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

Percentage Accurate: 68.3% → 88.6%

Time: 21.3s

Alternatives: 20

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+182}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+133}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.12e+182)
   (+ y (/ (- a z) (/ t (- y x))))
   (if (<= t 1.2e+133)
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (+ y (* (- z a) (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.12e+182) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else if (t <= 1.2e+133) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((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 (t <= (-1.12d+182)) then
        tmp = y + ((a - z) / (t / (y - x)))
    else if (t <= 1.2d+133) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y + ((z - a) * ((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 (t <= -1.12e+182) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else if (t <= 1.2e+133) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.12e+182:
		tmp = y + ((a - z) / (t / (y - x)))
	elif t <= 1.2e+133:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y + ((z - a) * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.12e+182)
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	elseif (t <= 1.2e+133)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.12e+182)
		tmp = y + ((a - z) / (t / (y - x)));
	elseif (t <= 1.2e+133)
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y + ((z - a) * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.12e+182], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+133], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.11999999999999994e182

   1. Initial program 29.2%

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

      1. associate-/l* 49.4%

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

   3. Simplified 49.4%

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

   5. Taylor expanded in t around inf 64.5%

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

      1. associate--l+ 64.5%

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

      2. associate-*r/ 64.5%

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

      3. associate-*r/ 64.5%

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

      4. div-sub 64.5%

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

      5. distribute-lft-out-- 64.5%

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

      6. associate-*r/ 64.5%

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

      7. mul-1-neg 64.5%

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

      8. unsub-neg 64.5%

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

      9. div-sub 64.5%

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

      10. associate-/l* 74.9%

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

      11. associate-/l* 94.8%

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

      12. distribute-rgt-out-- 94.7%

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

   7. Simplified 94.7%

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

      1. *-commutative 94.7%

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

      2. clear-num 94.8%

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

      3. un-div-inv 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -1.11999999999999994e182 < t < 1.1999999999999999e133

   1. Initial program 83.1%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   if 1.1999999999999999e133 < t

   1. Initial program 31.4%

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

      1. associate-/l* 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in t around inf 62.4%

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

      1. associate--l+ 62.4%

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

      2. associate-*r/ 62.4%

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

      3. associate-*r/ 62.4%

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

      4. div-sub 62.4%

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

      5. distribute-lft-out-- 62.4%

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

      6. associate-*r/ 62.4%

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

      7. mul-1-neg 62.4%

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

      8. unsub-neg 62.4%

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

      9. div-sub 62.4%

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

      10. associate-/l* 75.7%

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

      11. associate-/l* 90.2%

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

      12. distribute-rgt-out-- 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+182}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+133}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - x \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* x (/ (- a z) t)))))
   (if (<= t -2.1e+101)
     t_1
     (if (<= t -7e+55)
       (* z (/ (- y x) (- a t)))
       (if (<= t -4.6e-31)
         (/ (* y (- z t)) (- a t))
         (if (<= t 1.15e-99)
           (+ x (* (- y x) (/ z a)))
           (if (<= t 1.15e-21)
             (* y (/ (- z t) (- a t)))
             (if (<= t 4.2e+49) (+ x (* z (/ (- y x) a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x * ((a - z) / t));
	double tmp;
	if (t <= -2.1e+101) {
		tmp = t_1;
	} else if (t <= -7e+55) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 1.15e-99) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 1.15e-21) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 4.2e+49) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (x * ((a - z) / t))
    if (t <= (-2.1d+101)) then
        tmp = t_1
    else if (t <= (-7d+55)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-4.6d-31)) then
        tmp = (y * (z - t)) / (a - t)
    else if (t <= 1.15d-99) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 1.15d-21) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 4.2d+49) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x * ((a - z) / t));
	double tmp;
	if (t <= -2.1e+101) {
		tmp = t_1;
	} else if (t <= -7e+55) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 1.15e-99) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 1.15e-21) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 4.2e+49) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x * ((a - z) / t))
	tmp = 0
	if t <= -2.1e+101:
		tmp = t_1
	elif t <= -7e+55:
		tmp = z * ((y - x) / (a - t))
	elif t <= -4.6e-31:
		tmp = (y * (z - t)) / (a - t)
	elif t <= 1.15e-99:
		tmp = x + ((y - x) * (z / a))
	elif t <= 1.15e-21:
		tmp = y * ((z - t) / (a - t))
	elif t <= 4.2e+49:
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -2.1e+101)
		tmp = t_1;
	elseif (t <= -7e+55)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -4.6e-31)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(a - t));
	elseif (t <= 1.15e-99)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 1.15e-21)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 4.2e+49)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x * ((a - z) / t));
	tmp = 0.0;
	if (t <= -2.1e+101)
		tmp = t_1;
	elseif (t <= -7e+55)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -4.6e-31)
		tmp = (y * (z - t)) / (a - t);
	elseif (t <= 1.15e-99)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 1.15e-21)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 4.2e+49)
		tmp = x + (z * ((y - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+101], t$95$1, If[LessEqual[t, -7e+55], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-31], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-99], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-21], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+49], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.1e101 or 4.20000000000000022e49 < t

