97) {
		tmp = y;
	} else if (t <= 3.4e+103) {
		tmp = x;
	} else if (t <= 6e+129) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-4.5d-11)) then
        tmp = y
    else if (t <= (-1.75d-223)) then
        tmp = t_1
    else if (t <= 3.4d-276) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.55d+39) then
        tmp = t_1
    else if (t <= 1.35d+97) then
        tmp = y
    else if (t <= 3.4d+103) then
        tmp = x
    else if (t <= 6d+129) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -4.5e-11) {
		tmp = y;
	} else if (t <= -1.75e-223) {
		tmp = t_1;
	} else if (t <= 3.4e-276) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.55e+39) {
		tmp = t_1;
	} else if (t <= 1.35e+97) {
		tmp = y;
	} else if (t <= 3.4e+103) {
		tmp = x;
	} else if (t <= 6e+129) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -4.5e-11:
		tmp = y
	elif t <= -1.75e-223:
		tmp = t_1
	elif t <= 3.4e-276:
		tmp = z * ((y - x) / a)
	elif t <= 2.55e+39:
		tmp = t_1
	elif t <= 1.35e+97:
		tmp = y
	elif t <= 3.4e+103:
		tmp = x
	elif t <= 6e+129:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -4.5e-11)
		tmp = y;
	elseif (t <= -1.75e-223)
		tmp = t_1;
	elseif (t <= 3.4e-276)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.55e+39)
		tmp = t_1;
	elseif (t <= 1.35e+97)
		tmp = y;
	elseif (t <= 3.4e+103)
		tmp = x;
	elseif (t <= 6e+129)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -4.5e-11)
		tmp = y;
	elseif (t <= -1.75e-223)
		tmp = t_1;
	elseif (t <= 3.4e-276)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.55e+39)
		tmp = t_1;
	elseif (t <= 1.35e+97)
		tmp = y;
	elseif (t <= 3.4e+103)
		tmp = x;
	elseif (t <= 6e+129)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e-11], y, If[LessEqual[t, -1.75e-223], t$95$1, If[LessEqual[t, 3.4e-276], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e+39], t$95$1, If[LessEqual[t, 1.35e+97], y, If[LessEqual[t, 3.4e+103], x, If[LessEqual[t, 6e+129], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.5e-11 or 2.5499999999999999e39 < t < 1.34999999999999997e97 or 6.0000000000000006e129 < t

   1. Initial program 44.3%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around inf 51.7%

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

   if -4.5e-11 < t < -1.75000000000000005e-223 or 3.39999999999999992e-276 < t < 2.5499999999999999e39

   1. Initial program 88.8%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 61.6%

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

   6. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   8. Simplified 53.4%

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

   if -1.75000000000000005e-223 < t < 3.39999999999999992e-276

   1. Initial program 99.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 63.6%

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

      1. div-sub 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in a around inf 68.0%

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

   if 1.34999999999999997e97 < t < 3.3999999999999998e103

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if 3.3999999999999998e103 < t < 6.0000000000000006e129

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+104} \lor \neg \left(t \leq 9 \cdot 10^{+125}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.8e-18)
     t_2
     (if (<= t 1.3e-137)
       t_1
       (if (<= t 1.7e-54)
         (* (- z t) (/ y (- a t)))
         (if (<= t 3.9e+38)
           t_1
           (if (or (<= t 1.1e+104) (not (<= t 9e+125)))
             t_2
             (* x (/ (- z a) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.8e-18) {
		tmp = t_2;
	} else if (t <= 1.3e-137) {
		tmp = t_1;
	} else if (t <= 1.7e-54) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 3.9e+38) {
		tmp = t_1;
	} else if ((t <= 1.1e+104) || !(t <= 9e+125)) {
		tmp = t_2;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-2.8d-18)) then
        tmp = t_2
    else if (t <= 1.3d-137) then
        tmp = t_1
    else if (t <= 1.7d-54) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 3.9d+38) then
        tmp = t_1
    else if ((t <= 1.1d+104) .or. (.not. (t <= 9d+125))) then
        tmp = t_2
    else
        tmp = x * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.8e-18) {
		tmp = t_2;
	} else if (t <= 1.3e-137) {
		tmp = t_1;
	} else if (t <= 1.7e-54) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 3.9e+38) {
		tmp = t_1;
	} else if ((t <= 1.1e+104) || !(t <= 9e+125)) {
		tmp = t_2;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.8e-18:
		tmp = t_2
	elif t <= 1.3e-137:
		tmp = t_1
	elif t <= 1.7e-54:
		tmp = (z - t) * (y / (a - t))
	elif t <= 3.9e+38:
		tmp = t_1
	elif (t <= 1.1e+104) or not (t <= 9e+125):
		tmp = t_2
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.8e-18)
		tmp = t_2;
	elseif (t <= 1.3e-137)
		tmp = t_1;
	elseif (t <= 1.7e-54)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 3.9e+38)
		tmp = t_1;
	elseif ((t <= 1.1e+104) || !(t <= 9e+125))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.8e-18)
		tmp = t_2;
	elseif (t <= 1.3e-137)
		tmp = t_1;
	elseif (t <= 1.7e-54)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 3.9e+38)
		tmp = t_1;
	elseif ((t <= 1.1e+104) || ~((t <= 9e+125)))
		tmp = t_2;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-18], t$95$2, If[LessEqual[t, 1.3e-137], t$95$1, If[LessEqual[t, 1.7e-54], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+38], t$95$1, If[Or[LessEqual[t, 1.1e+104], N[Not[LessEqual[t, 9e+125]], $MachinePrecision]], t$95$2, N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000012e-18 or 3.90000000000000023e38 < t < 1.1e104 or 9.0000000000000001e125 < t

   1. Initial program 44.8%

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

      1. +-commutative 44.8%

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

      2. associate-*l/ 67.6%

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

      3. fma-def 67.5%

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

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 67.6%

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

      2. associate-/r/ 70.9%

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

      3. div-inv 70.9%

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

      4. clear-num 70.9%

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

   6. Applied egg-rr 70.9%

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

   7. Taylor expanded in y around inf 67.3%

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

      1. div-sub 67.3%

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

   9. Simplified 67.3%

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

   if -2.80000000000000012e-18 < t < 1.3e-137 or 1.69999999999999994e-54 < t < 3.90000000000000023e38

