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

Percentage Accurate: 67.2% → 88.9%

Time: 29.2s

Alternatives: 27

Speedup: 0.7×

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: 67.2% 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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+97)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t -5e-141)
     (-
      (/ (* y (- z t)) (- a t))
      (* x (+ (/ z (- a t)) (- -1.0 (/ t (- a t))))))
     (if (<= t 2.35e+132)
       (fma (/ (- z t) (- a t)) (- y x) x)
       (+ y (/ (- x y) (/ t (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+97) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= -5e-141) {
		tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
	} else if (t <= 2.35e+132) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+97)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= -5e-141)
		tmp = Float64(Float64(Float64(y * Float64(z - t)) / Float64(a - t)) - Float64(x * Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t))))));
	elseif (t <= 2.35e+132)
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+97], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-141], N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e+132], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.19999999999999962e97

   1. Initial program 36.4%

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

      1. associate-*l/ 43.5%

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

   3. Simplified 43.5%

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

   5. Taylor expanded in t around inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate-*r/ 70.2%

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

      3. associate-*r/ 70.2%

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

      4. div-sub 70.2%

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

      5. distribute-lft-out-- 70.2%

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

      6. associate-*r/ 70.2%

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

      7. mul-1-neg 70.2%

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

      8. unsub-neg 70.2%

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

      9. distribute-rgt-out-- 72.6%

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

      10. associate-/l* 95.2%

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

   7. Simplified 95.2%

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

      1. div-inv 95.1%

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

      2. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -6.19999999999999962e97 < t < -4.9999999999999999e-141

   1. Initial program 77.4%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in x around -inf 92.1%

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

   if -4.9999999999999999e-141 < t < 2.35e132

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-/l* 92.0%

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

      4. associate-/r/ 95.5%

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

      5. fma-def 95.5%

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

   3. Simplified 95.5%

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

   if 2.35e132 < t

   1. Initial program 28.9%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. mul-1-neg 68.3%

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

      8. unsub-neg 68.3%

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

      9. distribute-rgt-out-- 68.5%

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

      10. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-310}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.9e+152)
     y
     (if (<= t -7.2e+37)
       (* (- z a) (/ x t))
       (if (<= t -1.15e+16)
         y
         (if (<= t -3.25e-22)
           t_1
           (if (<= t -1.8e-189)
             t_2
             (if (<= t 5e-310)
               t_1
               (if (<= t 3.2e-143) t_2 (if (<= t 2.85e+26) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.9e+152) {
		tmp = y;
	} else if (t <= -7.2e+37) {
		tmp = (z - a) * (x / t);
	} else if (t <= -1.15e+16) {
		tmp = y;
	} else if (t <= -3.25e-22) {
		tmp = t_1;
	} else if (t <= -1.8e-189) {
		tmp = t_2;
	} else if (t <= 5e-310) {
		tmp = t_1;
	} else if (t <= 3.2e-143) {
		tmp = t_2;
	} else if (t <= 2.85e+26) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-1.9d+152)) then
        tmp = y
    else if (t <= (-7.2d+37)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-1.15d+16)) then
        tmp = y
    else if (t <= (-3.25d-22)) then
        tmp = t_1
    else if (t <= (-1.8d-189)) then
        tmp = t_2
    else if (t <= 5d-310) then
        tmp = t_1
    else if (t <= 3.2d-143) then
        tmp = t_2
    else if (t <= 2.85d+26) 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 + (y / (a / z));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.9e+152) {
		tmp = y;
	} else if (t <= -7.2e+37) {
		tmp = (z - a) * (x / t);
	} else if (t <= -1.15e+16) {
		tmp = y;
	} else if (t <= -3.25e-22) {
		tmp = t_1;
	} else if (t <= -1.8e-189) {
		tmp = t_2;
	} else if (t <= 5e-310) {
		tmp = t_1;
	} else if (t <= 3.2e-143) {
		tmp = t_2;
	} else if (t <= 2.85e+26) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.9e+152:
		tmp = y
	elif t <= -7.2e+37:
		tmp = (z - a) * (x / t)
	elif t <= -1.15e+16:
		tmp = y
	elif t <= -3.25e-22:
		tmp = t_1
	elif t <= -1.8e-189:
		tmp = t_2
	elif t <= 5e-310:
		tmp = t_1
	elif t <= 3.2e-143:
		tmp = t_2
	elif t <= 2.85e+26:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.9e+152)
		tmp = y;
	elseif (t <= -7.2e+37)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -1.15e+16)
		tmp = y;
	elseif (t <= -3.25e-22)
		tmp = t_1;
	elseif (t <= -1.8e-189)
		tmp = t_2;
	elseif (t <= 5e-310)
		tmp = t_1;
	elseif (t <= 3.2e-143)
		tmp = t_2;
	elseif (t <= 2.85e+26)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.9e+152)
		tmp = y;
	elseif (t <= -7.2e+37)
		tmp = (z - a) * (x / t);
	elseif (t <= -1.15e+16)
		tmp = y;
	elseif (t <= -3.25e-22)
		tmp = t_1;
	elseif (t <= -1.8e-189)
		tmp = t_2;
	elseif (t <= 5e-310)
		tmp = t_1;
	elseif (t <= 3.2e-143)
		tmp = t_2;
	elseif (t <= 2.85e+26)
		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[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+152], y, If[LessEqual[t, -7.2e+37], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e+16], y, If[LessEqual[t, -3.25e-22], t$95$1, If[LessEqual[t, -1.8e-189], t$95$2, If[LessEqual[t, 5e-310], t$95$1, If[LessEqual[t, 3.2e-143], t$95$2, If[LessEqual[t, 2.85e+26], t$95$1, y]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9e152 or -7.19999999999999995e37 < t < -1.15e16 or 2.8500000000000002e26 < t

   1. Initial program 38.7%

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

      1. associate-*l/ 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in t around inf 60.5%

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

   if -1.9e152 < t < -7.19999999999999995e37

   1. Initial program 66.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. div-sub 64.9%

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

      5. distribute-lft-out-- 64.9%

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

      6. associate-*r/ 64.9%

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

      7. mul-1-neg 64.9%

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

      8. unsub-neg 64.9%

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

      9. distribute-rgt-out-- 64.9%

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

      10. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 48.6%

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

   10. Simplified 48.6%

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

   if -1.15e16 < t < -3.25000000000000022e-22 or -1.80000000000000008e-189 < t < 4.999999999999985e-310 or 3.1999999999999998e-143 < t < 2.8500000000000002e26

   1. Initial program 86.7%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in a around inf 66.9%

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

   6. Taylor expanded in y around inf 57.7%

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

   7. Taylor expanded in z around inf 51.8%

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

      1. associate-/l* 57.2%

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

   9. Simplified 57.2%

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

   if -3.25000000000000022e-22 < t < -1.80000000000000008e-189 or 4.999999999999985e-310 < t < 3.1999999999999998e-143