   1. Initial program 42.4%

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

      1. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. associate-*r/ 61.7%

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

      3. associate-*r/ 61.7%

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

      4. div-sub 61.7%

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

      5. distribute-lft-out-- 61.7%

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

      6. associate-*r/ 61.7%

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

      7. mul-1-neg 61.7%

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

      8. unsub-neg 61.7%

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

      9. div-sub 61.7%

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

      10. associate-/l* 73.6%

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

      11. associate-/l* 84.9%

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

      12. distribute-rgt-out-- 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 76.7%

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

   10. Simplified 76.7%

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

   if -2.1e101 < t < -7.00000000000000021e55

   1. Initial program 81.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 80.2%

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

      1. div-sub 80.2%

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

   7. Simplified 80.2%

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

   if -7.00000000000000021e55 < t < -4.5999999999999997e-31

   1. Initial program 85.7%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 60.4%

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

   if -4.5999999999999997e-31 < t < 1.1499999999999999e-99

   1. Initial program 88.8%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around 0 77.5%

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

   if 1.1499999999999999e-99 < t < 1.15e-21

   1. Initial program 87.9%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0 63.8%

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

      1. associate-*r/ 69.6%

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

   7. Simplified 69.6%

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

   if 1.15e-21 < t < 4.20000000000000022e49

   1. Initial program 86.6%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 65.1%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+43}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+98)
   (+ y (/ x (/ t (- z a))))
   (if (<= t -1e+56)
     (* z (/ (- y x) (- a t)))
     (if (<= t -4.6e-31)
       (/ (* y (- z t)) (- a t))
       (if (<= t 1.3e-99)
         (+ x (* (- y x) (/ z a)))
         (if (<= t 7.8e-23)
           (* y (/ (- z t) (- a t)))
           (if (<= t 3.3e+43)
             (+ x (* z (/ (- y x) a)))
             (- y (* x (/ (- a z) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+98) {
		tmp = y + (x / (t / (z - a)));
	} else if (t <= -1e+56) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 1.3e-99) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 7.8e-23) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 3.3e+43) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y - (x * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d+98)) then
        tmp = y + (x / (t / (z - a)))
    else if (t <= (-1d+56)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-4.6d-31)) then
        tmp = (y * (z - t)) / (a - t)
    else if (t <= 1.3d-99) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 7.8d-23) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 3.3d+43) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = y - (x * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+98) {
		tmp = y + (x / (t / (z - a)));
	} else if (t <= -1e+56) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 1.3e-99) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 7.8e-23) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 3.3e+43) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y - (x * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+98:
		tmp = y + (x / (t / (z - a)))
	elif t <= -1e+56:
		tmp = z * ((y - x) / (a - t))
	elif t <= -4.6e-31:
		tmp = (y * (z - t)) / (a - t)
	elif t <= 1.3e-99:
		tmp = x + ((y - x) * (z / a))
	elif t <= 7.8e-23:
		tmp = y * ((z - t) / (a - t))
	elif t <= 3.3e+43:
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y - (x * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+98)
		tmp = Float64(y + Float64(x / Float64(t / Float64(z - a))));
	elseif (t <= -1e+56)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -4.6e-31)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(a - t));
	elseif (t <= 1.3e-99)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 7.8e-23)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 3.3e+43)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y - Float64(x * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+98)
		tmp = y + (x / (t / (z - a)));
	elseif (t <= -1e+56)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -4.6e-31)
		tmp = (y * (z - t)) / (a - t);
	elseif (t <= 1.3e-99)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 7.8e-23)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 3.3e+43)
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y - (x * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+98], N[(y + N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e+56], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-31], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-99], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-23], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+43], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.1999999999999999e98