   1. Initial program 90.8%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if 1.3e-137 < t < 1.69999999999999994e-54

   1. Initial program 89.3%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 65.9%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 67.5%

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

   7. Simplified 67.5%

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

   if 1.1e104 < t < 9.0000000000000001e125

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+104} \lor \neg \left(t \leq 9 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -2.22 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+84} \lor \neg \left(y \leq 1.95 \cdot 10^{+95}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -2.22e-131)
     t_1
     (if (<= y -5.5e-238)
       (* z (/ (- x y) t))
       (if (<= y 6e-52)
         (* x (- 1.0 (/ z a)))
         (if (or (<= y 3e+84) (not (<= y 1.95e+95)))
           t_1
           (* x (+ (/ t a) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -2.22e-131) {
		tmp = t_1;
	} else if (y <= -5.5e-238) {
		tmp = z * ((x - y) / t);
	} else if (y <= 6e-52) {
		tmp = x * (1.0 - (z / a));
	} else if ((y <= 3e+84) || !(y <= 1.95e+95)) {
		tmp = t_1;
	} else {
		tmp = x * ((t / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-2.22d-131)) then
        tmp = t_1
    else if (y <= (-5.5d-238)) then
        tmp = z * ((x - y) / t)
    else if (y <= 6d-52) then
        tmp = x * (1.0d0 - (z / a))
    else if ((y <= 3d+84) .or. (.not. (y <= 1.95d+95))) then
        tmp = t_1
    else
        tmp = x * ((t / a) + 1.0d0)
    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 - t));
	double tmp;
	if (y <= -2.22e-131) {
		tmp = t_1;
	} else if (y <= -5.5e-238) {
		tmp = z * ((x - y) / t);
	} else if (y <= 6e-52) {
		tmp = x * (1.0 - (z / a));
	} else if ((y <= 3e+84) || !(y <= 1.95e+95)) {
		tmp = t_1;
	} else {
		tmp = x * ((t / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -2.22e-131:
		tmp = t_1
	elif y <= -5.5e-238:
		tmp = z * ((x - y) / t)
	elif y <= 6e-52:
		tmp = x * (1.0 - (z / a))
	elif (y <= 3e+84) or not (y <= 1.95e+95):
		tmp = t_1
	else:
		tmp = x * ((t / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -2.22e-131)
		tmp = t_1;
	elseif (y <= -5.5e-238)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (y <= 6e-52)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((y <= 3e+84) || !(y <= 1.95e+95))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(t / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -2.22e-131)
		tmp = t_1;
	elseif (y <= -5.5e-238)
		tmp = z * ((x - y) / t);
	elseif (y <= 6e-52)
		tmp = x * (1.0 - (z / a));
	elseif ((y <= 3e+84) || ~((y <= 1.95e+95)))
		tmp = t_1;
	else
		tmp = x * ((t / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.22e-131], t$95$1, If[LessEqual[y, -5.5e-238], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-52], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3e+84], N[Not[LessEqual[y, 1.95e+95]], $MachinePrecision]], t$95$1, N[(x * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2200000000000001e-131 or 6e-52 < y < 2.99999999999999996e84 or 1.9499999999999999e95 < y

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-*l/ 85.5%

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

      3. fma-def 85.5%

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

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 85.5%

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

      2. associate-/r/ 90.5%

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

      3. div-inv 90.5%

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

      4. clear-num 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in y around inf 71.8%

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

      1. div-sub 71.7%

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

   9. Simplified 71.7%

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

   if -2.2200000000000001e-131 < y < -5.49999999999999995e-238

   1. Initial program 71.2%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in z around inf 68.1%

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

      1. div-sub 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in a around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. neg-mul-1 62.8%

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

   10. Simplified 62.8%

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

   if -5.49999999999999995e-238 < y < 6e-52

   1. Initial program 63.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in t around 0 55.7%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   8. Simplified 56.0%

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

   if 2.99999999999999996e84 < y < 1.9499999999999999e95

   1. Initial program 84.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in z around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

      3. associate-/l* 88.1%

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

   10. Simplified 88.1%

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

   11. Taylor expanded in x around inf 88.1%

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

       1. sub-neg 88.1%

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

       2. mul-1-neg 88.1%

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

       3. remove-double-neg 88.1%

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

       4. +-commutative 88.1%

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

   13. Simplified 88.1%

       \[\leadsto \color{blue}{x \cdot \left(\frac{t}{a} + 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.22 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+84} \lor \neg \left(y \leq 1.95 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -6.4e+47)
     t_2
     (if (<= t -4e-198)
       t_1
       (if (<= t 9e-116)
         (+ x (/ (* (- y x) (- z t)) (- a t)))
         (if (<= t 9.8e+103) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -6.4e+47) {
		tmp = t_2;
	} else if (t <= -4e-198) {
		tmp = t_1;
	} else if (t <= 9e-116) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 9.8e+103) {
		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 + ((z - t) * ((y - x) / (a - t)))
    t_2 = y + ((x - y) / (t / (z - a)))
    if (t <= (-6.4d+47)) then
        tmp = t_2
    else if (t <= (-4d-198)) then
        tmp = t_1
    else if (t <= 9d-116) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else if (t <= 9.8d+103) 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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -6.4e+47) {
		tmp = t_2;
	} else if (t <= -4e-198) {
		tmp = t_1;
	} else if (t <= 9e-116) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 9.8e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -6.4e+47:
		tmp = t_2
	elif t <= -4e-198:
		tmp = t_1
	elif t <= 9e-116:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	elif t <= 9.8e+103:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -6.4e+47)
		tmp = t_2;
	elseif (t <= -4e-198)
		tmp = t_1;
	elseif (t <= 9e-116)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	elseif (t <= 9.8e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -6.4e+47)
		tmp = t_2;
	elseif (t <= -4e-198)
		tmp = t_1;
	elseif (t <= 9e-116)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	elseif (t <= 9.8e+103)
		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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+47], t$95$2, If[LessEqual[t, -4e-198], t$95$1, If[LessEqual[t, 9e-116], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+103], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4e47 or 9.7999999999999997e103 < t

