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

Percentage Accurate: 67.4% → 85.9%

Time: 14.1s

Alternatives: 19

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.4% 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: 85.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+178}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+274}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+178)
   (+ y (* z (/ (- x y) t)))
   (if (<= t 3.8e+274)
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (* (/ (- y x) t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+178) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 3.8e+274) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+178)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 3.8e+274)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+178], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+274], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000001e178

   1. Initial program 20.5%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-*r/ 64.0%

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

      3. associate-*r/ 64.0%

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

      4. mul-1-neg 64.0%

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

      5. div-sub 64.0%

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

      6. mul-1-neg 64.0%

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

      7. distribute-lft-out-- 64.0%

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

      8. associate-*r/ 64.0%

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

      9. mul-1-neg 64.0%

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

      10. unsub-neg 64.0%

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

      11. distribute-rgt-out-- 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around inf 68.1%

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

      1. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

   if -2.6000000000000001e178 < t < 3.7999999999999998e274

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 92.7%

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

      3. fma-define 92.8%

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

   3. Simplified 92.8%

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

   if 3.7999999999999998e274 < t

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. associate-*r/ 61.6%

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

      3. associate-*r/ 61.6%

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

      4. mul-1-neg 61.6%

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

      5. div-sub 61.6%

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

      6. mul-1-neg 61.6%

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

      7. distribute-lft-out-- 61.6%

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

      8. associate-*r/ 61.6%

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

      9. mul-1-neg 61.6%

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

      10. unsub-neg 61.6%

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

      11. distribute-rgt-out-- 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 98.7%

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

      3. distribute-lft-neg-in 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+178}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+274}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-298}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 0.00036:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.25e+181)
     t_1
     (if (<= t -2.45e+42)
       (* x (/ (- z a) t))
       (if (<= t 1.5e-298)
         (+ x (* z (/ (- y x) a)))
         (if (<= t 0.00036)
           (+ x (* y (/ z (- a t))))
           (if (<= t 3e+75)
             (* z (/ (- y x) (- a t)))
             (if (<= t 1.05e+110) (* x (- 1.0 (/ z a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.25e+181) {
		tmp = t_1;
	} else if (t <= -2.45e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.5e-298) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 0.00036) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 3e+75) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.05e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-3.25d+181)) then
        tmp = t_1
    else if (t <= (-2.45d+42)) then
        tmp = x * ((z - a) / t)
    else if (t <= 1.5d-298) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 0.00036d0) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= 3d+75) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.05d+110) then
        tmp = x * (1.0d0 - (z / 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 * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.25e+181) {
		tmp = t_1;
	} else if (t <= -2.45e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.5e-298) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 0.00036) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 3e+75) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.05e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.25e+181:
		tmp = t_1
	elif t <= -2.45e+42:
		tmp = x * ((z - a) / t)
	elif t <= 1.5e-298:
		tmp = x + (z * ((y - x) / a))
	elif t <= 0.00036:
		tmp = x + (y * (z / (a - t)))
	elif t <= 3e+75:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.05e+110:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.25e+181)
		tmp = t_1;
	elseif (t <= -2.45e+42)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 1.5e-298)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 0.00036)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= 3e+75)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.05e+110)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.25e+181)
		tmp = t_1;
	elseif (t <= -2.45e+42)
		tmp = x * ((z - a) / t);
	elseif (t <= 1.5e-298)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 0.00036)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= 3e+75)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.05e+110)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.25e+181], t$95$1, If[LessEqual[t, -2.45e+42], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-298], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00036], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+75], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+110], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.25e181 or 1.05000000000000007e110 < t

   1. Initial program 27.7%

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

      1. div-inv 27.7%

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

      2. *-commutative 27.7%

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

      3. associate-*l* 65.5%

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

   4. Applied egg-rr 65.5%

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

   5. Taylor expanded in x around 0 36.9%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -3.25e181 < t < -2.4500000000000001e42

   1. Initial program 68.0%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-in 59.0%

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

      3. +-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 67.3%

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

      3. neg-mul-1 67.3%

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

      4. sub-neg 67.3%

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

   8. Simplified 67.3%

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

   if -2.4500000000000001e42 < t < 1.5e-298

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   if 1.5e-298 < t < 3.60000000000000023e-4

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around inf 74.9%

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

      1. associate-/l* 82.5%

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

   8. Simplified 82.5%

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

   if 3.60000000000000023e-4 < t < 3e75

   1. Initial program 99.0%

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

      1. associate-/l* 99.5%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. div-sub 99.5%