   1. Initial program 87.8%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 69.1%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   10. Simplified 69.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-310}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.55 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.5e+152)
     y
     (if (<= t -1.05e+38)
       (* (- z a) (/ x t))
       (if (<= t -1.22e+16)
         y
         (if (<= t -3.55e-22)
           t_1
           (if (<= t -1.7e-188)
             t_2
             (if (<= t 2e-309)
               t_1
               (if (<= t 5.5e-142)
                 t_2
                 (if (<= t 7e+29) (+ x (/ z (/ a y))) y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.5e+152) {
		tmp = y;
	} else if (t <= -1.05e+38) {
		tmp = (z - a) * (x / t);
	} else if (t <= -1.22e+16) {
		tmp = y;
	} else if (t <= -3.55e-22) {
		tmp = t_1;
	} else if (t <= -1.7e-188) {
		tmp = t_2;
	} else if (t <= 2e-309) {
		tmp = t_1;
	} else if (t <= 5.5e-142) {
		tmp = t_2;
	} else if (t <= 7e+29) {
		tmp = x + (z / (a / y));
	} 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 / (a / z))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-2.5d+152)) then
        tmp = y
    else if (t <= (-1.05d+38)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-1.22d+16)) then
        tmp = y
    else if (t <= (-3.55d-22)) then
        tmp = t_1
    else if (t <= (-1.7d-188)) then
        tmp = t_2
    else if (t <= 2d-309) then
        tmp = t_1
    else if (t <= 5.5d-142) then
        tmp = t_2
    else if (t <= 7d+29) then
        tmp = x + (z / (a / y))
    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 / (a / z));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.5e+152) {
		tmp = y;
	} else if (t <= -1.05e+38) {
		tmp = (z - a) * (x / t);
	} else if (t <= -1.22e+16) {
		tmp = y;
	} else if (t <= -3.55e-22) {
		tmp = t_1;
	} else if (t <= -1.7e-188) {
		tmp = t_2;
	} else if (t <= 2e-309) {
		tmp = t_1;
	} else if (t <= 5.5e-142) {
		tmp = t_2;
	} else if (t <= 7e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.5e+152:
		tmp = y
	elif t <= -1.05e+38:
		tmp = (z - a) * (x / t)
	elif t <= -1.22e+16:
		tmp = y
	elif t <= -3.55e-22:
		tmp = t_1
	elif t <= -1.7e-188:
		tmp = t_2
	elif t <= 2e-309:
		tmp = t_1
	elif t <= 5.5e-142:
		tmp = t_2
	elif t <= 7e+29:
		tmp = x + (z / (a / y))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -2.5e+152)
		tmp = y;
	elseif (t <= -1.05e+38)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -1.22e+16)
		tmp = y;
	elseif (t <= -3.55e-22)
		tmp = t_1;
	elseif (t <= -1.7e-188)
		tmp = t_2;
	elseif (t <= 2e-309)
		tmp = t_1;
	elseif (t <= 5.5e-142)
		tmp = t_2;
	elseif (t <= 7e+29)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -2.5e+152)
		tmp = y;
	elseif (t <= -1.05e+38)
		tmp = (z - a) * (x / t);
	elseif (t <= -1.22e+16)
		tmp = y;
	elseif (t <= -3.55e-22)
		tmp = t_1;
	elseif (t <= -1.7e-188)
		tmp = t_2;
	elseif (t <= 2e-309)
		tmp = t_1;
	elseif (t <= 5.5e-142)
		tmp = t_2;
	elseif (t <= 7e+29)
		tmp = x + (z / (a / y));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+152], y, If[LessEqual[t, -1.05e+38], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.22e+16], y, If[LessEqual[t, -3.55e-22], t$95$1, If[LessEqual[t, -1.7e-188], t$95$2, If[LessEqual[t, 2e-309], t$95$1, If[LessEqual[t, 5.5e-142], t$95$2, If[LessEqual[t, 7e+29], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5e152 or -1.05e38 < t < -1.22e16 or 6.99999999999999958e29 < t

   1. Initial program 38.7%

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

      1. associate-*l/ 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in t around inf 60.5%

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

   if -2.5e152 < t < -1.05e38

   1. Initial program 66.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. div-sub 64.9%

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

      5. distribute-lft-out-- 64.9%

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

      6. associate-*r/ 64.9%

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

      7. mul-1-neg 64.9%

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

      8. unsub-neg 64.9%

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

      9. distribute-rgt-out-- 64.9%

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

      10. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 48.6%

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

   10. Simplified 48.6%

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

   if -1.22e16 < t < -3.5499999999999999e-22 or -1.70000000000000014e-188 < t < 1.9999999999999988e-309

   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/ 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in a around inf 67.5%

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

   6. Taylor expanded in y around inf 53.9%

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

   7. Taylor expanded in z around inf 47.9%

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

      1. associate-/l* 56.6%

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

   9. Simplified 56.6%

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

   if -3.5499999999999999e-22 < t < -1.70000000000000014e-188 or 1.9999999999999988e-309 < t < 5.50000000000000023e-142

   1. Initial program 87.8%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 69.1%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   10. Simplified 69.0%

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

   if 5.50000000000000023e-142 < t < 6.99999999999999958e29

   1. Initial program 84.1%

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

      1. associate-*l/ 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in t around 0 57.3%

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

      1. associate-/l* 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 58.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.55 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-309}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x}{\frac{t}{z}}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -17000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-309}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+23}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ x (/ t z)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= t -17000000000.0)
     t_1
     (if (<= t -3.1e-89)
       (+ x (/ y (/ a z)))
       (if (<= t -1.12e-135)
         t_2
         (if (<= t -1.26e-183)
           (* x (- 1.0 (/ z a)))
           (if (<= t 4e-309)
             t_2
             (if (<= t 1.3e-119)
               (- x (/ x (/ a z)))
               (if (<= t 4.2e-6)
                 t_2
                 (if (<= t 3e+23) (- x (* t (/ y a))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x / (t / z));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -17000000000.0) {
		tmp = t_1;
	} else if (t <= -3.1e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= -1.12e-135) {
		tmp = t_2;
	} else if (t <= -1.26e-183) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-309) {
		tmp = t_2;
	} else if (t <= 1.3e-119) {
		tmp = x - (x / (a / z));
	} else if (t <= 4.2e-6) {
		tmp = t_2;
	} else if (t <= 3e+23) {
		tmp = x - (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x / (t / z))
    t_2 = z * ((y - x) / (a - t))
    if (t <= (-17000000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.1d-89)) then
        tmp = x + (y / (a / z))
    else if (t <= (-1.12d-135)) then
        tmp = t_2
    else if (t <= (-1.26d-183)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 4d-309) then
        tmp = t_2
    else if (t <= 1.3d-119) then
        tmp = x - (x / (a / z))
    else if (t <= 4.2d-6) then
        tmp = t_2
    else if (t <= 3d+23) then
        tmp = x - (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x / (t / z));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -17000000000.0) {
		tmp = t_1;
	} else if (t <= -3.1e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= -1.12e-135) {
		tmp = t_2;
	} else if (t <= -1.26e-183) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-309) {
		tmp = t_2;
	} else if (t <= 1.3e-119) {
		tmp = x - (x / (a / z));
	} else if (t <= 4.2e-6) {
		tmp = t_2;
	} else if (t <= 3e+23) {
		tmp = x - (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x / (t / z))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if t <= -17000000000.0:
		tmp = t_1
	elif t <= -3.1e-89:
		tmp = x + (y / (a / z))
	elif t <= -1.12e-135:
		tmp = t_2
	elif t <= -1.26e-183:
		tmp = x * (1.0 - (z / a))
	elif t <= 4e-309:
		tmp = t_2
	elif t <= 1.3e-119:
		tmp = x - (x / (a / z))
	elif t <= 4.2e-6:
		tmp = t_2
	elif t <= 3e+23:
		tmp = x - (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x / Float64(t / z)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (t <= -17000000000.0)
		tmp = t_1;
	elseif (t <= -3.1e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -1.12e-135)
		tmp = t_2;
	elseif (t <= -1.26e-183)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 4e-309)
		tmp = t_2;
	elseif (t <= 1.3e-119)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 4.2e-6)
		tmp = t_2;
	elseif (t <= 3e+23)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x / (t / z));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (t <= -17000000000.0)
		tmp = t_1;
	elseif (t <= -3.1e-89)
		tmp = x + (y / (a / z));
	elseif (t <= -1.12e-135)
		tmp = t_2;
	elseif (t <= -1.26e-183)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 4e-309)
		tmp = t_2;
	elseif (t <= 1.3e-119)
		tmp = x - (x / (a / z));
	elseif (t <= 4.2e-6)
		tmp = t_2;
	elseif (t <= 3e+23)
		tmp = x - (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -17000000000.0], t$95$1, If[LessEqual[t, -3.1e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e-135], t$95$2, If[LessEqual[t, -1.26e-183], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-309], t$95$2, If[LessEqual[t, 1.3e-119], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-6], t$95$2, If[LessEqual[t, 3e+23], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.7e10 or 3.0000000000000001e23 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around -inf 68.1%

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

   6. Taylor expanded in t around inf 79.9%

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

   7. Taylor expanded in a around 0 65.8%

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

      1. associate-/l* 73.5%

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

   9. Simplified 73.5%

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

   if -1.7e10 < t < -3.09999999999999996e-89

   1. Initial program 82.5%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in a around inf 67.3%

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

   6. Taylor expanded in y around inf 62.7%

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

   7. Taylor expanded in z around inf 66.7%

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

      1. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   if -3.09999999999999996e-89 < t < -1.12e-135 or -1.26e-183 < t < 3.9999999999999977e-309 or 1.30000000000000006e-119 < t < 4.1999999999999996e-6

   1. Initial program 84.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 69.1%

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

      1. div-sub 69.1%

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

   7. Simplified 69.1%

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

   if -1.12e-135 < t < -1.26e-183

   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/ 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 t around 0 79.3%

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

      1. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in x around inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   10. Simplified 79.8%