   1. Initial program 32.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. associate-*r/ 66.9%

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

      3. associate-*r/ 66.9%

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

      4. div-sub 66.9%

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

      5. distribute-lft-out-- 66.9%

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

      6. associate-*r/ 66.9%

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

      7. mul-1-neg 66.9%

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

      8. unsub-neg 66.9%

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

      9. distribute-rgt-out-- 67.1%

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

      10. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

   if -6.4e47 < t < -3.9999999999999996e-198 or 9.00000000000000023e-116 < t < 9.7999999999999997e103

   1. Initial program 81.2%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   if -3.9999999999999996e-198 < t < 9.00000000000000023e-116

   1. Initial program 98.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-198}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+103}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+102}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -7.5e+45)
     t_1
     (if (<= t -3.9e-209)
       (+ x (/ (- z t) (/ (- a t) (- y x))))
       (if (<= t 6e-116)
         (+ x (/ (* (- y x) (- z t)) (- a t)))
         (if (<= t 1.75e+102) (+ x (* (- z t) (/ (- y x) (- a t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -7.5e+45) {
		tmp = t_1;
	} else if (t <= -3.9e-209) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else if (t <= 6e-116) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.75e+102) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / (z - a)))
    if (t <= (-7.5d+45)) then
        tmp = t_1
    else if (t <= (-3.9d-209)) then
        tmp = x + ((z - t) / ((a - t) / (y - x)))
    else if (t <= 6d-116) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else if (t <= 1.75d+102) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -7.5e+45) {
		tmp = t_1;
	} else if (t <= -3.9e-209) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else if (t <= 6e-116) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.75e+102) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -7.5e+45:
		tmp = t_1
	elif t <= -3.9e-209:
		tmp = x + ((z - t) / ((a - t) / (y - x)))
	elif t <= 6e-116:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	elif t <= 1.75e+102:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -7.5e+45)
		tmp = t_1;
	elseif (t <= -3.9e-209)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(y - x))));
	elseif (t <= 6e-116)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	elseif (t <= 1.75e+102)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -7.5e+45)
		tmp = t_1;
	elseif (t <= -3.9e-209)
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	elseif (t <= 6e-116)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	elseif (t <= 1.75e+102)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+45], t$95$1, If[LessEqual[t, -3.9e-209], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-116], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+102], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.50000000000000058e45 or 1.75000000000000005e102 < t

   1. Initial program 32.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. associate-*r/ 66.9%

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

      3. associate-*r/ 66.9%

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

      4. div-sub 66.9%

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

      5. distribute-lft-out-- 66.9%

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

      6. associate-*r/ 66.9%

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

      7. mul-1-neg 66.9%

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

      8. unsub-neg 66.9%

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

      9. distribute-rgt-out-- 67.1%

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

      10. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

   if -7.50000000000000058e45 < t < -3.9e-209

   1. Initial program 84.5%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. clear-num 93.3%

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

      3. un-div-inv 94.8%

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

   6. Applied egg-rr 94.8%

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

   if -3.9e-209 < t < 6.00000000000000053e-116

   1. Initial program 98.1%

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

   if 6.00000000000000053e-116 < t < 1.75000000000000005e102

   1. Initial program 77.3%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+102}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e-16)
   y
   (if (<= t 1.08e+39)
     (* x (- 1.0 (/ z a)))
     (if (<= t 1.5e+99)
       y
       (if (<= t 5.6e+100) x (if (<= t 2.8e+129) (* x (/ (- z a) t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e-16) {
		tmp = y;
	} else if (t <= 1.08e+39) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.5e+99) {
		tmp = y;
	} else if (t <= 5.6e+100) {
		tmp = x;
	} else if (t <= 2.8e+129) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = 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 <= (-3d-16)) then
        tmp = y
    else if (t <= 1.08d+39) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.5d+99) then
        tmp = y
    else if (t <= 5.6d+100) then
        tmp = x
    else if (t <= 2.8d+129) then
        tmp = x * ((z - a) / t)
    else
        tmp = 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 <= -3e-16) {
		tmp = y;
	} else if (t <= 1.08e+39) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.5e+99) {
		tmp = y;
	} else if (t <= 5.6e+100) {
		tmp = x;
	} else if (t <= 2.8e+129) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e-16:
		tmp = y
	elif t <= 1.08e+39:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.5e+99:
		tmp = y
	elif t <= 5.6e+100:
		tmp = x
	elif t <= 2.8e+129:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e-16)
		tmp = y;
	elseif (t <= 1.08e+39)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.5e+99)
		tmp = y;
	elseif (t <= 5.6e+100)
		tmp = x;
	elseif (t <= 2.8e+129)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e-16)
		tmp = y;
	elseif (t <= 1.08e+39)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.5e+99)
		tmp = y;
	elseif (t <= 5.6e+100)
		tmp = x;
	elseif (t <= 2.8e+129)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e-16], y, If[LessEqual[t, 1.08e+39], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+99], y, If[LessEqual[t, 5.6e+100], x, If[LessEqual[t, 2.8e+129], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.99999999999999994e-16 or 1.07999999999999998e39 < t < 1.50000000000000007e99 or 2.79999999999999975e129 < t

   1. Initial program 44.3%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around inf 51.7%

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

   if -2.99999999999999994e-16 < t < 1.07999999999999998e39

   1. Initial program 90.6%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around 0 67.2%

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

   6. Taylor expanded in x around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. unsub-neg 50.9%

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

   8. Simplified 50.9%

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

   if 1.50000000000000007e99 < t < 5.5999999999999996e100

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if 5.5999999999999996e100 < t < 2.79999999999999975e129

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. associate-*l/ 41.9%

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

      3. fma-def 42.9%

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

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 41.9%

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

      2. associate-/r/ 41.6%

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

      3. div-inv 41.9%

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

      4. clear-num 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in y around 0 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

      3. associate-/l* 41.6%

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

   9. Simplified 41.6%

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

   10. Taylor expanded in t around inf 62.8%

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

       1. distribute-lft-out-- 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. distribute-lft-out-- 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in x around inf 62.8%