   1. Initial program 38.9%

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

      1. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in t around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. associate-*r/ 57.9%

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

      3. associate-*r/ 57.9%

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

      4. div-sub 57.9%

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

      5. distribute-lft-out-- 57.9%

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

      6. associate-*r/ 57.9%

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

      7. mul-1-neg 57.9%

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

      8. unsub-neg 57.9%

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

      9. div-sub 57.9%

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

      10. associate-/l* 70.5%

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

      11. associate-/l* 82.6%

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

      12. distribute-rgt-out-- 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-/l* 73.1%

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

   10. Simplified 73.1%

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

       1. clear-num 73.1%

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

       2. un-div-inv 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -1.1999999999999999e98 < t < -1.00000000000000009e56

   1. Initial program 81.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 80.2%

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

      1. div-sub 80.2%

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

   7. Simplified 80.2%

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

   if -1.00000000000000009e56 < t < -4.5999999999999997e-31

   1. Initial program 85.7%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 60.4%

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

   if -4.5999999999999997e-31 < t < 1.30000000000000003e-99

   1. Initial program 88.8%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around 0 77.5%

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

   if 1.30000000000000003e-99 < t < 7.8e-23

   1. Initial program 87.9%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0 63.8%

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

      1. associate-*r/ 69.6%

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

   7. Simplified 69.6%

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

   if 7.8e-23 < t < 3.3000000000000001e43

   1. Initial program 86.6%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 65.1%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

   if 3.3000000000000001e43 < t

   1. Initial program 44.6%

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

      1. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around inf 64.1%

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

      1. associate--l+ 64.1%

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

      2. associate-*r/ 64.1%

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

      3. associate-*r/ 64.1%

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

      4. div-sub 64.1%

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

      5. distribute-lft-out-- 64.1%

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

      6. associate-*r/ 64.1%

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

      7. mul-1-neg 64.1%

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

      8. unsub-neg 64.1%

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

      9. div-sub 64.1%

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

      10. associate-/l* 75.6%

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

      11. associate-/l* 86.4%

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

      12. distribute-rgt-out-- 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-/l* 79.0%

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

   10. Simplified 79.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+43}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ x t) (- a z)))))
   (if (<= t -7.6e+99)
     t_1
     (if (<= t -5.5e+55)
       (* z (/ (- y x) (- a t)))
       (if (<= t -4.6e-31)
         (/ (* y (- z t)) (- a t))
         (if (<= t 3.2e-101)
           (+ x (* (- y x) (/ z a)))
           (if (<= t 1.5e-24)
             (* y (/ (- z t) (- a t)))
             (if (<= t 6.2e+41) (+ x (* z (/ (- y x) a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -7.6e+99) {
		tmp = t_1;
	} else if (t <= -5.5e+55) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 3.2e-101) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 1.5e-24) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.2e+41) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - ((x / t) * (a - z))
    if (t <= (-7.6d+99)) then
        tmp = t_1
    else if (t <= (-5.5d+55)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-4.6d-31)) then
        tmp = (y * (z - t)) / (a - t)
    else if (t <= 3.2d-101) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 1.5d-24) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.2d+41) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -7.6e+99) {
		tmp = t_1;
	} else if (t <= -5.5e+55) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -4.6e-31) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 3.2e-101) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 1.5e-24) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.2e+41) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((x / t) * (a - z))
	tmp = 0
	if t <= -7.6e+99:
		tmp = t_1
	elif t <= -5.5e+55:
		tmp = z * ((y - x) / (a - t))
	elif t <= -4.6e-31:
		tmp = (y * (z - t)) / (a - t)
	elif t <= 3.2e-101:
		tmp = x + ((y - x) * (z / a))
	elif t <= 1.5e-24:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.2e+41:
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(x / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -7.6e+99)
		tmp = t_1;
	elseif (t <= -5.5e+55)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -4.6e-31)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(a - t));
	elseif (t <= 3.2e-101)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 1.5e-24)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.2e+41)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((x / t) * (a - z));
	tmp = 0.0;
	if (t <= -7.6e+99)
		tmp = t_1;
	elseif (t <= -5.5e+55)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -4.6e-31)
		tmp = (y * (z - t)) / (a - t);
	elseif (t <= 3.2e-101)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 1.5e-24)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.2e+41)
		tmp = x + (z * ((y - x) / 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[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+99], t$95$1, If[LessEqual[t, -5.5e+55], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-31], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-101], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-24], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+41], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.6e99 or 6.2e41 < t