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

   if 3.9999999999999977e-309 < t < 1.30000000000000006e-119

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

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

   8. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-/l* 82.4%

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

   10. Simplified 82.4%

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

   if 4.1999999999999996e-6 < t < 3.0000000000000001e23

   1. Initial program 80.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 89.9%

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

   6. Taylor expanded in y around inf 70.9%

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

   7. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. unsub-neg 70.8%

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

      3. associate-*r/ 70.9%

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

   9. Simplified 70.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -17000000000:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-309}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+23}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y + \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -430000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-136}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+29}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))) (t_2 (+ y (/ x (/ t z)))))
   (if (<= t -430000000000.0)
     t_2
     (if (<= t -2.1e-88)
       (+ x (/ y (/ a z)))
       (if (<= t -3.3e-136)
         (* (- y x) (/ z (- a t)))
         (if (<= t -6.2e-185)
           (* x (- 1.0 (/ z a)))
           (if (<= t 4e-309)
             t_1
             (if (<= t 1.05e-119)
               (- x (/ x (/ a z)))
               (if (<= t 1.16e-8)
                 t_1
                 (if (<= t 3.4e+29) (- x (* t (/ y a))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -430000000000.0) {
		tmp = t_2;
	} else if (t <= -2.1e-88) {
		tmp = x + (y / (a / z));
	} else if (t <= -3.3e-136) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= -6.2e-185) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-309) {
		tmp = t_1;
	} else if (t <= 1.05e-119) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.16e-8) {
		tmp = t_1;
	} else if (t <= 3.4e+29) {
		tmp = x - (t * (y / a));
	} 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 = z * ((y - x) / (a - t))
    t_2 = y + (x / (t / z))
    if (t <= (-430000000000.0d0)) then
        tmp = t_2
    else if (t <= (-2.1d-88)) then
        tmp = x + (y / (a / z))
    else if (t <= (-3.3d-136)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= (-6.2d-185)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 4d-309) then
        tmp = t_1
    else if (t <= 1.05d-119) then
        tmp = x - (x / (a / z))
    else if (t <= 1.16d-8) then
        tmp = t_1
    else if (t <= 3.4d+29) then
        tmp = x - (t * (y / a))
    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 = z * ((y - x) / (a - t));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -430000000000.0) {
		tmp = t_2;
	} else if (t <= -2.1e-88) {
		tmp = x + (y / (a / z));
	} else if (t <= -3.3e-136) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= -6.2e-185) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-309) {
		tmp = t_1;
	} else if (t <= 1.05e-119) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.16e-8) {
		tmp = t_1;
	} else if (t <= 3.4e+29) {
		tmp = x - (t * (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y + (x / (t / z))
	tmp = 0
	if t <= -430000000000.0:
		tmp = t_2
	elif t <= -2.1e-88:
		tmp = x + (y / (a / z))
	elif t <= -3.3e-136:
		tmp = (y - x) * (z / (a - t))
	elif t <= -6.2e-185:
		tmp = x * (1.0 - (z / a))
	elif t <= 4e-309:
		tmp = t_1
	elif t <= 1.05e-119:
		tmp = x - (x / (a / z))
	elif t <= 1.16e-8:
		tmp = t_1
	elif t <= 3.4e+29:
		tmp = x - (t * (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y + Float64(x / Float64(t / z)))
	tmp = 0.0
	if (t <= -430000000000.0)
		tmp = t_2;
	elseif (t <= -2.1e-88)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -3.3e-136)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= -6.2e-185)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 4e-309)
		tmp = t_1;
	elseif (t <= 1.05e-119)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 1.16e-8)
		tmp = t_1;
	elseif (t <= 3.4e+29)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y + (x / (t / z));
	tmp = 0.0;
	if (t <= -430000000000.0)
		tmp = t_2;
	elseif (t <= -2.1e-88)
		tmp = x + (y / (a / z));
	elseif (t <= -3.3e-136)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= -6.2e-185)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 4e-309)
		tmp = t_1;
	elseif (t <= 1.05e-119)
		tmp = x - (x / (a / z));
	elseif (t <= 1.16e-8)
		tmp = t_1;
	elseif (t <= 3.4e+29)
		tmp = x - (t * (y / a));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -430000000000.0], t$95$2, If[LessEqual[t, -2.1e-88], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-136], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-185], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-309], t$95$1, If[LessEqual[t, 1.05e-119], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e-8], t$95$1, If[LessEqual[t, 3.4e+29], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -4.3e11 or 3.39999999999999981e29 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around -inf 68.1%

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

   6. Taylor expanded in t around inf 79.9%

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

   7. Taylor expanded in a around 0 65.8%

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

      1. associate-/l* 73.5%

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

   9. Simplified 73.5%

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

   if -4.3e11 < t < -2.1e-88

   1. Initial program 82.5%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in a around inf 67.3%

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

   6. Taylor expanded in y around inf 62.7%

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

   7. Taylor expanded in z around inf 66.7%

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

      1. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   if -2.1e-88 < t < -3.30000000000000018e-136

   1. Initial program 77.6%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

      1. *-commutative 83.6%

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

      2. clear-num 83.0%

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

      3. un-div-inv 83.3%

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

   6. Applied egg-rr 83.3%

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

   7. Taylor expanded in z around -inf 61.8%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 67.8%

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

   9. Simplified 67.8%

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

   if -3.30000000000000018e-136 < t < -6.1999999999999994e-185

   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/ 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 t around 0 79.3%

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

      1. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in x around inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   10. Simplified 79.8%

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

   if -6.1999999999999994e-185 < t < 3.9999999999999977e-309 or 1.05e-119 < t < 1.15999999999999996e-8

   1. Initial program 87.7%

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

   5. Taylor expanded in z around inf 69.6%

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

      1. div-sub 69.6%

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

   7. Simplified 69.6%

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

   if 3.9999999999999977e-309 < t < 1.05e-119

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

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

   8. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-/l* 82.4%

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

   10. Simplified 82.4%

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

   if 1.15999999999999996e-8 < t < 3.39999999999999981e29

   1. Initial program 80.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 89.9%

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

   6. Taylor expanded in y around inf 70.9%

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

   7. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. unsub-neg 70.8%

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

      3. associate-*r/ 70.9%

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

   9. Simplified 70.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -430000000000:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-136}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-309}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+29}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y + \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -6500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-40} \lor \neg \left(t \leq 2 \cdot 10^{-15}\right) \land t \leq 2.85 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (+ y (/ x (/ t z)))))
   (if (<= t -6500.0)
     t_2
     (if (<= t -3e-113)
       t_1
       (if (<= t -8e-126)
         (* (- z t) (/ y (- a t)))
         (if (or (<= t 4.9e-40) (and (not (<= t 2e-15)) (<= t 2.85e+29)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -6500.0) {
		tmp = t_2;
	} else if (t <= -3e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if ((t <= 4.9e-40) || (!(t <= 2e-15) && (t <= 2.85e+29))) {
		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 * ((y - x) / a))
    t_2 = y + (x / (t / z))
    if (t <= (-6500.0d0)) then
        tmp = t_2
    else if (t <= (-3d-113)) then
        tmp = t_1
    else if (t <= (-8d-126)) then
        tmp = (z - t) * (y / (a - t))
    else if ((t <= 4.9d-40) .or. (.not. (t <= 2d-15)) .and. (t <= 2.85d+29)) 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 * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -6500.0) {
		tmp = t_2;
	} else if (t <= -3e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if ((t <= 4.9e-40) || (!(t <= 2e-15) && (t <= 2.85e+29))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y + (x / (t / z))
	tmp = 0
	if t <= -6500.0:
		tmp = t_2
	elif t <= -3e-113:
		tmp = t_1
	elif t <= -8e-126:
		tmp = (z - t) * (y / (a - t))
	elif (t <= 4.9e-40) or (not (t <= 2e-15) and (t <= 2.85e+29)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(x / Float64(t / z)))
	tmp = 0.0
	if (t <= -6500.0)
		tmp = t_2;
	elseif (t <= -3e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif ((t <= 4.9e-40) || (!(t <= 2e-15) && (t <= 2.85e+29)))
		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 * ((y - x) / a));
	t_2 = y + (x / (t / z));
	tmp = 0.0;
	if (t <= -6500.0)
		tmp = t_2;
	elseif (t <= -3e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = (z - t) * (y / (a - t));
	elseif ((t <= 4.9e-40) || (~((t <= 2e-15)) && (t <= 2.85e+29)))
		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[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6500.0], t$95$2, If[LessEqual[t, -3e-113], t$95$1, If[LessEqual[t, -8e-126], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.9e-40], And[N[Not[LessEqual[t, 2e-15]], $MachinePrecision], LessEqual[t, 2.85e+29]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6500 or 4.8999999999999997e-40 < t < 2.0000000000000002e-15 or 2.85e29 < t

   1. Initial program 46.7%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in x around -inf 69.1%

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

   6. Taylor expanded in t around inf 79.5%

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

   7. Taylor expanded in a around 0 66.2%

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

      1. associate-/l* 73.5%

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

   9. Simplified 73.5%

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

   if -6500 < t < -3.0000000000000001e-113 or -7.9999999999999996e-126 < t < 4.8999999999999997e-40 or 2.0000000000000002e-15 < t < 2.85e29

   1. Initial program 88.7%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 70.8%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