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

   7. Simplified 99.5%

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

   if 3e75 < t < 1.05000000000000007e110

   1. Initial program 84.8%

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

   3. Taylor expanded in x around -inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. distribute-rgt-neg-in 55.7%

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

      3. +-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 57.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-298}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 0.00036:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -3.5e-39)
     t_2
     (if (<= y -1.65e-102)
       t_1
       (if (<= y -1.52e-146)
         (/ (* x (- z a)) t)
         (if (<= y 5.8e-224)
           t_1
           (if (<= y 3.6e-152)
             (* x (/ (- z a) t))
             (if (<= y 8e+130) (+ x (/ (* y z) a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.5e-39) {
		tmp = t_2;
	} else if (y <= -1.65e-102) {
		tmp = t_1;
	} else if (y <= -1.52e-146) {
		tmp = (x * (z - a)) / t;
	} else if (y <= 5.8e-224) {
		tmp = t_1;
	} else if (y <= 3.6e-152) {
		tmp = x * ((z - a) / t);
	} else if (y <= 8e+130) {
		tmp = x + ((y * z) / 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 = x * (1.0d0 - (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-3.5d-39)) then
        tmp = t_2
    else if (y <= (-1.65d-102)) then
        tmp = t_1
    else if (y <= (-1.52d-146)) then
        tmp = (x * (z - a)) / t
    else if (y <= 5.8d-224) then
        tmp = t_1
    else if (y <= 3.6d-152) then
        tmp = x * ((z - a) / t)
    else if (y <= 8d+130) then
        tmp = x + ((y * z) / 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 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.5e-39) {
		tmp = t_2;
	} else if (y <= -1.65e-102) {
		tmp = t_1;
	} else if (y <= -1.52e-146) {
		tmp = (x * (z - a)) / t;
	} else if (y <= 5.8e-224) {
		tmp = t_1;
	} else if (y <= 3.6e-152) {
		tmp = x * ((z - a) / t);
	} else if (y <= 8e+130) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -3.5e-39:
		tmp = t_2
	elif y <= -1.65e-102:
		tmp = t_1
	elif y <= -1.52e-146:
		tmp = (x * (z - a)) / t
	elif y <= 5.8e-224:
		tmp = t_1
	elif y <= 3.6e-152:
		tmp = x * ((z - a) / t)
	elif y <= 8e+130:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -3.5e-39)
		tmp = t_2;
	elseif (y <= -1.65e-102)
		tmp = t_1;
	elseif (y <= -1.52e-146)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (y <= 5.8e-224)
		tmp = t_1;
	elseif (y <= 3.6e-152)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (y <= 8e+130)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -3.5e-39)
		tmp = t_2;
	elseif (y <= -1.65e-102)
		tmp = t_1;
	elseif (y <= -1.52e-146)
		tmp = (x * (z - a)) / t;
	elseif (y <= 5.8e-224)
		tmp = t_1;
	elseif (y <= 3.6e-152)
		tmp = x * ((z - a) / t);
	elseif (y <= 8e+130)
		tmp = x + ((y * z) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-39], t$95$2, If[LessEqual[y, -1.65e-102], t$95$1, If[LessEqual[y, -1.52e-146], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 5.8e-224], t$95$1, If[LessEqual[y, 3.6e-152], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+130], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.5e-39 or 8.0000000000000005e130 < y

   1. Initial program 61.0%

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

      1. div-inv 60.9%

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

      2. *-commutative 60.9%

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

      3. associate-*l* 90.8%

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

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in x around 0 48.3%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   if -3.5e-39 < y < -1.65e-102 or -1.52000000000000011e-146 < y < 5.8000000000000001e-224

   1. Initial program 81.5%

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

   3. Taylor expanded in x around -inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-in 78.1%

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

      3. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around 0 64.1%

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

   if -1.65e-102 < y < -1.52000000000000011e-146

   1. Initial program 61.1%

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

   3. Taylor expanded in x around -inf 43.1%

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

      1. mul-1-neg 43.1%

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

      2. distribute-rgt-neg-in 43.1%

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

      3. +-commutative 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in t around -inf 61.0%

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

   if 5.8000000000000001e-224 < y < 3.6e-152

   1. Initial program 59.4%

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

   3. Taylor expanded in x around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. +-commutative 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-/l* 64.5%

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

      3. neg-mul-1 64.5%

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

      4. sub-neg 64.5%

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

   8. Simplified 64.5%

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

   if 3.6e-152 < y < 8.0000000000000005e130

   1. Initial program 80.1%

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

   3. Taylor expanded in y around inf 71.0%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around 0 52.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t \leq -8.1 \cdot 10^{+102}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t -8.1e+102)
     (+ y (* z (/ (- x y) t)))
     (if (<= t -4.4e-110)
       t_1
       (if (<= t 7.8e-153)
         (+ x (* z (/ (- y x) (- a t))))
         (if (<= t 1.7e+110)
           t_1
           (if (<= t 3.3e+274)
             (- x (* y (/ (- z t) (- t a))))
             (+ y (* (/ (- y x) t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t <= -8.1e+102) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -4.4e-110) {
		tmp = t_1;
	} else if (t <= 7.8e-153) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.7e+110) {
		tmp = t_1;
	} else if (t <= 3.3e+274) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t <= (-8.1d+102)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= (-4.4d-110)) then
        tmp = t_1
    else if (t <= 7.8d-153) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 1.7d+110) then
        tmp = t_1
    else if (t <= 3.3d+274) then
        tmp = x - (y * ((z - t) / (t - a)))
    else
        tmp = y + (((y - x) / t) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t <= -8.1e+102) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -4.4e-110) {
		tmp = t_1;
	} else if (t <= 7.8e-153) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.7e+110) {
		tmp = t_1;
	} else if (t <= 3.3e+274) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t <= -8.1e+102:
		tmp = y + (z * ((x - y) / t))
	elif t <= -4.4e-110:
		tmp = t_1
	elif t <= 7.8e-153:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 1.7e+110:
		tmp = t_1
	elif t <= 3.3e+274:
		tmp = x - (y * ((z - t) / (t - a)))
	else:
		tmp = y + (((y - x) / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t <= -8.1e+102)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= -4.4e-110)
		tmp = t_1;
	elseif (t <= 7.8e-153)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 1.7e+110)
		tmp = t_1;
	elseif (t <= 3.3e+274)
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t <= -8.1e+102)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= -4.4e-110)
		tmp = t_1;
	elseif (t <= 7.8e-153)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 1.7e+110)
		tmp = t_1;
	elseif (t <= 3.3e+274)
		tmp = x - (y * ((z - t) / (t - a)));
	else
		tmp = y + (((y - x) / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.1e+102], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-110], t$95$1, If[LessEqual[t, 7.8e-153], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+110], t$95$1, If[LessEqual[t, 3.3e+274], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.10000000000000037e102