   1. Initial program 42.4%

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

      1. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. associate-*r/ 61.7%

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

      3. associate-*r/ 61.7%

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

      4. div-sub 61.7%

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

      5. distribute-lft-out-- 61.7%

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

      6. associate-*r/ 61.7%

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

      7. mul-1-neg 61.7%

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

      8. unsub-neg 61.7%

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

      9. div-sub 61.7%

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

      10. associate-/l* 73.6%

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

      11. associate-/l* 84.9%

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

      12. distribute-rgt-out-- 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in y around 0 79.0%

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

      1. neg-mul-1 79.0%

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

      2. distribute-neg-frac2 79.0%

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

   10. Simplified 79.0%

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

   if -7.6e99 < t < -5.5000000000000004e55

   1. Initial program 81.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 80.2%

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

      1. div-sub 80.2%

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

   7. Simplified 80.2%

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

   if -5.5000000000000004e55 < t < -4.5999999999999997e-31

   1. Initial program 85.7%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 60.4%

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

   if -4.5999999999999997e-31 < t < 3.19999999999999978e-101

   1. Initial program 88.8%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around 0 77.5%

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

   if 3.19999999999999978e-101 < t < 1.49999999999999998e-24

   1. Initial program 87.9%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0 63.8%

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

      1. associate-*r/ 69.6%

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

   7. Simplified 69.6%

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

   if 1.49999999999999998e-24 < t < 6.2e41

   1. Initial program 86.6%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 65.1%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+99}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - a \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+115}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+165}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (- y (* a (/ x t)))))
   (if (<= t -4.5e+85)
     t_2
     (if (<= t 2.6e+53)
       t_1
       (if (<= t 1.55e+115)
         (+ x (- y x))
         (if (<= t 2.4e+133)
           t_1
           (if (<= t 6e+165) (* (- z a) (/ x t)) 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 - (a * (x / t));
	double tmp;
	if (t <= -4.5e+85) {
		tmp = t_2;
	} else if (t <= 2.6e+53) {
		tmp = t_1;
	} else if (t <= 1.55e+115) {
		tmp = x + (y - x);
	} else if (t <= 2.4e+133) {
		tmp = t_1;
	} else if (t <= 6e+165) {
		tmp = (z - a) * (x / t);
	} 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 - (a * (x / t))
    if (t <= (-4.5d+85)) then
        tmp = t_2
    else if (t <= 2.6d+53) then
        tmp = t_1
    else if (t <= 1.55d+115) then
        tmp = x + (y - x)
    else if (t <= 2.4d+133) then
        tmp = t_1
    else if (t <= 6d+165) then
        tmp = (z - a) * (x / t)
    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 - (a * (x / t));
	double tmp;
	if (t <= -4.5e+85) {
		tmp = t_2;
	} else if (t <= 2.6e+53) {
		tmp = t_1;
	} else if (t <= 1.55e+115) {
		tmp = x + (y - x);
	} else if (t <= 2.4e+133) {
		tmp = t_1;
	} else if (t <= 6e+165) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y - (a * (x / t))
	tmp = 0
	if t <= -4.5e+85:
		tmp = t_2
	elif t <= 2.6e+53:
		tmp = t_1
	elif t <= 1.55e+115:
		tmp = x + (y - x)
	elif t <= 2.4e+133:
		tmp = t_1
	elif t <= 6e+165:
		tmp = (z - a) * (x / t)
	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(a * Float64(x / t)))
	tmp = 0.0
	if (t <= -4.5e+85)
		tmp = t_2;
	elseif (t <= 2.6e+53)
		tmp = t_1;
	elseif (t <= 1.55e+115)
		tmp = Float64(x + Float64(y - x));
	elseif (t <= 2.4e+133)
		tmp = t_1;
	elseif (t <= 6e+165)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	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 - (a * (x / t));
	tmp = 0.0;
	if (t <= -4.5e+85)
		tmp = t_2;
	elseif (t <= 2.6e+53)
		tmp = t_1;
	elseif (t <= 1.55e+115)
		tmp = x + (y - x);
	elseif (t <= 2.4e+133)
		tmp = t_1;
	elseif (t <= 6e+165)
		tmp = (z - a) * (x / t);
	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[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+85], t$95$2, If[LessEqual[t, 2.6e+53], t$95$1, If[LessEqual[t, 1.55e+115], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+133], t$95$1, If[LessEqual[t, 6e+165], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.50000000000000007e85 or 5.99999999999999981e165 < t