      1. div-inv 76.2%

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

      2. clear-num 76.2%

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

   9. Applied egg-rr 76.2%

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

   if -3.0000000000000001e-113 < t < -7.9999999999999996e-126

   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/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 92.1%

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

      2. associate-/r/ 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6500:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-113}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-40} \lor \neg \left(t \leq 2 \cdot 10^{-15}\right) \land t \leq 2.85 \cdot 10^{+29}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y + \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -3700:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-15} \lor \neg \left(t \leq 1.25 \cdot 10^{+29}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (+ y (/ x (/ t z)))))
   (if (<= t -3700.0)
     t_2
     (if (<= t -2.8e-113)
       t_1
       (if (<= t -8e-126)
         (* (- z t) (/ y (- a t)))
         (if (<= t 2e-38)
           (+ x (/ z (/ a (- y x))))
           (if (or (<= t 1.9e-15) (not (<= t 1.25e+29))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -3700.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if ((t <= 1.9e-15) || !(t <= 1.25e+29)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    t_2 = y + (x / (t / z))
    if (t <= (-3700.0d0)) then
        tmp = t_2
    else if (t <= (-2.8d-113)) then
        tmp = t_1
    else if (t <= (-8d-126)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 2d-38) then
        tmp = x + (z / (a / (y - x)))
    else if ((t <= 1.9d-15) .or. (.not. (t <= 1.25d+29))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -3700.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 2e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if ((t <= 1.9e-15) || !(t <= 1.25e+29)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y + (x / (t / z))
	tmp = 0
	if t <= -3700.0:
		tmp = t_2
	elif t <= -2.8e-113:
		tmp = t_1
	elif t <= -8e-126:
		tmp = (z - t) * (y / (a - t))
	elif t <= 2e-38:
		tmp = x + (z / (a / (y - x)))
	elif (t <= 1.9e-15) or not (t <= 1.25e+29):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(x / Float64(t / z)))
	tmp = 0.0
	if (t <= -3700.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 2e-38)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif ((t <= 1.9e-15) || !(t <= 1.25e+29))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	t_2 = y + (x / (t / z));
	tmp = 0.0;
	if (t <= -3700.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 2e-38)
		tmp = x + (z / (a / (y - x)));
	elseif ((t <= 1.9e-15) || ~((t <= 1.25e+29)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3700.0], t$95$2, If[LessEqual[t, -2.8e-113], t$95$1, If[LessEqual[t, -8e-126], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-38], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.9e-15], N[Not[LessEqual[t, 1.25e+29]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3700 or 1.9999999999999999e-38 < t < 1.9000000000000001e-15 or 1.25e29 < t

   1. Initial program 46.7%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in x around -inf 69.1%

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

   6. Taylor expanded in t around inf 79.5%

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

   7. Taylor expanded in a around 0 66.2%

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

      1. associate-/l* 73.5%

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

   9. Simplified 73.5%

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

   if -3700 < t < -2.8e-113 or 1.9000000000000001e-15 < t < 1.25e29

   1. Initial program 82.5%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

      1. div-inv 73.7%

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

      2. clear-num 73.8%

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

   9. Applied egg-rr 73.8%

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

   if -2.8e-113 < t < -7.9999999999999996e-126

   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/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 92.1%

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

      2. associate-/r/ 78.0%

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

   7. Simplified 78.0%

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

   if -7.9999999999999996e-126 < t < 1.9999999999999999e-38

   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/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3700:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-15} \lor \neg \left(t \leq 1.25 \cdot 10^{+29}\right):\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y + \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -165000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (+ y (/ x (/ t z)))))
   (if (<= t -165000.0)
     t_2
     (if (<= t -2.8e-113)
       t_1
       (if (<= t -8e-126)
         (* (- z t) (/ y (- a t)))
         (if (<= t 1.2e-38)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 3.1e-15)
             (+ y (/ (* x (- z a)) t))
             (if (<= t 1.1e+26) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -165000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.2e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3.1e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 1.1e+26) {
		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 * ((y - x) / a))
    t_2 = y + (x / (t / z))
    if (t <= (-165000.0d0)) then
        tmp = t_2
    else if (t <= (-2.8d-113)) then
        tmp = t_1
    else if (t <= (-8d-126)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 1.2d-38) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 3.1d-15) then
        tmp = y + ((x * (z - a)) / t)
    else if (t <= 1.1d+26) 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 * ((y - x) / a));
	double t_2 = y + (x / (t / z));
	double tmp;
	if (t <= -165000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.2e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 3.1e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 1.1e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y + (x / (t / z))
	tmp = 0
	if t <= -165000.0:
		tmp = t_2
	elif t <= -2.8e-113:
		tmp = t_1
	elif t <= -8e-126:
		tmp = (z - t) * (y / (a - t))
	elif t <= 1.2e-38:
		tmp = x + (z / (a / (y - x)))
	elif t <= 3.1e-15:
		tmp = y + ((x * (z - a)) / t)
	elif t <= 1.1e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(x / Float64(t / z)))
	tmp = 0.0
	if (t <= -165000.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 1.2e-38)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 3.1e-15)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t <= 1.1e+26)
		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 * ((y - x) / a));
	t_2 = y + (x / (t / z));
	tmp = 0.0;
	if (t <= -165000.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 1.2e-38)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 3.1e-15)
		tmp = y + ((x * (z - a)) / t);
	elseif (t <= 1.1e+26)
		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[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -165000.0], t$95$2, If[LessEqual[t, -2.8e-113], t$95$1, If[LessEqual[t, -8e-126], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-38], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-15], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+26], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -165000 or 1.10000000000000004e26 < t

   1. Initial program 45.8%

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

      1. associate-*l/ 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in x around -inf 68.3%

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

   6. Taylor expanded in t around inf 79.2%

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

   7. Taylor expanded in a around 0 65.3%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

   if -165000 < t < -2.8e-113 or 3.0999999999999999e-15 < t < 1.10000000000000004e26

   1. Initial program 82.5%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

      1. div-inv 73.7%

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

      2. clear-num 73.8%

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

   9. Applied egg-rr 73.8%

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

   if -2.8e-113 < t < -7.9999999999999996e-126

   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/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 92.1%

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

      2. associate-/r/ 78.0%

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

   7. Simplified 78.0%

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

   if -7.9999999999999996e-126 < t < 1.20000000000000011e-38

   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/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if 1.20000000000000011e-38 < t < 3.0999999999999999e-15

   1. Initial program 65.1%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in x around -inf 84.5%

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

   6. Taylor expanded in t around inf 85.3%

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

   7. Taylor expanded in t around -inf 99.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -165000:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -3900000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (+ y (* (- z a) (/ x t)))))
   (if (<= t -3900000.0)
     t_2
     (if (<= t -2.8e-113)
       t_1
       (if (<= t -8e-126)
         (* (- z t) (/ y (- a t)))
         (if (<= t 1.7e-38)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 1.75e-15)
             (+ y (/ (* x (- z a)) t))
             (if (<= t 1.46e+26) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + ((z - a) * (x / t));
	double tmp;
	if (t <= -3900000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.7e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.75e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 1.46e+26) {
		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 * ((y - x) / a))
    t_2 = y + ((z - a) * (x / t))
    if (t <= (-3900000.0d0)) then
        tmp = t_2
    else if (t <= (-2.8d-113)) then
        tmp = t_1
    else if (t <= (-8d-126)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 1.7d-38) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 1.75d-15) then
        tmp = y + ((x * (z - a)) / t)
    else if (t <= 1.46d+26) 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 * ((y - x) / a));
	double t_2 = y + ((z - a) * (x / t));
	double tmp;
	if (t <= -3900000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -8e-126) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.7e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.75e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 1.46e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y + ((z - a) * (x / t))
	tmp = 0
	if t <= -3900000.0:
		tmp = t_2
	elif t <= -2.8e-113:
		tmp = t_1
	elif t <= -8e-126:
		tmp = (z - t) * (y / (a - t))
	elif t <= 1.7e-38:
		tmp = x + (z / (a / (y - x)))
	elif t <= 1.75e-15:
		tmp = y + ((x * (z - a)) / t)
	elif t <= 1.46e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(x / t)))
	tmp = 0.0
	if (t <= -3900000.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 1.7e-38)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 1.75e-15)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t <= 1.46e+26)
		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 * ((y - x) / a));
	t_2 = y + ((z - a) * (x / t));
	tmp = 0.0;
	if (t <= -3900000.0)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -8e-126)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 1.7e-38)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 1.75e-15)
		tmp = y + ((x * (z - a)) / t);
	elseif (t <= 1.46e+26)
		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[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3900000.0], t$95$2, If[LessEqual[t, -2.8e-113], t$95$1, If[LessEqual[t, -8e-126], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-38], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-15], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.46e+26], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.9e6 or 1.45999999999999992e26 < t