   1. Initial program 28.4%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. associate-*r/ 63.4%

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

      3. associate-*r/ 63.4%

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

      4. mul-1-neg 63.4%

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

      5. div-sub 63.4%

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

      6. mul-1-neg 63.4%

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

      7. distribute-lft-out-- 63.4%

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

      8. associate-*r/ 63.4%

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

      9. mul-1-neg 63.4%

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

      10. unsub-neg 63.4%

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

      11. distribute-rgt-out-- 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in z around inf 64.3%

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

      1. associate-/l* 78.3%

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

   8. Simplified 78.3%

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

   if -8.10000000000000037e102 < t < -4.3999999999999999e-110 or 7.8000000000000004e-153 < t < 1.7000000000000001e110

   1. Initial program 90.1%

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

   if -4.3999999999999999e-110 < t < 7.8000000000000004e-153

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 96.3%

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

   5. Simplified 96.3%

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

   if 1.7000000000000001e110 < t < 3.30000000000000014e274

   1. Initial program 39.6%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if 3.30000000000000014e274 < t

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. associate-*r/ 61.6%

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

      3. associate-*r/ 61.6%

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

      4. mul-1-neg 61.6%

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

      5. div-sub 61.6%

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

      6. mul-1-neg 61.6%

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

      7. distribute-lft-out-- 61.6%

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

      8. associate-*r/ 61.6%

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

      9. mul-1-neg 61.6%

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

      10. unsub-neg 61.6%

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

      11. distribute-rgt-out-- 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 98.7%

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

      3. distribute-lft-neg-in 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+102}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ z (- a t))))))
   (if (<= t -1.4e+182)
     t_1
     (if (<= t -1.05e+42)
       (* x (/ (- z a) t))
       (if (<= t -1.32e-166)
         t_2
         (if (<= t -4e-301)
           (* z (/ (- y x) (- a t)))
           (if (<= t 8e+114) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.4e+182) {
		tmp = t_1;
	} else if (t <= -1.05e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.32e-166) {
		tmp = t_2;
	} else if (t <= -4e-301) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 8e+114) {
		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 = y * ((z - t) / (a - t))
    t_2 = x + (y * (z / (a - t)))
    if (t <= (-1.4d+182)) then
        tmp = t_1
    else if (t <= (-1.05d+42)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.32d-166)) then
        tmp = t_2
    else if (t <= (-4d-301)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 8d+114) 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 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.4e+182) {
		tmp = t_1;
	} else if (t <= -1.05e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.32e-166) {
		tmp = t_2;
	} else if (t <= -4e-301) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 8e+114) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * (z / (a - t)))
	tmp = 0
	if t <= -1.4e+182:
		tmp = t_1
	elif t <= -1.05e+42:
		tmp = x * ((z - a) / t)
	elif t <= -1.32e-166:
		tmp = t_2
	elif t <= -4e-301:
		tmp = z * ((y - x) / (a - t))
	elif t <= 8e+114:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.4e+182)
		tmp = t_1;
	elseif (t <= -1.05e+42)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.32e-166)
		tmp = t_2;
	elseif (t <= -4e-301)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 8e+114)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (t <= -1.4e+182)
		tmp = t_1;
	elseif (t <= -1.05e+42)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.32e-166)
		tmp = t_2;
	elseif (t <= -4e-301)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 8e+114)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+182], t$95$1, If[LessEqual[t, -1.05e+42], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.32e-166], t$95$2, If[LessEqual[t, -4e-301], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+114], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.40000000000000003e182 or 8e114 < t

   1. Initial program 27.0%

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

      1. div-inv 27.0%

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

      2. *-commutative 27.0%

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

      3. associate-*l* 66.0%

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

   4. Applied egg-rr 66.0%

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

   5. Taylor expanded in x around 0 36.5%

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

      1. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

   if -1.40000000000000003e182 < t < -1.04999999999999998e42

   1. Initial program 69.5%

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

   3. Taylor expanded in x around -inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-rgt-neg-in 60.8%

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

      3. +-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in t around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. associate-/l* 68.8%

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

      3. neg-mul-1 68.8%

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

      4. sub-neg 68.8%

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

   8. Simplified 68.8%

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

   if -1.04999999999999998e42 < t < -1.31999999999999998e-166 or -4.00000000000000027e-301 < t < 8e114

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 76.6%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 71.6%

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

   8. Simplified 71.6%

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

   if -1.31999999999999998e-166 < t < -4.00000000000000027e-301

   1. Initial program 90.1%

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

      1. associate-/l* 96.6%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 65.5%