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

       1. associate-*r/ 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-294}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e-13)
   x
   (if (<= a 7.8e-294)
     y
     (if (<= a 2.55e-216)
       (/ (* x z) t)
       (if (<= a 1.42e-52) y (if (<= a 2.8e+80) (/ (- x) (/ a z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-13) {
		tmp = x;
	} else if (a <= 7.8e-294) {
		tmp = y;
	} else if (a <= 2.55e-216) {
		tmp = (x * z) / t;
	} else if (a <= 1.42e-52) {
		tmp = y;
	} else if (a <= 2.8e+80) {
		tmp = -x / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8d-13)) then
        tmp = x
    else if (a <= 7.8d-294) then
        tmp = y
    else if (a <= 2.55d-216) then
        tmp = (x * z) / t
    else if (a <= 1.42d-52) then
        tmp = y
    else if (a <= 2.8d+80) then
        tmp = -x / (a / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-13) {
		tmp = x;
	} else if (a <= 7.8e-294) {
		tmp = y;
	} else if (a <= 2.55e-216) {
		tmp = (x * z) / t;
	} else if (a <= 1.42e-52) {
		tmp = y;
	} else if (a <= 2.8e+80) {
		tmp = -x / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e-13:
		tmp = x
	elif a <= 7.8e-294:
		tmp = y
	elif a <= 2.55e-216:
		tmp = (x * z) / t
	elif a <= 1.42e-52:
		tmp = y
	elif a <= 2.8e+80:
		tmp = -x / (a / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e-13)
		tmp = x;
	elseif (a <= 7.8e-294)
		tmp = y;
	elseif (a <= 2.55e-216)
		tmp = Float64(Float64(x * z) / t);
	elseif (a <= 1.42e-52)
		tmp = y;
	elseif (a <= 2.8e+80)
		tmp = Float64(Float64(-x) / Float64(a / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e-13)
		tmp = x;
	elseif (a <= 7.8e-294)
		tmp = y;
	elseif (a <= 2.55e-216)
		tmp = (x * z) / t;
	elseif (a <= 1.42e-52)
		tmp = y;
	elseif (a <= 2.8e+80)
		tmp = -x / (a / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e-13], x, If[LessEqual[a, 7.8e-294], y, If[LessEqual[a, 2.55e-216], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.42e-52], y, If[LessEqual[a, 2.8e+80], N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.0000000000000002e-13 or 2.79999999999999984e80 < a

   1. Initial program 71.2%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in a around inf 44.0%

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

   if -8.0000000000000002e-13 < a < 7.8000000000000005e-294 or 2.5500000000000001e-216 < a < 1.4200000000000001e-52

   1. Initial program 64.6%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 42.0%

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

   if 7.8000000000000005e-294 < a < 2.5500000000000001e-216

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-*l/ 88.7%

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

      3. fma-def 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 88.7%

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

      2. associate-/r/ 88.6%

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

      3. div-inv 88.7%

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

      4. clear-num 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. unsub-neg 44.4%

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

      3. associate-/l* 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in t around inf 44.6%

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

       1. distribute-lft-out-- 44.6%

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

       2. mul-1-neg 44.6%

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

       3. *-commutative 44.6%

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

       4. distribute-lft-out-- 44.6%

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

   12. Simplified 44.6%

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

   13. Taylor expanded in a around 0 44.6%

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

   if 1.4200000000000001e-52 < a < 2.79999999999999984e80

   1. Initial program 78.1%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 59.6%

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

   6. Taylor expanded in x around inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in z around inf 40.9%

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

       1. neg-mul-1 40.9%

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

       2. associate-*r/ 40.8%

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

       3. *-commutative 40.8%

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

       4. distribute-rgt-neg-in 40.8%

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

   11. Simplified 40.8%

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

       1. *-commutative 40.8%

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

       2. distribute-lft-neg-out 40.8%

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

       3. add-sqr-sqrt 31.6%

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

       4. sqrt-unprod 33.4%

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

       5. sqr-neg 33.4%

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

       6. sqrt-unprod 1.7%

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

       7. add-sqr-sqrt 2.3%

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

       8. clear-num 2.3%

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

       9. un-div-inv 2.3%

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

       10. add-sqr-sqrt 1.7%

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

       11. sqrt-unprod 33.4%

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

       12. sqr-neg 33.4%

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

       13. sqrt-unprod 31.7%

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

       14. add-sqr-sqrt 40.8%

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

   13. Applied egg-rr 40.8%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-294}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-293}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+80}:\\ \;\;\;\;\frac{x \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e-10)
   x
   (if (<= a 9.2e-293)
     y
     (if (<= a 2.7e-216)
       (/ (* x z) t)
       (if (<= a 1.12e-58) y (if (<= a 2.25e+80) (/ (* x z) (- a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-10) {
		tmp = x;
	} else if (a <= 9.2e-293) {
		tmp = y;
	} else if (a <= 2.7e-216) {
		tmp = (x * z) / t;
	} else if (a <= 1.12e-58) {
		tmp = y;
	} else if (a <= 2.25e+80) {
		tmp = (x * z) / -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d-10)) then
        tmp = x
    else if (a <= 9.2d-293) then
        tmp = y
    else if (a <= 2.7d-216) then
        tmp = (x * z) / t
    else if (a <= 1.12d-58) then
        tmp = y
    else if (a <= 2.25d+80) then
        tmp = (x * z) / -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-10) {
		tmp = x;
	} else if (a <= 9.2e-293) {
		tmp = y;
	} else if (a <= 2.7e-216) {
		tmp = (x * z) / t;
	} else if (a <= 1.12e-58) {
		tmp = y;
	} else if (a <= 2.25e+80) {
		tmp = (x * z) / -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e-10:
		tmp = x
	elif a <= 9.2e-293:
		tmp = y
	elif a <= 2.7e-216:
		tmp = (x * z) / t
	elif a <= 1.12e-58:
		tmp = y
	elif a <= 2.25e+80:
		tmp = (x * z) / -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e-10)
		tmp = x;
	elseif (a <= 9.2e-293)
		tmp = y;
	elseif (a <= 2.7e-216)
		tmp = Float64(Float64(x * z) / t);
	elseif (a <= 1.12e-58)
		tmp = y;
	elseif (a <= 2.25e+80)
		tmp = Float64(Float64(x * z) / Float64(-a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e-10)
		tmp = x;
	elseif (a <= 9.2e-293)
		tmp = y;
	elseif (a <= 2.7e-216)
		tmp = (x * z) / t;
	elseif (a <= 1.12e-58)
		tmp = y;
	elseif (a <= 2.25e+80)
		tmp = (x * z) / -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e-10], x, If[LessEqual[a, 9.2e-293], y, If[LessEqual[a, 2.7e-216], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.12e-58], y, If[LessEqual[a, 2.25e+80], N[(N[(x * z), $MachinePrecision] / (-a)), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5e-10 or 2.25000000000000003e80 < a