   1. Initial program 45.8%

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

      1. associate-*l/ 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in x around -inf 68.3%

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

   6. Taylor expanded in t around inf 79.2%

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

   7. Taylor expanded in t around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

      3. associate-/l* 80.6%

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

      4. associate-/r/ 79.4%

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

      5. mul-1-neg 79.4%

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

      6. unsub-neg 79.4%

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

   9. Simplified 79.4%

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

   if -3.9e6 < t < -2.8e-113 or 1.75e-15 < t < 1.45999999999999992e26

   1. Initial program 82.5%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

      1. div-inv 73.7%

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

      2. clear-num 73.8%

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

   9. Applied egg-rr 73.8%

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

   if -2.8e-113 < t < -7.9999999999999996e-126

   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/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 92.1%

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

      2. associate-/r/ 78.0%

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

   7. Simplified 78.0%

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

   if -7.9999999999999996e-126 < t < 1.7000000000000001e-38

   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/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if 1.7000000000000001e-38 < t < 1.75e-15

   1. Initial program 65.1%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in x around -inf 84.5%

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

   6. Taylor expanded in t around inf 85.3%

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

   7. Taylor expanded in t around -inf 99.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3900000:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -30500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+123}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))))
   (if (<= t -3.8e+254)
     (+ y (* (- z a) (/ x t)))
     (if (<= t -30500000000.0)
       t_1
       (if (<= t 2e-38)
         (- x (/ (- x y) (/ a (- z t))))
         (if (<= t 1.55e-15)
           (+ y (/ (* x (- z a)) t))
           (if (<= t 3.2e+123) (+ x (/ (- z t) (/ (- a t) y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -3.8e+254) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -30500000000.0) {
		tmp = t_1;
	} else if (t <= 2e-38) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 1.55e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 3.2e+123) {
		tmp = x + ((z - t) / ((a - t) / y));
	} 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))
    if (t <= (-3.8d+254)) then
        tmp = y + ((z - a) * (x / t))
    else if (t <= (-30500000000.0d0)) then
        tmp = t_1
    else if (t <= 2d-38) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (t <= 1.55d-15) then
        tmp = y + ((x * (z - a)) / t)
    else if (t <= 3.2d+123) then
        tmp = x + ((z - t) / ((a - t) / y))
    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));
	double tmp;
	if (t <= -3.8e+254) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -30500000000.0) {
		tmp = t_1;
	} else if (t <= 2e-38) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 1.55e-15) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t <= 3.2e+123) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	tmp = 0
	if t <= -3.8e+254:
		tmp = y + ((z - a) * (x / t))
	elif t <= -30500000000.0:
		tmp = t_1
	elif t <= 2e-38:
		tmp = x - ((x - y) / (a / (z - t)))
	elif t <= 1.55e-15:
		tmp = y + ((x * (z - a)) / t)
	elif t <= 3.2e+123:
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (t <= -3.8e+254)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	elseif (t <= -30500000000.0)
		tmp = t_1;
	elseif (t <= 2e-38)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (t <= 1.55e-15)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t <= 3.2e+123)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	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));
	tmp = 0.0;
	if (t <= -3.8e+254)
		tmp = y + ((z - a) * (x / t));
	elseif (t <= -30500000000.0)
		tmp = t_1;
	elseif (t <= 2e-38)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (t <= 1.55e-15)
		tmp = y + ((x * (z - a)) / t);
	elseif (t <= 3.2e+123)
		tmp = x + ((z - t) / ((a - t) / y));
	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 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+254], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -30500000000.0], t$95$1, If[LessEqual[t, 2e-38], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-15], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+123], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.80000000000000002e254

   1. Initial program 17.4%

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

      1. associate-*l/ 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in x around -inf 31.3%

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

   6. Taylor expanded in t around inf 65.3%

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

   7. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

      3. associate-/l* 93.2%

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

      4. associate-/r/ 99.7%

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

      5. mul-1-neg 99.7%

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

      6. unsub-neg 99.7%

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

   9. Simplified 99.7%

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

   if -3.80000000000000002e254 < t < -3.05e10 or 3.20000000000000005e123 < 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. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in t around inf 71.5%

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

      1. associate--l+ 71.5%

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

      2. associate-*r/ 71.5%

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

      3. associate-*r/ 71.5%

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

      4. div-sub 71.5%

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

      5. distribute-lft-out-- 71.5%

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

      6. associate-*r/ 71.5%

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

      7. mul-1-neg 71.5%

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

      8. unsub-neg 71.5%

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

      9. distribute-rgt-out-- 72.6%

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

      10. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around inf 87.4%

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

   if -3.05e10 < t < 1.9999999999999999e-38

   1. Initial program 88.5%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in a around inf 70.8%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   if 1.9999999999999999e-38 < t < 1.5499999999999999e-15

   1. Initial program 65.1%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in x around -inf 84.5%

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

   6. Taylor expanded in t around inf 85.3%

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

   7. Taylor expanded in t around -inf 99.7%

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

   if 1.5499999999999999e-15 < t < 3.20000000000000005e123

   1. Initial program 80.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.4%

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

      3. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around inf 80.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -30500000000:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-15}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+123}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+98}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+98)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t -3e-165)
     (-
      (/ (* y (- z t)) (- a t))
      (* x (+ (/ z (- a t)) (- -1.0 (/ t (- a t))))))
     (if (<= t 1.7e+119)
       (+ x (/ (- z t) (/ (- a t) (- y x))))
       (+ y (/ (- x y) (/ t (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+98) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= -3e-165) {
		tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
	} else if (t <= 1.7e+119) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.2d+98)) then
        tmp = y + ((y - x) * ((a - z) / t))
    else if (t <= (-3d-165)) then
        tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + ((-1.0d0) - (t / (a - t)))))
    else if (t <= 1.7d+119) then
        tmp = x + ((z - t) / ((a - t) / (y - x)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+98) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= -3e-165) {
		tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
	} else if (t <= 1.7e+119) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+98:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t <= -3e-165:
		tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))))
	elif t <= 1.7e+119:
		tmp = x + ((z - t) / ((a - t) / (y - x)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+98)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= -3e-165)
		tmp = Float64(Float64(Float64(y * Float64(z - t)) / Float64(a - t)) - Float64(x * Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t))))));
	elseif (t <= 1.7e+119)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(y - x))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e+98)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t <= -3e-165)
		tmp = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
	elseif (t <= 1.7e+119)
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+98], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-165], N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+119], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.20000000000000053e98

   1. Initial program 36.4%

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

      1. associate-*l/ 43.5%

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

   3. Simplified 43.5%

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

   5. Taylor expanded in t around inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate-*r/ 70.2%

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

      3. associate-*r/ 70.2%

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

      4. div-sub 70.2%

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

      5. distribute-lft-out-- 70.2%

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

      6. associate-*r/ 70.2%

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

      7. mul-1-neg 70.2%

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

      8. unsub-neg 70.2%

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

      9. distribute-rgt-out-- 72.6%

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

      10. associate-/l* 95.2%

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

   7. Simplified 95.2%

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

      1. div-inv 95.1%

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

      2. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -9.20000000000000053e98 < t < -2.99999999999999979e-165

   1. Initial program 78.7%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in x around -inf 92.6%

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

   if -2.99999999999999979e-165 < t < 1.70000000000000007e119

   1. Initial program 86.9%

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

      1. *-commutative 92.0%

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

      2. clear-num 92.0%

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

      3. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   if 1.70000000000000007e119 < t

   1. Initial program 28.9%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. mul-1-neg 68.3%

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

      8. unsub-neg 68.3%

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

      9. distribute-rgt-out-- 68.5%

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

      10. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+98}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -6000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-15} \lor \neg \left(t \leq 6.8 \cdot 10^{+112}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -6000000000.0)
     t_1
     (if (<= t 2.15e-70)
       (- x (/ (- x y) (/ a (- z t))))
       (if (or (<= t 1.5e-15) (not (<= t 6.8e+112)))
         t_1
         (+ x (/ (- z t) (/ (- a t) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -6000000000.0) {
		tmp = t_1;
	} else if (t <= 2.15e-70) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if ((t <= 1.5e-15) || !(t <= 6.8e+112)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) / ((a - t) / 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 = y + ((y - x) * ((a - z) / t))
    if (t <= (-6000000000.0d0)) then
        tmp = t_1
    else if (t <= 2.15d-70) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if ((t <= 1.5d-15) .or. (.not. (t <= 6.8d+112))) then
        tmp = t_1
    else
        tmp = x + ((z - t) / ((a - t) / 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 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -6000000000.0) {
		tmp = t_1;
	} else if (t <= 2.15e-70) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if ((t <= 1.5e-15) || !(t <= 6.8e+112)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -6000000000.0:
		tmp = t_1
	elif t <= 2.15e-70:
		tmp = x - ((x - y) / (a / (z - t)))
	elif (t <= 1.5e-15) or not (t <= 6.8e+112):
		tmp = t_1
	else:
		tmp = x + ((z - t) / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -6000000000.0)
		tmp = t_1;
	elseif (t <= 2.15e-70)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif ((t <= 1.5e-15) || !(t <= 6.8e+112))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -6000000000.0)
		tmp = t_1;
	elseif (t <= 2.15e-70)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif ((t <= 1.5e-15) || ~((t <= 6.8e+112)))
		tmp = t_1;
	else
		tmp = x + ((z - t) / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6000000000.0], t$95$1, If[LessEqual[t, 2.15e-70], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.5e-15], N[Not[LessEqual[t, 6.8e+112]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e9 or 2.15e-70 < t < 1.5e-15 or 6.79999999999999987e112 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in t around inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. associate-*r/ 70.3%