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

      1. div-sub 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-166}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -1.75e+181)
     y
     (if (<= t -1.9e+42)
       (* x (/ (- z a) t))
       (if (<= t -5.6e-255)
         t_1
         (if (<= t -2.6e-305)
           (* x (- 1.0 (/ z a)))
           (if (<= t 6.2e+115) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.75e+181) {
		tmp = y;
	} else if (t <= -1.9e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.6e-255) {
		tmp = t_1;
	} else if (t <= -2.6e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+115) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-1.75d+181)) then
        tmp = y
    else if (t <= (-1.9d+42)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-5.6d-255)) then
        tmp = t_1
    else if (t <= (-2.6d-305)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6.2d+115) 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 * (z / a));
	double tmp;
	if (t <= -1.75e+181) {
		tmp = y;
	} else if (t <= -1.9e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.6e-255) {
		tmp = t_1;
	} else if (t <= -2.6e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+115) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -1.75e+181:
		tmp = y
	elif t <= -1.9e+42:
		tmp = x * ((z - a) / t)
	elif t <= -5.6e-255:
		tmp = t_1
	elif t <= -2.6e-305:
		tmp = x * (1.0 - (z / a))
	elif t <= 6.2e+115:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.75e+181)
		tmp = y;
	elseif (t <= -1.9e+42)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -5.6e-255)
		tmp = t_1;
	elseif (t <= -2.6e-305)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.2e+115)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.75e+181)
		tmp = y;
	elseif (t <= -1.9e+42)
		tmp = x * ((z - a) / t);
	elseif (t <= -5.6e-255)
		tmp = t_1;
	elseif (t <= -2.6e-305)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6.2e+115)
		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[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+181], y, If[LessEqual[t, -1.9e+42], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e-255], t$95$1, If[LessEqual[t, -2.6e-305], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+115], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75000000000000004e181 or 6.2000000000000001e115 < t

   1. Initial program 27.0%

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

   3. Taylor expanded in t around inf 58.4%

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

   if -1.75000000000000004e181 < t < -1.8999999999999999e42

   1. Initial program 68.0%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-in 59.0%

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

      3. +-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 67.3%

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

      3. neg-mul-1 67.3%

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

      4. sub-neg 67.3%

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

   8. Simplified 67.3%

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

   if -1.8999999999999999e42 < t < -5.60000000000000023e-255 or -2.6000000000000002e-305 < t < 6.2000000000000001e115

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 64.3%

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

   if -5.60000000000000023e-255 < t < -2.6000000000000002e-305

   1. Initial program 92.0%

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

   3. Taylor expanded in x around -inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-in 84.6%

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

      3. +-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 84.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-255}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -5.8e+172)
     y
     (if (<= t -2.4e+42)
       (* x (/ z t))
       (if (<= t -5.5e-255)
         t_1
         (if (<= t -1.2e-305)
           (* x (- 1.0 (/ z a)))
           (if (<= t 6.2e+115) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -5.8e+172) {
		tmp = y;
	} else if (t <= -2.4e+42) {
		tmp = x * (z / t);
	} else if (t <= -5.5e-255) {
		tmp = t_1;
	} else if (t <= -1.2e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+115) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-5.8d+172)) then
        tmp = y
    else if (t <= (-2.4d+42)) then
        tmp = x * (z / t)
    else if (t <= (-5.5d-255)) then
        tmp = t_1
    else if (t <= (-1.2d-305)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6.2d+115) 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 * (z / a));
	double tmp;
	if (t <= -5.8e+172) {
		tmp = y;
	} else if (t <= -2.4e+42) {
		tmp = x * (z / t);
	} else if (t <= -5.5e-255) {
		tmp = t_1;
	} else if (t <= -1.2e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+115) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -5.8e+172:
		tmp = y
	elif t <= -2.4e+42:
		tmp = x * (z / t)
	elif t <= -5.5e-255:
		tmp = t_1
	elif t <= -1.2e-305:
		tmp = x * (1.0 - (z / a))
	elif t <= 6.2e+115:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -5.8e+172)
		tmp = y;
	elseif (t <= -2.4e+42)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= -5.5e-255)
		tmp = t_1;
	elseif (t <= -1.2e-305)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.2e+115)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -5.8e+172)
		tmp = y;
	elseif (t <= -2.4e+42)
		tmp = x * (z / t);
	elseif (t <= -5.5e-255)
		tmp = t_1;
	elseif (t <= -1.2e-305)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6.2e+115)
		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[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+172], y, If[LessEqual[t, -2.4e+42], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-255], t$95$1, If[LessEqual[t, -1.2e-305], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+115], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.7999999999999999e172 or 6.2000000000000001e115 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -5.7999999999999999e172 < t < -2.3999999999999999e42

   1. Initial program 71.2%

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

   3. Taylor expanded in x around -inf 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-rgt-neg-in 61.8%

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

      3. +-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in a around 0 47.9%

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

      1. associate-/l* 52.5%

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

   8. Simplified 52.5%

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

   if -2.3999999999999999e42 < t < -5.5000000000000003e-255 or -1.2000000000000001e-305 < t < 6.2000000000000001e115