   1. Initial program 36.0%

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

      1. associate-/l* 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. associate-*r/ 63.1%

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

      3. associate-*r/ 63.1%

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

      4. div-sub 63.1%

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

      5. distribute-lft-out-- 63.1%

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

      6. associate-*r/ 63.1%

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

      7. mul-1-neg 63.1%

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

      8. unsub-neg 63.1%

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

      9. div-sub 63.1%

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

      10. associate-/l* 75.7%

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

      11. associate-/l* 86.6%

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

      12. distribute-rgt-out-- 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. associate-/l* 76.0%

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

   10. Simplified 76.0%

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

   11. Taylor expanded in z around 0 54.9%

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

       1. mul-1-neg 54.9%

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

       2. unsub-neg 54.9%

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

       3. associate-/l* 59.8%

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

   13. Simplified 59.8%

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

   if -4.50000000000000007e85 < t < 2.59999999999999998e53 or 1.55000000000000002e115 < t < 2.3999999999999999e133

   1. Initial program 87.7%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around 0 66.3%

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

   6. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. sub-neg 51.5%

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

   8. Simplified 51.5%

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

   if 2.59999999999999998e53 < t < 1.55000000000000002e115

   1. Initial program 84.3%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 67.5%

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

   if 2.3999999999999999e133 < t < 5.99999999999999981e165

   1. Initial program 36.6%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in t around inf 35.6%

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

      1. associate--l+ 35.6%

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

      2. associate-*r/ 35.6%

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

      3. associate-*r/ 35.6%

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

      4. div-sub 35.6%

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

      5. distribute-lft-out-- 35.6%

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

      6. associate-*r/ 35.6%

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

      7. mul-1-neg 35.6%

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

      8. unsub-neg 35.6%

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

      9. div-sub 35.6%

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

      10. associate-/l* 47.5%

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

      11. associate-/l* 78.7%

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

      12. distribute-rgt-out-- 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in y around 0 15.2%

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

      1. add0 15.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 36.2%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 36.2%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 15.2%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 15.2%