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

      3. associate-*r/ 70.3%

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

      4. div-sub 70.3%

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

      5. distribute-lft-out-- 70.3%

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

      6. associate-*r/ 70.3%

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

      7. mul-1-neg 70.3%

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

      8. unsub-neg 70.3%

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

      9. distribute-rgt-out-- 71.3%

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

      10. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

      1. div-inv 90.5%

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

      2. clear-num 90.5%

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

   9. Applied egg-rr 90.5%

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

   if -6e9 < t < 2.15e-70

   1. Initial program 88.0%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 71.9%

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

      1. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   if 1.5e-15 < t < 6.79999999999999987e112

   1. Initial program 80.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.4%

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

      3. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around inf 80.5%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6000000000:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-15} \lor \neg \left(t \leq 6.8 \cdot 10^{+112}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -31000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -31000000000.0)
     t_1
     (if (<= t 4.3e-70)
       (- x (/ (- x y) (/ a (- z t))))
       (if (<= t 3.6e-15)
         t_1
         (if (<= t 8.6e+114)
           (+ x (/ (- z t) (/ (- a t) y)))
           (+ y (/ (- x y) (/ t (- z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -31000000000.0) {
		tmp = t_1;
	} else if (t <= 4.3e-70) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 3.6e-15) {
		tmp = t_1;
	} else if (t <= 8.6e+114) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((y - x) * ((a - z) / t))
    if (t <= (-31000000000.0d0)) then
        tmp = t_1
    else if (t <= 4.3d-70) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (t <= 3.6d-15) then
        tmp = t_1
    else if (t <= 8.6d+114) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -31000000000.0) {
		tmp = t_1;
	} else if (t <= 4.3e-70) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 3.6e-15) {
		tmp = t_1;
	} else if (t <= 8.6e+114) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -31000000000.0:
		tmp = t_1
	elif t <= 4.3e-70:
		tmp = x - ((x - y) / (a / (z - t)))
	elif t <= 3.6e-15:
		tmp = t_1
	elif t <= 8.6e+114:
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -31000000000.0)
		tmp = t_1;
	elseif (t <= 4.3e-70)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (t <= 3.6e-15)
		tmp = t_1;
	elseif (t <= 8.6e+114)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -31000000000.0)
		tmp = t_1;
	elseif (t <= 4.3e-70)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (t <= 3.6e-15)
		tmp = t_1;
	elseif (t <= 8.6e+114)
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -31000000000.0], t$95$1, If[LessEqual[t, 4.3e-70], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-15], t$95$1, If[LessEqual[t, 8.6e+114], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.1e10 or 4.3e-70 < t < 3.6000000000000001e-15

   1. Initial program 52.7%

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

      1. associate-*l/ 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in t around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-*r/ 71.2%

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

      3. associate-*r/ 71.2%

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

      4. div-sub 71.2%

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

      5. distribute-lft-out-- 71.2%

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

      6. associate-*r/ 71.2%

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

      7. mul-1-neg 71.2%

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

      8. unsub-neg 71.2%

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

      9. distribute-rgt-out-- 72.5%

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

      10. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

      1. div-inv 87.5%

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

      2. clear-num 87.6%

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

   9. Applied egg-rr 87.6%

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

   if -3.1e10 < t < 4.3e-70

   1. Initial program 88.0%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 71.9%

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

      1. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   if 3.6000000000000001e-15 < t < 8.6000000000000001e114

   1. Initial program 80.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.4%

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

      3. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around inf 80.5%

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

   if 8.6000000000000001e114 < t

   1. Initial program 28.9%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. mul-1-neg 68.3%

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

      8. unsub-neg 68.3%

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

      9. distribute-rgt-out-- 68.5%

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

      10. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -31000000000:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+38}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+152)
   y
   (if (<= t -1.08e+38)
     (* (- z a) (/ x t))
     (if (<= t -7.6e+20) y (if (<= t 1.02e+30) (* x (- 1.0 (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+152) {
		tmp = y;
	} else if (t <= -1.08e+38) {
		tmp = (z - a) * (x / t);
	} else if (t <= -7.6e+20) {
		tmp = y;
	} else if (t <= 1.02e+30) {
		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 <= (-1.35d+152)) then
        tmp = y
    else if (t <= (-1.08d+38)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-7.6d+20)) then
        tmp = y
    else if (t <= 1.02d+30) 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 <= -1.35e+152) {
		tmp = y;
	} else if (t <= -1.08e+38) {
		tmp = (z - a) * (x / t);
	} else if (t <= -7.6e+20) {
		tmp = y;
	} else if (t <= 1.02e+30) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+152:
		tmp = y
	elif t <= -1.08e+38:
		tmp = (z - a) * (x / t)
	elif t <= -7.6e+20:
		tmp = y
	elif t <= 1.02e+30:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+152)
		tmp = y;
	elseif (t <= -1.08e+38)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -7.6e+20)
		tmp = y;
	elseif (t <= 1.02e+30)
		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 <= -1.35e+152)
		tmp = y;
	elseif (t <= -1.08e+38)
		tmp = (z - a) * (x / t);
	elseif (t <= -7.6e+20)
		tmp = y;
	elseif (t <= 1.02e+30)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+152], y, If[LessEqual[t, -1.08e+38], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.6e+20], y, If[LessEqual[t, 1.02e+30], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000007e152 or -1.07999999999999995e38 < t < -7.6e20 or 1.02e30 < t

   1. Initial program 39.0%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in t around inf 61.2%

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

   if -1.35000000000000007e152 < t < -1.07999999999999995e38

   1. Initial program 66.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. div-sub 64.9%

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

      5. distribute-lft-out-- 64.9%

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

      6. associate-*r/ 64.9%

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

      7. mul-1-neg 64.9%

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

      8. unsub-neg 64.9%

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

      9. distribute-rgt-out-- 64.9%

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

      10. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 48.6%

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

   10. Simplified 48.6%

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

   if -7.6e20 < t < 1.02e30

   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/ 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around 0 64.4%

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

      1. associate-/l* 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in x around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

   10. Simplified 57.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+38}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-178}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ x (/ t z)))))
   (if (<= a -6.5e+69)
     (+ x (/ y (/ a z)))
     (if (<= a 8.2e-220)
       t_1
       (if (<= a 1.95e-178)
         (/ y (/ (- a t) z))
         (if (<= a 1.3e+119) t_1 (- x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x / (t / z));
	double tmp;
	if (a <= -6.5e+69) {
		tmp = x + (y / (a / z));
	} else if (a <= 8.2e-220) {
		tmp = t_1;
	} else if (a <= 1.95e-178) {
		tmp = y / ((a - t) / z);
	} else if (a <= 1.3e+119) {
		tmp = t_1;
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x / (t / z))
    if (a <= (-6.5d+69)) then
        tmp = x + (y / (a / z))
    else if (a <= 8.2d-220) then
        tmp = t_1
    else if (a <= 1.95d-178) then
        tmp = y / ((a - t) / z)
    else if (a <= 1.3d+119) then
        tmp = t_1
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x / (t / z));
	double tmp;
	if (a <= -6.5e+69) {
		tmp = x + (y / (a / z));
	} else if (a <= 8.2e-220) {
		tmp = t_1;
	} else if (a <= 1.95e-178) {
		tmp = y / ((a - t) / z);
	} else if (a <= 1.3e+119) {
		tmp = t_1;
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x / (t / z))
	tmp = 0
	if a <= -6.5e+69:
		tmp = x + (y / (a / z))
	elif a <= 8.2e-220:
		tmp = t_1
	elif a <= 1.95e-178:
		tmp = y / ((a - t) / z)
	elif a <= 1.3e+119:
		tmp = t_1
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x / Float64(t / z)))
	tmp = 0.0
	if (a <= -6.5e+69)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= 8.2e-220)
		tmp = t_1;
	elseif (a <= 1.95e-178)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (a <= 1.3e+119)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x / (t / z));
	tmp = 0.0;
	if (a <= -6.5e+69)
		tmp = x + (y / (a / z));
	elseif (a <= 8.2e-220)
		tmp = t_1;
	elseif (a <= 1.95e-178)
		tmp = y / ((a - t) / z);
	elseif (a <= 1.3e+119)
		tmp = t_1;
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+69], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-220], t$95$1, If[LessEqual[a, 1.95e-178], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+119], t$95$1, N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.5000000000000001e69