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 64.3%

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

   if -5.5000000000000003e-255 < t < -1.2000000000000001e-305

   1. Initial program 92.0%

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

   3. Taylor expanded in x around -inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-in 84.6%

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

      3. +-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 84.6%

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

Alternative 8: 45.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.7e+172)
     y
     (if (<= t -3e+87)
       (* x (/ z t))
       (if (<= t 2.6e-280)
         t_1
         (if (<= t 3.65e-159)
           (* y (/ z (- a t)))
           (if (<= t 4.6e+114) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.7e+172) {
		tmp = y;
	} else if (t <= -3e+87) {
		tmp = x * (z / t);
	} else if (t <= 2.6e-280) {
		tmp = t_1;
	} else if (t <= 3.65e-159) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.6e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.7d+172)) then
        tmp = y
    else if (t <= (-3d+87)) then
        tmp = x * (z / t)
    else if (t <= 2.6d-280) then
        tmp = t_1
    else if (t <= 3.65d-159) then
        tmp = y * (z / (a - t))
    else if (t <= 4.6d+114) 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 * (1.0 - (z / a));
	double tmp;
	if (t <= -1.7e+172) {
		tmp = y;
	} else if (t <= -3e+87) {
		tmp = x * (z / t);
	} else if (t <= 2.6e-280) {
		tmp = t_1;
	} else if (t <= 3.65e-159) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.6e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.7e+172:
		tmp = y
	elif t <= -3e+87:
		tmp = x * (z / t)
	elif t <= 2.6e-280:
		tmp = t_1
	elif t <= 3.65e-159:
		tmp = y * (z / (a - t))
	elif t <= 4.6e+114:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.7e+172)
		tmp = y;
	elseif (t <= -3e+87)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 2.6e-280)
		tmp = t_1;
	elseif (t <= 3.65e-159)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4.6e+114)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.7e+172)
		tmp = y;
	elseif (t <= -3e+87)
		tmp = x * (z / t);
	elseif (t <= 2.6e-280)
		tmp = t_1;
	elseif (t <= 3.65e-159)
		tmp = y * (z / (a - t));
	elseif (t <= 4.6e+114)
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+172], y, If[LessEqual[t, -3e+87], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-280], t$95$1, If[LessEqual[t, 3.65e-159], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+114], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6999999999999999e172 or 4.6000000000000001e114 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -1.6999999999999999e172 < t < -2.9999999999999999e87

   1. Initial program 65.8%

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

   3. Taylor expanded in x around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-rgt-neg-in 66.4%

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

      3. +-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 53.3%

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

      1. associate-/l* 60.0%

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

   8. Simplified 60.0%

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

   if -2.9999999999999999e87 < t < 2.6e-280 or 3.6499999999999998e-159 < t < 4.6000000000000001e114

   1. Initial program 88.8%

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

   3. Taylor expanded in x around -inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. +-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in t around 0 52.9%

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

   if 2.6e-280 < t < 3.6499999999999998e-159

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 84.0%

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

      1. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. *-commutative 76.2%

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

      3. times-frac 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in z around inf 59.7%

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

       1. associate-/l* 67.4%

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

   11. Simplified 67.4%

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

Alternative 9: 45.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.1e+172)
     y
     (if (<= t -9.5e+86)
       (* x (/ z t))
       (if (<= t 1.75e-273)
         t_1
         (if (<= t 3.6e-134) (* y (/ z a)) (if (<= t 4.5e+114) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.1e+172) {
		tmp = y;
	} else if (t <= -9.5e+86) {
		tmp = x * (z / t);
	} else if (t <= 1.75e-273) {
		tmp = t_1;
	} else if (t <= 3.6e-134) {
		tmp = y * (z / a);
	} else if (t <= 4.5e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.1d+172)) then
        tmp = y
    else if (t <= (-9.5d+86)) then
        tmp = x * (z / t)
    else if (t <= 1.75d-273) then
        tmp = t_1
    else if (t <= 3.6d-134) then
        tmp = y * (z / a)
    else if (t <= 4.5d+114) 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 * (1.0 - (z / a));
	double tmp;
	if (t <= -3.1e+172) {
		tmp = y;
	} else if (t <= -9.5e+86) {
		tmp = x * (z / t);
	} else if (t <= 1.75e-273) {
		tmp = t_1;
	} else if (t <= 3.6e-134) {
		tmp = y * (z / a);
	} else if (t <= 4.5e+114) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.1e+172:
		tmp = y
	elif t <= -9.5e+86:
		tmp = x * (z / t)
	elif t <= 1.75e-273:
		tmp = t_1
	elif t <= 3.6e-134:
		tmp = y * (z / a)
	elif t <= 4.5e+114:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.1e+172)
		tmp = y;
	elseif (t <= -9.5e+86)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.75e-273)
		tmp = t_1;
	elseif (t <= 3.6e-134)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4.5e+114)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.1e+172)
		tmp = y;
	elseif (t <= -9.5e+86)
		tmp = x * (z / t);
	elseif (t <= 1.75e-273)
		tmp = t_1;
	elseif (t <= 3.6e-134)
		tmp = y * (z / a);
	elseif (t <= 4.5e+114)
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+172], y, If[LessEqual[t, -9.5e+86], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-273], t$95$1, If[LessEqual[t, 3.6e-134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+114], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.09999999999999988e172 or 4.5000000000000001e114 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -3.09999999999999988e172 < t < -9.50000000000000028e86

   1. Initial program 65.8%

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

   3. Taylor expanded in x around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-rgt-neg-in 66.4%

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

      3. +-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around 0 53.3%

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

      1. associate-/l* 60.0%

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

   8. Simplified 60.0%

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

   if -9.50000000000000028e86 < t < 1.74999999999999996e-273 or 3.5999999999999999e-134 < t < 4.5000000000000001e114