   1. Initial program 71.2%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in a around inf 44.0%

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

   if -1.5e-10 < a < 9.1999999999999998e-293 or 2.6999999999999999e-216 < a < 1.11999999999999992e-58

   1. Initial program 64.6%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 42.0%

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

   if 9.1999999999999998e-293 < a < 2.6999999999999999e-216

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-*l/ 88.7%

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

      3. fma-def 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 88.7%

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

      2. associate-/r/ 88.6%

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

      3. div-inv 88.7%

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

      4. clear-num 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. unsub-neg 44.4%

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

      3. associate-/l* 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in t around inf 44.6%

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

       1. distribute-lft-out-- 44.6%

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

       2. mul-1-neg 44.6%

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

       3. *-commutative 44.6%

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

       4. distribute-lft-out-- 44.6%

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

   12. Simplified 44.6%

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

   13. Taylor expanded in a around 0 44.6%

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

   if 1.11999999999999992e-58 < a < 2.25000000000000003e80

   1. Initial program 78.1%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 59.6%

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

   6. Taylor expanded in x around inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in z around inf 40.9%

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

       1. neg-mul-1 40.9%

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

       2. associate-*r/ 40.8%

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

       3. *-commutative 40.8%

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

       4. distribute-rgt-neg-in 40.8%

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

   11. Simplified 40.8%

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

       1. associate-*l/ 40.9%

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

       2. frac-2neg 40.9%

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

       3. add-sqr-sqrt 9.1%

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

       4. sqrt-unprod 9.6%

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

       5. sqr-neg 9.6%

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

       6. sqrt-unprod 0.5%

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

       7. add-sqr-sqrt 2.3%

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

       8. distribute-rgt-neg-out 2.3%

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

       9. add-sqr-sqrt 1.7%

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

       10. sqrt-unprod 33.5%

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

       11. sqr-neg 33.5%

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

       12. sqrt-unprod 31.7%

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

       13. add-sqr-sqrt 40.9%

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

   13. Applied egg-rr 40.9%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-293}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+80}:\\ \;\;\;\;\frac{x \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -1.4e-57)
     t_1
     (if (<= t 1.3e-137)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 3.8e-41)
         (* (- z t) (/ y (- a t)))
         (if (<= t 3.9e+38) (* x (+ (/ (- t z) (- a t)) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.4e-57) {
		tmp = t_1;
	} else if (t <= 1.3e-137) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3.8e-41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 3.9e+38) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (z / (t / (y - x)))
    if (t <= (-1.4d-57)) then
        tmp = t_1
    else if (t <= 1.3d-137) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 3.8d-41) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 3.9d+38) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.4e-57) {
		tmp = t_1;
	} else if (t <= 1.3e-137) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3.8e-41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 3.9e+38) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (t / (y - x)))
	tmp = 0
	if t <= -1.4e-57:
		tmp = t_1
	elif t <= 1.3e-137:
		tmp = x + (z / (a / (y - x)))
	elif t <= 3.8e-41:
		tmp = (z - t) * (y / (a - t))
	elif t <= 3.9e+38:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -1.4e-57)
		tmp = t_1;
	elseif (t <= 1.3e-137)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 3.8e-41)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 3.9e+38)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -1.4e-57)
		tmp = t_1;
	elseif (t <= 1.3e-137)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 3.8e-41)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 3.9e+38)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-57], t$95$1, If[LessEqual[t, 1.3e-137], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-41], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+38], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4e-57 or 3.90000000000000023e38 < t

   1. Initial program 45.1%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. associate--l+ 67.8%

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

      2. associate-*r/ 67.8%

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

      3. associate-*r/ 67.8%

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

      4. div-sub 67.8%

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

      5. distribute-lft-out-- 67.8%

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

      6. associate-*r/ 67.8%

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

      7. mul-1-neg 67.8%

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

      8. unsub-neg 67.8%

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

      9. distribute-rgt-out-- 68.0%

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

      10. associate-/l* 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in z around inf 64.0%

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

      1. associate-/l* 75.4%

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

   10. Simplified 75.4%

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

   if -1.4e-57 < t < 1.3e-137

   1. Initial program 93.1%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. associate-/l* 80.8%

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

   7. Simplified 80.8%

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

   if 1.3e-137 < t < 3.79999999999999979e-41

   1. Initial program 87.6%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 65.1%

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

      1. associate-/l* 69.9%

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

      2. associate-/r/ 70.0%

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

   7. Simplified 70.0%

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

   if 3.79999999999999979e-41 < t < 3.90000000000000023e38

   1. Initial program 82.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   7. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ t_2 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))) (t_2 (- y (/ z (/ t (- y x))))))
   (if (<= t -7.8e-53)
     t_2
     (if (<= t 3.5e-111)
       t_1
       (if (<= t 4.2e-69)
         (* (- z t) (/ y (- a t)))
         (if (<= t 2.3e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double t_2 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -7.8e-53) {
		tmp = t_2;
	} else if (t <= 3.5e-111) {
		tmp = t_1;
	} else if (t <= 4.2e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.3e+38) {
		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 - x) / (a / (z - t)))
    t_2 = y - (z / (t / (y - x)))
    if (t <= (-7.8d-53)) then
        tmp = t_2
    else if (t <= 3.5d-111) then
        tmp = t_1
    else if (t <= 4.2d-69) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 2.3d+38) 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 - x) / (a / (z - t)));
	double t_2 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -7.8e-53) {
		tmp = t_2;
	} else if (t <= 3.5e-111) {
		tmp = t_1;
	} else if (t <= 4.2e-69) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.3e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	t_2 = y - (z / (t / (y - x)))
	tmp = 0
	if t <= -7.8e-53:
		tmp = t_2
	elif t <= 3.5e-111:
		tmp = t_1
	elif t <= 4.2e-69:
		tmp = (z - t) * (y / (a - t))
	elif t <= 2.3e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	t_2 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -7.8e-53)
		tmp = t_2;
	elseif (t <= 3.5e-111)
		tmp = t_1;
	elseif (t <= 4.2e-69)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 2.3e+38)
		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 - x) / (a / (z - t)));
	t_2 = y - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -7.8e-53)
		tmp = t_2;
	elseif (t <= 3.5e-111)
		tmp = t_1;
	elseif (t <= 4.2e-69)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 2.3e+38)
		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 - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e-53], t$95$2, If[LessEqual[t, 3.5e-111], t$95$1, If[LessEqual[t, 4.2e-69], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8000000000000004e-53 or 2.3000000000000001e38 < t