   1. Initial program 75.6%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 75.1%

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

   6. Taylor expanded in y around inf 69.8%

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

   7. Taylor expanded in z around inf 63.3%

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

      1. associate-/l* 68.0%

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

   9. Simplified 68.0%

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

   if -6.5000000000000001e69 < a < 8.19999999999999982e-220 or 1.95000000000000013e-178 < a < 1.3e119

   1. Initial program 64.3%

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

      1. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in x around -inf 76.9%

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

   6. Taylor expanded in t around inf 79.1%

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

   7. Taylor expanded in a around 0 63.2%

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

      1. associate-/l* 67.6%

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

   9. Simplified 67.6%

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

   if 8.19999999999999982e-220 < a < 1.95000000000000013e-178

   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 x around -inf 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 100.0%

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

       1. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if 1.3e119 < a

   1. Initial program 67.1%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 75.7%

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

   6. Taylor expanded in y around inf 67.0%

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

   7. Taylor expanded in z around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

      3. associate-*r/ 63.9%

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

   9. Simplified 63.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-220}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-178}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+119}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+132}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+16)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 2e+132)
     (- x (* (- z t) (/ (- x y) (- a t))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+16) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 2e+132) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.22d+16)) then
        tmp = y + ((y - x) * ((a - z) / t))
    else if (t <= 2d+132) then
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+16) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 2e+132) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e+16:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t <= 2e+132:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+16)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 2e+132)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e+16)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t <= 2e+132)
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+16], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+132], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e16

   1. Initial program 46.8%

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

      1. associate-*l/ 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.1%

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

      5. distribute-lft-out-- 70.1%

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

      6. associate-*r/ 70.1%

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

      7. mul-1-neg 70.1%

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

      8. unsub-neg 70.1%

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

      9. distribute-rgt-out-- 71.6%

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

      10. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

      1. div-inv 89.5%

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

      2. clear-num 89.6%

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

   9. Applied egg-rr 89.6%

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

   if -1.22e16 < t < 1.99999999999999998e132

   1. Initial program 86.1%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   if 1.99999999999999998e132 < t

   1. Initial program 28.9%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. mul-1-neg 68.3%

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

      8. unsub-neg 68.3%

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

      9. distribute-rgt-out-- 68.5%

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

      10. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+132}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+16)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 6e+124)
     (+ x (/ (- z t) (/ (- a t) (- y x))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+16) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 6e+124) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.22d+16)) then
        tmp = y + ((y - x) * ((a - z) / t))
    else if (t <= 6d+124) then
        tmp = x + ((z - t) / ((a - t) / (y - x)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+16) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 6e+124) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e+16:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t <= 6e+124:
		tmp = x + ((z - t) / ((a - t) / (y - x)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+16)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 6e+124)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(y - x))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e+16)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t <= 6e+124)
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+16], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+124], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e16

   1. Initial program 46.8%

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

      1. associate-*l/ 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.1%

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

      5. distribute-lft-out-- 70.1%

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

      6. associate-*r/ 70.1%

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

      7. mul-1-neg 70.1%

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

      8. unsub-neg 70.1%

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

      9. distribute-rgt-out-- 71.6%

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

      10. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

      1. div-inv 89.5%

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

      2. clear-num 89.6%

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

   9. Applied egg-rr 89.6%

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

   if -1.22e16 < t < 5.9999999999999999e124

   1. Initial program 86.1%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

      1. *-commutative 89.2%

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

      2. clear-num 89.1%

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

      3. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   if 5.9999999999999999e124 < t

   1. Initial program 28.9%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. mul-1-neg 68.3%

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

      8. unsub-neg 68.3%

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

      9. distribute-rgt-out-- 68.5%

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

      10. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e-9)
   y
   (if (<= t -3.6e-184)
     x
     (if (<= t 1.2e-308) (/ y (/ a z)) (if (<= t 1.85e+25) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e-9) {
		tmp = y;
	} else if (t <= -3.6e-184) {
		tmp = x;
	} else if (t <= 1.2e-308) {
		tmp = y / (a / z);
	} else if (t <= 1.85e+25) {
		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 <= (-2d-9)) then
        tmp = y
    else if (t <= (-3.6d-184)) then
        tmp = x
    else if (t <= 1.2d-308) then
        tmp = y / (a / z)
    else if (t <= 1.85d+25) 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 <= -2e-9) {
		tmp = y;
	} else if (t <= -3.6e-184) {
		tmp = x;
	} else if (t <= 1.2e-308) {
		tmp = y / (a / z);
	} else if (t <= 1.85e+25) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e-9:
		tmp = y
	elif t <= -3.6e-184:
		tmp = x
	elif t <= 1.2e-308:
		tmp = y / (a / z)
	elif t <= 1.85e+25:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e-9)
		tmp = y;
	elseif (t <= -3.6e-184)
		tmp = x;
	elseif (t <= 1.2e-308)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.85e+25)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e-9)
		tmp = y;
	elseif (t <= -3.6e-184)
		tmp = x;
	elseif (t <= 1.2e-308)
		tmp = y / (a / z);
	elseif (t <= 1.85e+25)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e-9], y, If[LessEqual[t, -3.6e-184], x, If[LessEqual[t, 1.2e-308], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+25], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.00000000000000012e-9 or 1.8499999999999999e25 < t

   1. Initial program 47.1%

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

      1. associate-*l/ 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in t around inf 51.2%

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

   if -2.00000000000000012e-9 < t < -3.6000000000000001e-184 or 1.1999999999999998e-308 < t < 1.8499999999999999e25

   1. Initial program 86.1%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in a around inf 42.3%

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

   if -3.6000000000000001e-184 < t < 1.1999999999999998e-308

   1. Initial program 91.0%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 90.8%

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

   6. Taylor expanded in x around 0 58.5%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in t around 0 31.2%

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

       1. associate-/l* 43.0%

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

   11. Simplified 43.0%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+49} \lor \neg \left(a \leq 1.3 \cdot 10^{+119}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.5e+49) (not (<= a 1.3e+119)))
   (+ x (* (- z t) (/ (- y x) a)))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+49) || !(a <= 1.3e+119)) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.5d+49)) .or. (.not. (a <= 1.3d+119))) then
        tmp = x + ((z - t) * ((y - x) / a))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+49) || !(a <= 1.3e+119)) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.5e+49) or not (a <= 1.3e+119):
		tmp = x + ((z - t) * ((y - x) / a))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.5e+49) || !(a <= 1.3e+119))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.5e+49) || ~((a <= 1.3e+119)))
		tmp = x + ((z - t) * ((y - x) / a));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.5e+49], N[Not[LessEqual[a, 1.3e+119]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999982e49 or 1.3e119 < a

   1. Initial program 73.9%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in a around inf 74.6%

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

   if -4.49999999999999982e49 < a < 1.3e119

   1. Initial program 64.3%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in t around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-*r/ 69.6%

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

      3. associate-*r/ 69.6%

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

      4. div-sub 70.8%

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

      5. distribute-lft-out-- 70.8%

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

      6. associate-*r/ 70.8%

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

      7. mul-1-neg 70.8%

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

      8. unsub-neg 70.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in z around inf 77.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+49} \lor \neg \left(a \leq 1.3 \cdot 10^{+119}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+48} \lor \neg \left(a \leq 1.3 \cdot 10^{+119}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e+48) (not (<= a 1.3e+119)))
   (- x (/ (- x y) (/ a (- z t))))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+48) || !(a <= 1.3e+119)) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d+48)) .or. (.not. (a <= 1.3d+119))) then
        tmp = x - ((x - y) / (a / (z - t)))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+48) || !(a <= 1.3e+119)) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e+48) or not (a <= 1.3e+119):
		tmp = x - ((x - y) / (a / (z - t)))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e+48) || !(a <= 1.3e+119))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e+48) || ~((a <= 1.3e+119)))
		tmp = x - ((x - y) / (a / (z - t)));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e+48], N[Not[LessEqual[a, 1.3e+119]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e48 or 1.3e119 < a

   1. Initial program 73.9%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in a around inf 66.8%

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

      1. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

   if -1.9e48 < a < 1.3e119

   1. Initial program 64.3%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in t around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-*r/ 69.6%