   1. Initial program 88.5%

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

   3. Taylor expanded in x around -inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

      3. +-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in t around 0 53.0%

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

   if 1.74999999999999996e-273 < t < 3.5999999999999999e-134

   1. Initial program 96.5%

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

   3. Taylor expanded in y around inf 83.0%

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

      1. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in t around 0 79.8%

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

   7. Taylor expanded in x around 0 51.8%

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

      1. associate-*r/ 58.4%

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

   9. Simplified 58.4%

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

Alternative 10: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{t - a}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) (- t a))))))
   (if (<= t -1.15e+42)
     (+ y (* z (/ (- x y) t)))
     (if (<= t -5.2e-110)
       t_1
       (if (<= t 8e+68)
         (+ x (* z (/ (- y x) (- a t))))
         (if (<= t 3.3e+274) t_1 (+ y (* (/ (- y x) t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double tmp;
	if (t <= -1.15e+42) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -5.2e-110) {
		tmp = t_1;
	} else if (t <= 8e+68) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 3.3e+274) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((z - t) / (t - a)))
    if (t <= (-1.15d+42)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= (-5.2d-110)) then
        tmp = t_1
    else if (t <= 8d+68) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 3.3d+274) then
        tmp = t_1
    else
        tmp = y + (((y - x) / t) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / (t - a)));
	double tmp;
	if (t <= -1.15e+42) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -5.2e-110) {
		tmp = t_1;
	} else if (t <= 8e+68) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 3.3e+274) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / (t - a)))
	tmp = 0
	if t <= -1.15e+42:
		tmp = y + (z * ((x - y) / t))
	elif t <= -5.2e-110:
		tmp = t_1
	elif t <= 8e+68:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 3.3e+274:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))))
	tmp = 0.0
	if (t <= -1.15e+42)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= -5.2e-110)
		tmp = t_1;
	elseif (t <= 8e+68)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 3.3e+274)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / (t - a)));
	tmp = 0.0;
	if (t <= -1.15e+42)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= -5.2e-110)
		tmp = t_1;
	elseif (t <= 8e+68)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 3.3e+274)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+42], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-110], t$95$1, If[LessEqual[t, 8e+68], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+274], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e42

   1. Initial program 41.9%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. associate-*r/ 69.5%

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

      3. associate-*r/ 69.5%

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

      4. mul-1-neg 69.5%

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

      5. div-sub 69.5%

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

      6. mul-1-neg 69.5%

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

      7. distribute-lft-out-- 69.5%

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

      8. associate-*r/ 69.5%

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

      9. mul-1-neg 69.5%

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

      10. unsub-neg 69.5%

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

      11. distribute-rgt-out-- 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in z around inf 68.2%

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

      1. associate-/l* 79.1%

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

   8. Simplified 79.1%

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

   if -1.15e42 < t < -5.19999999999999979e-110 or 7.99999999999999962e68 < t < 3.30000000000000014e274

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -5.19999999999999979e-110 < t < 7.99999999999999962e68

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 92.4%

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

   5. Simplified 92.4%

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

   if 3.30000000000000014e274 < t

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. associate-*r/ 61.6%

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

      3. associate-*r/ 61.6%

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

      4. mul-1-neg 61.6%

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

      5. div-sub 61.6%

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

      6. mul-1-neg 61.6%

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

      7. distribute-lft-out-- 61.6%

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

      8. associate-*r/ 61.6%

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

      9. mul-1-neg 61.6%

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

      10. unsub-neg 61.6%

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

      11. distribute-rgt-out-- 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 98.7%

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

      3. distribute-lft-neg-in 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -1.2:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= a -1.2)
     (+ x (* z (/ (- y x) a)))
     (if (<= a 4.4e-105)
       t_1
       (if (<= a 6.2e-49)
         (* y (/ (- z t) (- a t)))
         (if (<= a 1e+38) t_1 (+ x (* y (/ (- z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (a <= -1.2) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 4.4e-105) {
		tmp = t_1;
	} else if (a <= 6.2e-49) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1e+38) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * ((x - y) / t))
    if (a <= (-1.2d0)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= 4.4d-105) then
        tmp = t_1
    else if (a <= 6.2d-49) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1d+38) then
        tmp = t_1
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (a <= -1.2) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 4.4e-105) {
		tmp = t_1;
	} else if (a <= 6.2e-49) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1e+38) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if a <= -1.2:
		tmp = x + (z * ((y - x) / a))
	elif a <= 4.4e-105:
		tmp = t_1
	elif a <= 6.2e-49:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1e+38:
		tmp = t_1
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (a <= -1.2)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= 4.4e-105)
		tmp = t_1;
	elseif (a <= 6.2e-49)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1e+38)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (a <= -1.2)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= 4.4e-105)
		tmp = t_1;
	elseif (a <= 6.2e-49)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1e+38)
		tmp = t_1;
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-105], t$95$1, If[LessEqual[a, 6.2e-49], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+38], t$95$1, N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.19999999999999996

   1. Initial program 62.0%

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

   3. Taylor expanded in t around 0 53.3%

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

      1. associate-/l* 65.1%

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

   5. Simplified 65.1%

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

   if -1.19999999999999996 < a < 4.40000000000000008e-105 or 6.2e-49 < a < 9.99999999999999977e37

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. associate-*r/ 77.5%

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

      3. associate-*r/ 77.5%

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

      4. mul-1-neg 77.5%

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

      5. div-sub 77.5%

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

      6. mul-1-neg 77.5%

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

      7. distribute-lft-out-- 77.5%

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

      8. associate-*r/ 77.5%

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

      9. mul-1-neg 77.5%

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

      10. unsub-neg 77.5%

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

      11. distribute-rgt-out-- 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in z around inf 73.4%

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

      1. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

   if 4.40000000000000008e-105 < a < 6.2e-49

   1. Initial program 85.4%

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

      1. div-inv 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*l* 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in x around 0 66.9%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

   if 9.99999999999999977e37 < a

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in a around inf 68.1%

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

      1. associate-/l* 75.1%

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

   8. Simplified 75.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-105}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 10^{+38}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-154}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 54000000000000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -5.8e-7)
     t_1
     (if (<= z 3.5e-154)
       (- x (* t (/ y a)))
       (if (<= z 54000000000000.0) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e-7) {
		tmp = t_1;
	} else if (z <= 3.5e-154) {
		tmp = x - (t * (y / a));
	} else if (z <= 54000000000000.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (z <= (-5.8d-7)) then
        tmp = t_1
    else if (z <= 3.5d-154) then
        tmp = x - (t * (y / a))
    else if (z <= 54000000000000.0d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.8e-7) {
		tmp = t_1;
	} else if (z <= 3.5e-154) {
		tmp = x - (t * (y / a));
	} else if (z <= 54000000000000.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -5.8e-7:
		tmp = t_1
	elif z <= 3.5e-154:
		tmp = x - (t * (y / a))
	elif z <= 54000000000000.0:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -5.8e-7)
		tmp = t_1;
	elseif (z <= 3.5e-154)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (z <= 54000000000000.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -5.8e-7)
		tmp = t_1;
	elseif (z <= 3.5e-154)
		tmp = x - (t * (y / a));
	elseif (z <= 54000000000000.0)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-7], t$95$1, If[LessEqual[z, 3.5e-154], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 54000000000000.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999995e-7 or 5.4e13 < z