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

       3. *-commutative 15.2%

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

       4. associate-*r/ 36.3%

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

   12. Simplified 36.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+115}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+165}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-104}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* z (/ (- x y) t))))
   (if (<= a -4e+52)
     t_1
     (if (<= a -2.3e-104)
       (- y (* a (/ x t)))
       (if (<= a -1.12e-170)
         t_2
         (if (<= a -3.2e-186) y (if (<= a 4.8e+21) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (a <= -4e+52) {
		tmp = t_1;
	} else if (a <= -2.3e-104) {
		tmp = y - (a * (x / t));
	} else if (a <= -1.12e-170) {
		tmp = t_2;
	} else if (a <= -3.2e-186) {
		tmp = y;
	} else if (a <= 4.8e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = z * ((x - y) / t)
    if (a <= (-4d+52)) then
        tmp = t_1
    else if (a <= (-2.3d-104)) then
        tmp = y - (a * (x / t))
    else if (a <= (-1.12d-170)) then
        tmp = t_2
    else if (a <= (-3.2d-186)) then
        tmp = y
    else if (a <= 4.8d+21) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (a <= -4e+52) {
		tmp = t_1;
	} else if (a <= -2.3e-104) {
		tmp = y - (a * (x / t));
	} else if (a <= -1.12e-170) {
		tmp = t_2;
	} else if (a <= -3.2e-186) {
		tmp = y;
	} else if (a <= 4.8e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = z * ((x - y) / t)
	tmp = 0
	if a <= -4e+52:
		tmp = t_1
	elif a <= -2.3e-104:
		tmp = y - (a * (x / t))
	elif a <= -1.12e-170:
		tmp = t_2
	elif a <= -3.2e-186:
		tmp = y
	elif a <= 4.8e+21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -4e+52)
		tmp = t_1;
	elseif (a <= -2.3e-104)
		tmp = Float64(y - Float64(a * Float64(x / t)));
	elseif (a <= -1.12e-170)
		tmp = t_2;
	elseif (a <= -3.2e-186)
		tmp = y;
	elseif (a <= 4.8e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = z * ((x - y) / t);
	tmp = 0.0;
	if (a <= -4e+52)
		tmp = t_1;
	elseif (a <= -2.3e-104)
		tmp = y - (a * (x / t));
	elseif (a <= -1.12e-170)
		tmp = t_2;
	elseif (a <= -3.2e-186)
		tmp = y;
	elseif (a <= 4.8e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+52], t$95$1, If[LessEqual[a, -2.3e-104], N[(y - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e-170], t$95$2, If[LessEqual[a, -3.2e-186], y, If[LessEqual[a, 4.8e+21], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4e52 or 4.8e21 < a

   1. Initial program 66.8%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 63.6%

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

   6. Taylor expanded in x around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. sub-neg 52.9%

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

   8. Simplified 52.9%

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

   if -4e52 < a < -2.2999999999999999e-104

   1. Initial program 78.8%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate--l+ 61.8%

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

      2. associate-*r/ 61.8%

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

      3. associate-*r/ 61.8%

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

      4. div-sub 61.9%

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

      5. distribute-lft-out-- 61.9%

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

      6. associate-*r/ 61.9%

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

      7. mul-1-neg 61.9%

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

      8. unsub-neg 61.9%

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

      9. div-sub 61.8%

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

      10. associate-/l* 64.5%

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

      11. associate-/l* 67.1%

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

      12. distribute-rgt-out-- 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in y around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate-/l* 59.5%

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

   10. Simplified 59.5%

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

   11. Taylor expanded in z around 0 45.9%

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

       1. mul-1-neg 45.9%

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

       2. unsub-neg 45.9%

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

       3. associate-/l* 48.6%

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

   13. Simplified 48.6%

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

   if -2.2999999999999999e-104 < a < -1.12000000000000009e-170 or -3.2e-186 < a < 4.8e21