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

      3. associate-*r/ 69.6%

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

      4. div-sub 70.8%

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

      5. distribute-lft-out-- 70.8%

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

      6. associate-*r/ 70.8%

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

      7. mul-1-neg 70.8%

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

      8. unsub-neg 70.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in z around inf 77.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+48} \lor \neg \left(a \leq 1.3 \cdot 10^{+119}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+122}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.06e+55)
   (+ x (/ z (/ a (- y x))))
   (if (<= a 1.5e+122)
     (+ y (/ (- x y) (/ t z)))
     (* x (+ 1.0 (/ (- t z) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e+55) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 1.5e+122) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x * (1.0 + ((t - 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 (a <= (-1.06d+55)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 1.5d+122) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x * (1.0d0 + ((t - 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 (a <= -1.06e+55) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 1.5e+122) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x * (1.0 + ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.06e+55:
		tmp = x + (z / (a / (y - x)))
	elif a <= 1.5e+122:
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x * (1.0 + ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e+55)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 1.5e+122)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.06e+55)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 1.5e+122)
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x * (1.0 + ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e+55], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+122], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.06000000000000004e55

   1. Initial program 77.8%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in t around 0 66.3%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   if -1.06000000000000004e55 < a < 1.49999999999999993e122

   1. Initial program 64.3%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in t around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-*r/ 69.6%

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

      3. associate-*r/ 69.6%

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

      4. div-sub 70.8%

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

      5. distribute-lft-out-- 70.8%

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

      6. associate-*r/ 70.8%

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

      7. mul-1-neg 70.8%

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

      8. unsub-neg 70.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in z around inf 77.2%

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

   if 1.49999999999999993e122 < a

   1. Initial program 67.1%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+122}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+119}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.1e+53)
   (+ x (/ z (/ a (- y x))))
   (if (<= a 1.3e+119) (+ y (/ (- x y) (/ t z))) (- x (* (/ y a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.1e+53) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 1.3e+119) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.1d+53)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 1.3d+119) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x - ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.1e+53) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 1.3e+119) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.1e+53:
		tmp = x + (z / (a / (y - x)))
	elif a <= 1.3e+119:
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x - ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.1e+53)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 1.3e+119)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.1e+53)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 1.3e+119)
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x - ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.1e+53], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+119], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.0999999999999998e53

   1. Initial program 77.8%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in t around 0 66.3%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   if -5.0999999999999998e53 < a < 1.3e119

   1. Initial program 64.3%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in t around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-*r/ 69.6%

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

      3. associate-*r/ 69.6%

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

      4. div-sub 70.8%

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

      5. distribute-lft-out-- 70.8%

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

      6. associate-*r/ 70.8%

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

      7. mul-1-neg 70.8%

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

      8. unsub-neg 70.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in z around inf 77.2%

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

   if 1.3e119 < a

   1. Initial program 67.1%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 75.7%

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

   6. Taylor expanded in y around inf 67.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+119}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+90}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e+90) y (if (<= t 7.2e+24) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+90) {
		tmp = y;
	} else if (t <= 7.2e+24) {
		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 <= (-4.8d+90)) then
        tmp = y
    else if (t <= 7.2d+24) 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 <= -4.8e+90) {
		tmp = y;
	} else if (t <= 7.2e+24) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e+90:
		tmp = y
	elif t <= 7.2e+24:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e+90)
		tmp = y;
	elseif (t <= 7.2e+24)
		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 <= -4.8e+90)
		tmp = y;
	elseif (t <= 7.2e+24)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e+90], y, If[LessEqual[t, 7.2e+24], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000002e90 or 7.19999999999999966e24 < t

   1. Initial program 41.3%

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

      1. associate-*l/ 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in t around inf 56.1%

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

   if -4.8000000000000002e90 < t < 7.19999999999999966e24

   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/ 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in x around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

   10. Simplified 55.0%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+90}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+130}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+72)
   (+ x (/ y (/ a z)))
   (if (<= a 7.4e+130) (+ y (/ x (/ t z))) (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+72) {
		tmp = x + (y / (a / z));
	} else if (a <= 7.4e+130) {
		tmp = y + (x / (t / z));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d+72)) then
        tmp = x + (y / (a / z))
    else if (a <= 7.4d+130) then
        tmp = y + (x / (t / z))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+72) {
		tmp = x + (y / (a / z));
	} else if (a <= 7.4e+130) {
		tmp = y + (x / (t / z));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+72:
		tmp = x + (y / (a / z))
	elif a <= 7.4e+130:
		tmp = y + (x / (t / z))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+72)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= 7.4e+130)
		tmp = Float64(y + Float64(x / Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+72)
		tmp = x + (y / (a / z));
	elseif (a <= 7.4e+130)
		tmp = y + (x / (t / z));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+72], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e+130], N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000002e72

   1. Initial program 75.6%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 75.1%

      \[\leadsto x + \color{blue}{\frac{y - x}{a}} \cdot \left(z - t\right) \]

   6. Taylor expanded in y around inf 69.8%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(z - t\right) \]

   7. Taylor expanded in z around inf 63.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 68.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   9. Simplified 68.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -7.0000000000000002e72 < a < 7.4000000000000003e130

   1. Initial program 65.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 77.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around inf 77.8%

      \[\leadsto -1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right) + \color{blue}{y} \]

   7. Taylor expanded in a around 0 60.8%

      \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 65.6%

         \[\leadsto y + \color{blue}{\frac{x}{\frac{t}{z}}} \]

   9. Simplified 65.6%

      \[\leadsto \color{blue}{y + \frac{x}{\frac{t}{z}}} \]

   if 7.4000000000000003e130 < a

   1. Initial program 68.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.0%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.8%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 64.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 64.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 64.5%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+130}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+119}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+73)
   (+ x (/ y (/ a z)))
   (if (<= a 6.8e+119) (+ y (/ x (/ t z))) (- x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+73) {
		tmp = x + (y / (a / z));
	} else if (a <= 6.8e+119) {
		tmp = y + (x / (t / z));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+73)) then
        tmp = x + (y / (a / z))
    else if (a <= 6.8d+119) then
        tmp = y + (x / (t / z))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+73) {
		tmp = x + (y / (a / z));
	} else if (a <= 6.8e+119) {
		tmp = y + (x / (t / z));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+73:
		tmp = x + (y / (a / z))
	elif a <= 6.8e+119:
		tmp = y + (x / (t / z))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+73)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= 6.8e+119)
		tmp = Float64(y + Float64(x / Float64(t / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+73)
		tmp = x + (y / (a / z));
	elseif (a <= 6.8e+119)
		tmp = y + (x / (t / z));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+73], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+119], N[(y + N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.90000000000000011e73

   1. Initial program 75.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 75.1%

      \[\leadsto x + \color{blue}{\frac{y - x}{a}} \cdot \left(z - t\right) \]

   6. Taylor expanded in y around inf 69.8%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(z - t\right) \]

   7. Taylor expanded in z around inf 63.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 68.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   9. Simplified 68.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -1.90000000000000011e73 < a < 6.80000000000000027e119

   1. Initial program 65.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 77.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around inf 78.1%

      \[\leadsto -1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right) + \color{blue}{y} \]

   7. Taylor expanded in a around 0 61.5%

      \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 65.8%

         \[\leadsto y + \color{blue}{\frac{x}{\frac{t}{z}}} \]

   9. Simplified 65.8%

      \[\leadsto \color{blue}{y + \frac{x}{\frac{t}{z}}} \]

   if 6.80000000000000027e119 < a

   1. Initial program 67.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 75.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{a}} \cdot \left(z - t\right) \]

   6. Taylor expanded in y around inf 67.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(z - t\right) \]

   7. Taylor expanded in z around 0 66.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.8%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a}\right)} \]

      2. unsub-neg 66.8%

         \[\leadsto \color{blue}{x - \frac{t \cdot y}{a}} \]

      3. associate-*r/ 63.9%

         \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 63.9%

      \[\leadsto \color{blue}{x - t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+119}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e-9) y (if (<= t 2.55e+26) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-9) {
		tmp = y;
	} else if (t <= 2.55e+26) {
		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 <= (-2.4d-9)) then
        tmp = y
    else if (t <= 2.55d+26) 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 <= -2.4e-9) {
		tmp = y;
	} else if (t <= 2.55e+26) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e-9:
		tmp = y
	elif t <= 2.55e+26:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e-9)
		tmp = y;
	elseif (t <= 2.55e+26)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e-9)
		tmp = y;
	elseif (t <= 2.55e+26)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e-9], y, If[LessEqual[t, 2.55e+26], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e-9 or 2.5499999999999999e26 < t

   1. Initial program 47.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 61.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 51.2%

      \[\leadsto \color{blue}{y} \]

   if -2.4e-9 < t < 2.5499999999999999e26

   1. Initial program 86.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 37.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 24.9% 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 67.6%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 75.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 75.7%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 24.8%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 24.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.5% 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 2024027 
(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))))