   1. Initial program 74.0%

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

      1. associate-/l* 90.7%

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

      2. clear-num 90.7%

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

      3. un-div-inv 90.7%

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

   4. Applied egg-rr 90.7%

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

   5. Taylor expanded in z around inf 68.7%

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

      1. div-sub 70.2%

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

   7. Simplified 70.2%

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

   if -5.7999999999999995e-7 < z < 3.5000000000000001e-154

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in a around inf 55.7%

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

      1. associate-/l* 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around 0 53.1%

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

       1. mul-1-neg 53.1%

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

       2. unsub-neg 53.1%

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

       3. associate-/l* 54.2%

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

   11. Simplified 54.2%

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

   if 3.5000000000000001e-154 < z < 5.4e13

   1. Initial program 60.4%

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

      1. div-inv 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*l* 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/l* 69.3%

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

   7. Simplified 69.3%

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

Alternative 13: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+176}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+176)
   (+ y (* z (/ (- x y) t)))
   (if (<= t 4.1e+274)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* (/ (- y x) t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+176) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 4.1e+274) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d+176)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= 4.1d+274) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (((y - x) / t) * 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 <= -3.4e+176) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 4.1e+274) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+176:
		tmp = y + (z * ((x - y) / t))
	elif t <= 4.1e+274:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+176)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 4.1e+274)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+176)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= 4.1e+274)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+176], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+274], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.40000000000000014e176

   1. Initial program 20.5%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-*r/ 64.0%

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

      3. associate-*r/ 64.0%

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

      4. mul-1-neg 64.0%

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

      5. div-sub 64.0%

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

      6. mul-1-neg 64.0%

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

      7. distribute-lft-out-- 64.0%

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

      8. associate-*r/ 64.0%

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

      9. mul-1-neg 64.0%

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

      10. unsub-neg 64.0%

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

      11. distribute-rgt-out-- 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around inf 68.1%

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

      1. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

   if -3.40000000000000014e176 < t < 4.1e274

   1. Initial program 80.2%

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

      1. associate-/l* 92.7%

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

      2. clear-num 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if 4.1e274 < t

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. associate-*r/ 61.6%

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

      3. associate-*r/ 61.6%

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

      4. mul-1-neg 61.6%

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

      5. div-sub 61.6%

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

      6. mul-1-neg 61.6%

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

      7. distribute-lft-out-- 61.6%

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

      8. associate-*r/ 61.6%

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

      9. mul-1-neg 61.6%

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

      10. unsub-neg 61.6%

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

      11. distribute-rgt-out-- 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 98.7%

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

      3. distribute-lft-neg-in 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+176}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-84}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.75e+172)
   y
   (if (<= t -1.5e+42)
     (* x (/ z t))
     (if (<= t -3.5e-84) (+ y x) (if (<= t 2.05e+114) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e+172) {
		tmp = y;
	} else if (t <= -1.5e+42) {
		tmp = x * (z / t);
	} else if (t <= -3.5e-84) {
		tmp = y + x;
	} else if (t <= 2.05e+114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.75d+172)) then
        tmp = y
    else if (t <= (-1.5d+42)) then
        tmp = x * (z / t)
    else if (t <= (-3.5d-84)) then
        tmp = y + x
    else if (t <= 2.05d+114) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e+172) {
		tmp = y;
	} else if (t <= -1.5e+42) {
		tmp = x * (z / t);
	} else if (t <= -3.5e-84) {
		tmp = y + x;
	} else if (t <= 2.05e+114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.75e+172:
		tmp = y
	elif t <= -1.5e+42:
		tmp = x * (z / t)
	elif t <= -3.5e-84:
		tmp = y + x
	elif t <= 2.05e+114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.75e+172)
		tmp = y;
	elseif (t <= -1.5e+42)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= -3.5e-84)
		tmp = Float64(y + x);
	elseif (t <= 2.05e+114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.75e+172)
		tmp = y;
	elseif (t <= -1.5e+42)
		tmp = x * (z / t);
	elseif (t <= -3.5e-84)
		tmp = y + x;
	elseif (t <= 2.05e+114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.75e+172], y, If[LessEqual[t, -1.5e+42], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-84], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.05e+114], x, y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.74999999999999989e172 or 2.05e114 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -1.74999999999999989e172 < t < -1.50000000000000014e42

   1. Initial program 72.6%

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

   3. Taylor expanded in x around -inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-rgt-neg-in 63.6%

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

      3. +-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in a around 0 50.3%

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

      1. associate-/l* 54.8%

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

   8. Simplified 54.8%

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

   if -1.50000000000000014e42 < t < -3.5000000000000001e-84

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in t around inf 49.7%

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

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -3.5000000000000001e-84 < t < 2.05e114