   1. Initial program 44.1%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r/ 68.2%

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

      3. associate-*r/ 68.2%

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

      4. div-sub 68.2%

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

      5. distribute-lft-out-- 68.2%

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

      6. associate-*r/ 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. distribute-rgt-out-- 68.3%

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

      10. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around inf 64.2%

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

      1. associate-/l* 75.8%

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

   10. Simplified 75.8%

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

   if -7.8000000000000004e-53 < t < 3.5e-111 or 4.1999999999999999e-69 < t < 2.3000000000000001e38

   1. Initial program 91.2%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if 3.5e-111 < t < 4.1999999999999999e-69

   1. Initial program 86.8%

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

      1. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around 0 72.5%

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

      1. associate-/l* 72.1%

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

      2. associate-/r/ 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-53}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-69}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \frac{-x}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -8e+155)
     t_1
     (if (<= z -4.5e+126)
       (* x (- 1.0 (/ z a)))
       (if (<= z -4.5e+111)
         (* z (/ (- x) (- a t)))
         (if (<= z 7e+79) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8e+155) {
		tmp = t_1;
	} else if (z <= -4.5e+126) {
		tmp = x * (1.0 - (z / a));
	} else if (z <= -4.5e+111) {
		tmp = z * (-x / (a - t));
	} else if (z <= 7e+79) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (z <= (-8d+155)) then
        tmp = t_1
    else if (z <= (-4.5d+126)) then
        tmp = x * (1.0d0 - (z / a))
    else if (z <= (-4.5d+111)) then
        tmp = z * (-x / (a - t))
    else if (z <= 7d+79) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8e+155) {
		tmp = t_1;
	} else if (z <= -4.5e+126) {
		tmp = x * (1.0 - (z / a));
	} else if (z <= -4.5e+111) {
		tmp = z * (-x / (a - t));
	} else if (z <= 7e+79) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -8e+155:
		tmp = t_1
	elif z <= -4.5e+126:
		tmp = x * (1.0 - (z / a))
	elif z <= -4.5e+111:
		tmp = z * (-x / (a - t))
	elif z <= 7e+79:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -8e+155)
		tmp = t_1;
	elseif (z <= -4.5e+126)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (z <= -4.5e+111)
		tmp = Float64(z * Float64(Float64(-x) / Float64(a - t)));
	elseif (z <= 7e+79)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -8e+155)
		tmp = t_1;
	elseif (z <= -4.5e+126)
		tmp = x * (1.0 - (z / a));
	elseif (z <= -4.5e+111)
		tmp = z * (-x / (a - t));
	elseif (z <= 7e+79)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+155], t$95$1, If[LessEqual[z, -4.5e+126], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+111], N[(z * N[((-x) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+79], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.00000000000000006e155 or 6.99999999999999961e79 < z

   1. Initial program 73.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. div-sub 79.6%

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

   7. Simplified 79.6%

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

   if -8.00000000000000006e155 < z < -4.49999999999999974e126

   1. Initial program 83.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 83.9%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in x around inf 92.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 92.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 92.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   8. Simplified 92.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -4.49999999999999974e126 < z < -4.50000000000000001e111

   1. Initial program 34.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 34.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   8. Taylor expanded in y around 0 100.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \frac{x}{a - t}\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 100.0%

         \[\leadsto z \cdot \color{blue}{\left(-\frac{x}{a - t}\right)} \]

      2. distribute-neg-frac 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{-x}{a - t}} \]

   10. Simplified 100.0%

       \[\leadsto z \cdot \color{blue}{\frac{-x}{a - t}} \]

   if -4.50000000000000001e111 < z < 6.99999999999999961e79

   1. Initial program 68.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 68.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 73.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 73.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 73.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 73.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 79.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 79.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 79.6%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 79.6%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 61.2%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \frac{-x}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-55}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (- y (/ z (/ t (- y x))))))
   (if (<= t -1.45e-55)
     t_2
     (if (<= t 9.6e-138)
       t_1
       (if (<= t 9e-55)
         (* (- z t) (/ y (- a t)))
         (if (<= t 2.85e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.45e-55) {
		tmp = t_2;
	} else if (t <= 9.6e-138) {
		tmp = t_1;
	} else if (t <= 9e-55) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.85e+38) {
		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 + (z / (a / (y - x)))
    t_2 = y - (z / (t / (y - x)))
    if (t <= (-1.45d-55)) then
        tmp = t_2
    else if (t <= 9.6d-138) then
        tmp = t_1
    else if (t <= 9d-55) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 2.85d+38) 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 + (z / (a / (y - x)));
	double t_2 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.45e-55) {
		tmp = t_2;
	} else if (t <= 9.6e-138) {
		tmp = t_1;
	} else if (t <= 9e-55) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2.85e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y - (z / (t / (y - x)))
	tmp = 0
	if t <= -1.45e-55:
		tmp = t_2
	elif t <= 9.6e-138:
		tmp = t_1
	elif t <= 9e-55:
		tmp = (z - t) * (y / (a - t))
	elif t <= 2.85e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -1.45e-55)
		tmp = t_2;
	elseif (t <= 9.6e-138)
		tmp = t_1;
	elseif (t <= 9e-55)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 2.85e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -1.45e-55)
		tmp = t_2;
	elseif (t <= 9.6e-138)
		tmp = t_1;
	elseif (t <= 9e-55)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 2.85e+38)
		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[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-55], t$95$2, If[LessEqual[t, 9.6e-138], t$95$1, If[LessEqual[t, 9e-55], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.85e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-55 or 2.8499999999999999e38 < t

   1. Initial program 45.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 67.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 67.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 67.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 67.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 67.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 67.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 67.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 67.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 68.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 83.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 64.0%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 75.4%