   1. Initial program 70.5%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 64.2%

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

      1. div-sub 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-neg-frac2 56.5%

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

   10. Simplified 56.5%

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

   if -1.12000000000000009e-170 < a < -3.2e-186

   1. Initial program 59.8%

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

      1. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in t around inf 74.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-104}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-170}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z - t}{a}\\ t_2 := y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ (- z t) a)))) (t_2 (- y (* (/ x t) (- a z)))))
   (if (<= t -5.8e+94)
     t_2
     (if (<= t -1.6e+31)
       t_1
       (if (<= t -1.9e-29)
         (- y (* x (/ (- a z) t)))
         (if (<= t 1.4e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / a));
	double t_2 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -5.8e+94) {
		tmp = t_2;
	} else if (t <= -1.6e+31) {
		tmp = t_1;
	} else if (t <= -1.9e-29) {
		tmp = y - (x * ((a - z) / t));
	} else if (t <= 1.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) * ((z - t) / a))
    t_2 = y - ((x / t) * (a - z))
    if (t <= (-5.8d+94)) then
        tmp = t_2
    else if (t <= (-1.6d+31)) then
        tmp = t_1
    else if (t <= (-1.9d-29)) then
        tmp = y - (x * ((a - z) / t))
    else if (t <= 1.4d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / a));
	double t_2 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -5.8e+94) {
		tmp = t_2;
	} else if (t <= -1.6e+31) {
		tmp = t_1;
	} else if (t <= -1.9e-29) {
		tmp = y - (x * ((a - z) / t));
	} else if (t <= 1.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * ((z - t) / a))
	t_2 = y - ((x / t) * (a - z))
	tmp = 0
	if t <= -5.8e+94:
		tmp = t_2
	elif t <= -1.6e+31:
		tmp = t_1
	elif t <= -1.9e-29:
		tmp = y - (x * ((a - z) / t))
	elif t <= 1.4e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)))
	t_2 = Float64(y - Float64(Float64(x / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -5.8e+94)
		tmp = t_2;
	elseif (t <= -1.6e+31)
		tmp = t_1;
	elseif (t <= -1.9e-29)
		tmp = Float64(y - Float64(x * Float64(Float64(a - z) / t)));
	elseif (t <= 1.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * ((z - t) / a));
	t_2 = y - ((x / t) * (a - z));
	tmp = 0.0;
	if (t <= -5.8e+94)
		tmp = t_2;
	elseif (t <= -1.6e+31)
		tmp = t_1;
	elseif (t <= -1.9e-29)
		tmp = y - (x * ((a - z) / t));
	elseif (t <= 1.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+94], t$95$2, If[LessEqual[t, -1.6e+31], t$95$1, If[LessEqual[t, -1.9e-29], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999997e94 or 1.4e52 < t

   1. Initial program 43.5%

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

      1. associate-/l* 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in t around inf 62.1%

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

      1. associate--l+ 62.1%

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

      2. associate-*r/ 62.1%

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

      3. associate-*r/ 62.1%

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

      4. div-sub 62.1%

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

      5. distribute-lft-out-- 62.1%

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

      6. associate-*r/ 62.1%

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

      7. mul-1-neg 62.1%

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

      8. unsub-neg 62.1%

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

      9. div-sub 62.1%

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

      10. associate-/l* 73.8%

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

      11. associate-/l* 84.9%

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

      12. distribute-rgt-out-- 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in y around 0 78.2%

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

      1. neg-mul-1 78.2%

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

      2. distribute-neg-frac2 78.2%

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

   10. Simplified 78.2%

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

   if -5.7999999999999997e94 < t < -1.6e31 or -1.89999999999999988e-29 < t < 1.4e52

   1. Initial program 87.9%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

   if -1.6e31 < t < -1.89999999999999988e-29

   1. Initial program 82.3%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in t around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. associate-*r/ 82.3%

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

      3. associate-*r/ 82.3%

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

      4. div-sub 82.3%

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

      5. distribute-lft-out-- 82.3%

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

      6. associate-*r/ 82.3%

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

      7. mul-1-neg 82.3%

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

      8. unsub-neg 82.3%

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

      9. div-sub 82.3%

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

      10. associate-/l* 82.3%

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

      11. associate-/l* 82.6%

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

      12. distribute-rgt-out-- 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-/l* 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+52}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+123}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.7e+123)
     (* (- z a) (/ x t))
     (if (<= x -1.2e+80)
       t_1
       (if (<= x -3.5e-14)
         (* z (/ (- x y) t))
         (if (<= x 1.0) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.7e+123) {
		tmp = (z - a) * (x / t);
	} else if (x <= -1.2e+80) {
		tmp = t_1;
	} else if (x <= -3.5e-14) {
		tmp = z * ((x - y) / t);
	} else if (x <= 1.0) {
		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 = x * (1.0d0 - (z / a))
    if (x <= (-1.7d+123)) then
        tmp = (z - a) * (x / t)
    else if (x <= (-1.2d+80)) then
        tmp = t_1
    else if (x <= (-3.5d-14)) then
        tmp = z * ((x - y) / t)
    else if (x <= 1.0d0) 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 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.7e+123) {
		tmp = (z - a) * (x / t);
	} else if (x <= -1.2e+80) {
		tmp = t_1;
	} else if (x <= -3.5e-14) {
		tmp = z * ((x - y) / t);
	} else if (x <= 1.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.7e+123:
		tmp = (z - a) * (x / t)
	elif x <= -1.2e+80:
		tmp = t_1
	elif x <= -3.5e-14:
		tmp = z * ((x - y) / t)
	elif x <= 1.0:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.7e+123)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (x <= -1.2e+80)
		tmp = t_1;
	elseif (x <= -3.5e-14)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (x <= 1.0)
		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 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.7e+123)
		tmp = (z - a) * (x / t);
	elseif (x <= -1.2e+80)
		tmp = t_1;
	elseif (x <= -3.5e-14)
		tmp = z * ((x - y) / t);
	elseif (x <= 1.0)
		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[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+123], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e+80], t$95$1, If[LessEqual[x, -3.5e-14], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.70000000000000001e123