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 35.2%

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

Alternative 15: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-57} \lor \neg \left(a \leq 1.3 \cdot 10^{-100}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e-57) (not (<= a 1.3e-100)))
   (- x (* y (/ (- z t) (- t a))))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e-57) || !(a <= 1.3e-100)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (z * ((x - y) / 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 <= (-7.6d-57)) .or. (.not. (a <= 1.3d-100))) then
        tmp = x - (y * ((z - t) / (t - a)))
    else
        tmp = y + (z * ((x - y) / 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 <= -7.6e-57) || !(a <= 1.3e-100)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.6e-57) or not (a <= 1.3e-100):
		tmp = x - (y * ((z - t) / (t - a)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.6e-57) || !(a <= 1.3e-100))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.6e-57) || ~((a <= 1.3e-100)))
		tmp = x - (y * ((z - t) / (t - a)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.6e-57], N[Not[LessEqual[a, 1.3e-100]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5999999999999995e-57 or 1.2999999999999999e-100 < a

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 62.8%

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

      1. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   if -7.5999999999999995e-57 < a < 1.2999999999999999e-100

   1. Initial program 72.1%

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

   3. Taylor expanded in t around inf 84.2%

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

      1. associate--l+ 84.2%

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

      2. associate-*r/ 84.2%

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

      3. associate-*r/ 84.2%

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

      4. mul-1-neg 84.2%

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

      5. div-sub 84.2%

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

      6. mul-1-neg 84.2%

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

      7. distribute-lft-out-- 84.2%

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

      8. associate-*r/ 84.2%

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

      9. mul-1-neg 84.2%

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

      10. unsub-neg 84.2%

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

      11. distribute-rgt-out-- 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in z around inf 82.0%

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

      1. associate-/l* 85.3%

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

   8. Simplified 85.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-57} \lor \neg \left(a \leq 1.3 \cdot 10^{-100}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+174}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-83}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+174) y (if (<= t -1.5e-83) (+ y x) (if (<= t 2e+114) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+174) {
		tmp = y;
	} else if (t <= -1.5e-83) {
		tmp = y + x;
	} else if (t <= 2e+114) {
		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 <= (-3.4d+174)) then
        tmp = y
    else if (t <= (-1.5d-83)) then
        tmp = y + x
    else if (t <= 2d+114) 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 <= -3.4e+174) {
		tmp = y;
	} else if (t <= -1.5e-83) {
		tmp = y + x;
	} else if (t <= 2e+114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+174:
		tmp = y
	elif t <= -1.5e-83:
		tmp = y + x
	elif t <= 2e+114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+174)
		tmp = y;
	elseif (t <= -1.5e-83)
		tmp = Float64(y + x);
	elseif (t <= 2e+114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+174)
		tmp = y;
	elseif (t <= -1.5e-83)
		tmp = y + x;
	elseif (t <= 2e+114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+174], y, If[LessEqual[t, -1.5e-83], N[(y + x), $MachinePrecision], If[LessEqual[t, 2e+114], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000001e174 or 2e114 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -3.4000000000000001e174 < t < -1.50000000000000005e-83

   1. Initial program 80.8%

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

   3. Taylor expanded in y around inf 62.0%

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

      1. associate-/l* 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in t around inf 32.9%

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

      1. +-commutative 32.9%

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

   8. Simplified 32.9%

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

   if -1.50000000000000005e-83 < t < 2e114

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 35.2%

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

Alternative 17: 38.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+25}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+81) (* x (/ z t)) (if (<= z 3.5e+25) (+ y x) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+81) {
		tmp = x * (z / t);
	} else if (z <= 3.5e+25) {
		tmp = y + x;
	} else {
		tmp = y * (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 (z <= (-1d+81)) then
        tmp = x * (z / t)
    else if (z <= 3.5d+25) then
        tmp = y + x
    else
        tmp = y * (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 (z <= -1e+81) {
		tmp = x * (z / t);
	} else if (z <= 3.5e+25) {
		tmp = y + x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+81:
		tmp = x * (z / t)
	elif z <= 3.5e+25:
		tmp = y + x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+81)
		tmp = Float64(x * Float64(z / t));
	elseif (z <= 3.5e+25)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+81)
		tmp = x * (z / t);
	elseif (z <= 3.5e+25)
		tmp = y + x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+81], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+25], N[(y + x), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999921e80

   1. Initial program 71.8%

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

   3. Taylor expanded in x around -inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-rgt-neg-in 56.3%

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

      3. +-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in a around 0 35.6%

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

      1. associate-/l* 44.9%

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

   8. Simplified 44.9%

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

   if -9.99999999999999921e80 < z < 3.49999999999999999e25

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around inf 43.7%

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

      1. +-commutative 43.7%

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

   8. Simplified 43.7%

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

   if 3.49999999999999999e25 < z

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 36.8%

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

   7. Taylor expanded in x around 0 33.2%

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

      1. associate-*r/ 41.4%

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

   9. Simplified 41.4%

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

Alternative 18: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+172} \lor \neg \left(t \leq 2 \cdot 10^{+114}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e+172) (not (<= t 2e+114))) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+172) || !(t <= 2e+114)) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.7d+172)) .or. (.not. (t <= 2d+114))) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+172) || !(t <= 2e+114)) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e+172) or not (t <= 2e+114):
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e+172) || !(t <= 2e+114))
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.7e+172) || ~((t <= 2e+114)))
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e+172], N[Not[LessEqual[t, 2e+114]], $MachinePrecision]], y, x]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e172 or 2e114 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -1.6999999999999999e172 < t < 2e114

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 32.3%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+172} \lor \neg \left(t \leq 2 \cdot 10^{+114}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in a around inf 24.9%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.4% 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 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (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))))