         \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   10. Simplified 75.4%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   if -1.45e-55 < t < 9.5999999999999997e-138 or 8.99999999999999941e-55 < t < 2.8499999999999999e38

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.8%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 78.9%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   if 9.5999999999999997e-138 < t < 8.99999999999999941e-55

   1. Initial program 89.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 65.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

      2. associate-/r/ 67.5%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-55}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-55}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ t a) 1.0))))
   (if (<= t -2.4e+66)
     y
     (if (<= t 9.4e-119)
       t_1
       (if (<= t 1.1e-30) (/ (- x) (/ a z)) (if (<= t 1e+39) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((t / a) + 1.0);
	double tmp;
	if (t <= -2.4e+66) {
		tmp = y;
	} else if (t <= 9.4e-119) {
		tmp = t_1;
	} else if (t <= 1.1e-30) {
		tmp = -x / (a / z);
	} else if (t <= 1e+39) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((t / a) + 1.0d0)
    if (t <= (-2.4d+66)) then
        tmp = y
    else if (t <= 9.4d-119) then
        tmp = t_1
    else if (t <= 1.1d-30) then
        tmp = -x / (a / z)
    else if (t <= 1d+39) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((t / a) + 1.0);
	double tmp;
	if (t <= -2.4e+66) {
		tmp = y;
	} else if (t <= 9.4e-119) {
		tmp = t_1;
	} else if (t <= 1.1e-30) {
		tmp = -x / (a / z);
	} else if (t <= 1e+39) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((t / a) + 1.0)
	tmp = 0
	if t <= -2.4e+66:
		tmp = y
	elif t <= 9.4e-119:
		tmp = t_1
	elif t <= 1.1e-30:
		tmp = -x / (a / z)
	elif t <= 1e+39:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(t / a) + 1.0))
	tmp = 0.0
	if (t <= -2.4e+66)
		tmp = y;
	elseif (t <= 9.4e-119)
		tmp = t_1;
	elseif (t <= 1.1e-30)
		tmp = Float64(Float64(-x) / Float64(a / z));
	elseif (t <= 1e+39)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((t / a) + 1.0);
	tmp = 0.0;
	if (t <= -2.4e+66)
		tmp = y;
	elseif (t <= 9.4e-119)
		tmp = t_1;
	elseif (t <= 1.1e-30)
		tmp = -x / (a / z);
	elseif (t <= 1e+39)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+66], y, If[LessEqual[t, 9.4e-119], t$95$1, If[LessEqual[t, 1.1e-30], N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+39], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4000000000000002e66 or 9.9999999999999994e38 < t

   1. Initial program 37.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 53.9%

      \[\leadsto \color{blue}{y} \]

   if -2.4000000000000002e66 < t < 9.40000000000000004e-119 or 1.09999999999999992e-30 < t < 9.9999999999999994e38

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.1%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 74.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   8. Taylor expanded in z around 0 42.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot \left(y - x\right)}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot \left(y - x\right)}{a}\right)} \]

      2. unsub-neg 42.8%

         \[\leadsto \color{blue}{x - \frac{t \cdot \left(y - x\right)}{a}} \]

      3. associate-/l* 44.5%

         \[\leadsto x - \color{blue}{\frac{t}{\frac{a}{y - x}}} \]

   10. Simplified 44.5%

       \[\leadsto \color{blue}{x - \frac{t}{\frac{a}{y - x}}} \]

   11. Taylor expanded in x around inf 36.1%

       \[\leadsto \color{blue}{x \cdot \left(1 - -1 \cdot \frac{t}{a}\right)} \]
   12. Step-by-step derivation

       1. sub-neg 36.1%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(--1 \cdot \frac{t}{a}\right)\right)} \]

       2. mul-1-neg 36.1%

          \[\leadsto x \cdot \left(1 + \left(-\color{blue}{\left(-\frac{t}{a}\right)}\right)\right) \]

       3. remove-double-neg 36.1%

          \[\leadsto x \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) \]

       4. +-commutative 36.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{t}{a} + 1\right)} \]

   13. Simplified 36.1%

       \[\leadsto \color{blue}{x \cdot \left(\frac{t}{a} + 1\right)} \]

   if 9.40000000000000004e-119 < t < 1.09999999999999992e-30

   1. Initial program 81.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 42.0%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in x around inf 42.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 42.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   9. Taylor expanded in z around inf 22.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

       1. neg-mul-1 22.7%

          \[\leadsto \color{blue}{-\frac{x \cdot z}{a}} \]

       2. associate-*r/ 35.8%

          \[\leadsto -\color{blue}{x \cdot \frac{z}{a}} \]

       3. *-commutative 35.8%

          \[\leadsto -\color{blue}{\frac{z}{a} \cdot x} \]

       4. distribute-rgt-neg-in 35.8%

          \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-x\right)} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-x\right)} \]
   12. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{z}{a}} \]

       2. distribute-lft-neg-out 35.8%

          \[\leadsto \color{blue}{-x \cdot \frac{z}{a}} \]

       3. add-sqr-sqrt 16.2%

          \[\leadsto -\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{z}{a} \]

       4. sqrt-unprod 16.7%

          \[\leadsto -\color{blue}{\sqrt{x \cdot x}} \cdot \frac{z}{a} \]

       5. sqr-neg 16.7%

          \[\leadsto -\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{z}{a} \]

       6. sqrt-unprod 0.8%

          \[\leadsto -\color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{z}{a} \]

       7. add-sqr-sqrt 2.3%

          \[\leadsto -\color{blue}{\left(-x\right)} \cdot \frac{z}{a} \]

       8. clear-num 2.3%

          \[\leadsto -\left(-x\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

       9. un-div-inv 2.3%

          \[\leadsto -\color{blue}{\frac{-x}{\frac{a}{z}}} \]

       10. add-sqr-sqrt 0.8%

           \[\leadsto -\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{\frac{a}{z}} \]

       11. sqrt-unprod 16.7%

           \[\leadsto -\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{\frac{a}{z}} \]

       12. sqr-neg 16.7%

           \[\leadsto -\frac{\sqrt{\color{blue}{x \cdot x}}}{\frac{a}{z}} \]

       13. sqrt-unprod 16.2%

           \[\leadsto -\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{\frac{a}{z}} \]

       14. add-sqr-sqrt 35.8%

           \[\leadsto -\frac{\color{blue}{x}}{\frac{a}{z}} \]

   13. Applied egg-rr 35.8%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{+39}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+47} \lor \neg \left(t \leq 2.45 \cdot 10^{+101}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.4e+47) (not (<= t 2.45e+101)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.4e+47) || !(t <= 2.45e+101)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - 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 ((t <= (-6.4d+47)) .or. (.not. (t <= 2.45d+101))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * ((y - x) / (a - 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 ((t <= -6.4e+47) || !(t <= 2.45e+101)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.4e+47) or not (t <= 2.45e+101):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.4e+47) || !(t <= 2.45e+101))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.4e+47) || ~((t <= 2.45e+101)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.4e+47], N[Not[LessEqual[t, 2.45e+101]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4e47 or 2.44999999999999991e101 < t

   1. Initial program 32.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 61.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 66.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 66.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 66.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 66.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 66.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 66.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 66.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -6.4e47 < t < 2.44999999999999991e101

   1. Initial program 88.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+47} \lor \neg \left(t \leq 2.45 \cdot 10^{+101}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+44} \lor \neg \left(t \leq 5.9 \cdot 10^{+103}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.1e+44) (not (<= t 5.9e+103)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- y x) (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.1e+44) || !(t <= 5.9e+103)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - 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 ((t <= (-5.1d+44)) .or. (.not. (t <= 5.9d+103))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) * ((z - t) / (a - 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 ((t <= -5.1e+44) || !(t <= 5.9e+103)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.1e+44) or not (t <= 5.9e+103):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.1e+44) || !(t <= 5.9e+103))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.1e+44) || ~((t <= 5.9e+103)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.1e+44], N[Not[LessEqual[t, 5.9e+103]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1e44 or 5.8999999999999999e103 < t

   1. Initial program 32.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 61.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 66.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 66.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 66.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 66.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 66.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 66.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 66.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -5.1e44 < t < 5.8999999999999999e103

   1. Initial program 88.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 90.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 90.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 94.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 94.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 94.4%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 94.4%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+44} \lor \neg \left(t \leq 5.9 \cdot 10^{+103}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00022 \lor \neg \left(t \leq 4.1 \cdot 10^{+38}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.00022) (not (<= t 4.1e+38)))
   (- y (/ z (/ t (- y x))))
   (+ x (* (- y x) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.00022) || !(t <= 4.1e+38)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) * (z / (a - 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 ((t <= (-0.00022d0)) .or. (.not. (t <= 4.1d+38))) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x + ((y - x) * (z / (a - 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 ((t <= -0.00022) || !(t <= 4.1e+38)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.00022) or not (t <= 4.1e+38):
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x + ((y - x) * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.00022) || !(t <= 4.1e+38))
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.00022) || ~((t <= 4.1e+38)))
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x + ((y - x) * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.00022], N[Not[LessEqual[t, 4.1e+38]], $MachinePrecision]], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000008e-4 or 4.1000000000000003e38 < t

   1. Initial program 42.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 67.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 67.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 67.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 67.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 67.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 67.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 67.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 67.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 84.0%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 64.3%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 76.5%

         \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   10. Simplified 76.5%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   if -2.20000000000000008e-4 < t < 4.1000000000000003e38

   1. Initial program 90.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 92.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 92.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 92.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 96.0%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 95.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 96.0%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 96.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in z around inf 85.1%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{a - t}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00022 \lor \neg \left(t \leq 4.1 \cdot 10^{+38}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-41} \lor \neg \left(t \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e-41) (not (<= t 6e+38)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- y x) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e-41) || !(t <= 6e+38)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * (z / (a - 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 ((t <= (-7.2d-41)) .or. (.not. (t <= 6d+38))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) * (z / (a - 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 ((t <= -7.2e-41) || !(t <= 6e+38)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e-41) or not (t <= 6e+38):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e-41) || !(t <= 6e+38))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e-41) || ~((t <= 6e+38)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e-41], N[Not[LessEqual[t, 6e+38]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e-41 or 6.0000000000000002e38 < t

   1. Initial program 43.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 68.5%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 68.5%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 68.5%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 68.5%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 68.5%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 68.5%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 68.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 68.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 68.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 84.5%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 84.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -7.2e-41 < t < 6.0000000000000002e38

   1. Initial program 91.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 92.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 92.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 92.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 96.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 96.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 96.6%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in z around inf 85.4%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{a - t}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-41} \lor \neg \left(t \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e-12) y (if (<= t 4.9e+38) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-12) {
		tmp = y;
	} else if (t <= 4.9e+38) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = 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 <= (-5.5d-12)) then
        tmp = y
    else if (t <= 4.9d+38) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = 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 <= -5.5e-12) {
		tmp = y;
	} else if (t <= 4.9e+38) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e-12:
		tmp = y
	elif t <= 4.9e+38:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e-12)
		tmp = y;
	elseif (t <= 4.9e+38)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e-12)
		tmp = y;
	elseif (t <= 4.9e+38)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e-12], y, If[LessEqual[t, 4.9e+38], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000004e-12 or 4.90000000000000002e38 < t

   1. Initial program 43.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{y} \]

   if -5.5000000000000004e-12 < t < 4.90000000000000002e38

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.2%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in x around inf 50.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 50.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 50.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e-10) y (if (<= t 1.9e+38) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e-10) {
		tmp = y;
	} else if (t <= 1.9e+38) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.5d-10)) then
        tmp = y
    else if (t <= 1.9d+38) then
        tmp = x
    else
        tmp = 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 <= -1.5e-10) {
		tmp = y;
	} else if (t <= 1.9e+38) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e-10:
		tmp = y
	elif t <= 1.9e+38:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e-10)
		tmp = y;
	elseif (t <= 1.9e+38)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e-10)
		tmp = y;
	elseif (t <= 1.9e+38)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e-10], y, If[LessEqual[t, 1.9e+38], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e-10 or 1.8999999999999999e38 < t

   1. Initial program 42.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.5%

      \[\leadsto \color{blue}{y} \]

   if -1.5e-10 < t < 1.8999999999999999e38

   1. Initial program 90.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 31.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 26.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 70.3%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 81.2%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 81.2%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 22.4%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 22.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))