   1. Initial program 45.0%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. associate-*r/ 50.5%

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

      3. associate-*r/ 50.5%

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

      4. div-sub 50.5%

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

      5. distribute-lft-out-- 50.5%

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

      6. associate-*r/ 50.5%

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

      7. mul-1-neg 50.5%

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

      8. unsub-neg 50.5%

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

      9. div-sub 50.5%

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

      10. associate-/l* 52.7%

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

      11. associate-/l* 65.9%

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

      12. distribute-rgt-out-- 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in y around 0 39.5%

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

      1. add0 39.5%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 53.2%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 53.2%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 39.5%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 39.5%

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

       3. *-commutative 39.5%

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

       4. associate-*r/ 55.8%

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

   12. Simplified 55.8%

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

   if -1.70000000000000001e123 < x < -1.1999999999999999e80 or 1 < x

   1. Initial program 64.7%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in t around 0 65.1%

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

   6. Taylor expanded in x around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. sub-neg 59.9%

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

   8. Simplified 59.9%

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

   if -1.1999999999999999e80 < x < -3.5000000000000002e-14

   1. Initial program 73.6%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 55.4%

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

      1. div-sub 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   10. Simplified 48.2%

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

   if -3.5000000000000002e-14 < x < 1

   1. Initial program 79.3%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. associate-*r/ 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+123}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 6:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -8e+121)
     (* (- z a) (/ x t))
     (if (<= x -4.1e+80)
       t_1
       (if (<= x -1.4e-18)
         (* z (/ (- y x) (- a t)))
         (if (<= x 6.0) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -8e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -4.1e+80) {
		tmp = t_1;
	} else if (x <= -1.4e-18) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 6.0) {
		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 = x * (1.0d0 - (z / a))
    if (x <= (-8d+121)) then
        tmp = (z - a) * (x / t)
    else if (x <= (-4.1d+80)) then
        tmp = t_1
    else if (x <= (-1.4d-18)) then
        tmp = z * ((y - x) / (a - t))
    else if (x <= 6.0d0) 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 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -8e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -4.1e+80) {
		tmp = t_1;
	} else if (x <= -1.4e-18) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 6.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -8e+121:
		tmp = (z - a) * (x / t)
	elif x <= -4.1e+80:
		tmp = t_1
	elif x <= -1.4e-18:
		tmp = z * ((y - x) / (a - t))
	elif x <= 6.0:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -8e+121)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (x <= -4.1e+80)
		tmp = t_1;
	elseif (x <= -1.4e-18)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (x <= 6.0)
		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 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -8e+121)
		tmp = (z - a) * (x / t);
	elseif (x <= -4.1e+80)
		tmp = t_1;
	elseif (x <= -1.4e-18)
		tmp = z * ((y - x) / (a - t));
	elseif (x <= 6.0)
		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[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+121], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.1e+80], t$95$1, If[LessEqual[x, -1.4e-18], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.0000000000000003e121

   1. Initial program 45.0%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. associate-*r/ 50.5%

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

      3. associate-*r/ 50.5%

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

      4. div-sub 50.5%

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

      5. distribute-lft-out-- 50.5%

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

      6. associate-*r/ 50.5%

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

      7. mul-1-neg 50.5%

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

      8. unsub-neg 50.5%

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

      9. div-sub 50.5%

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

      10. associate-/l* 52.7%

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

      11. associate-/l* 65.9%

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

      12. distribute-rgt-out-- 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in y around 0 39.5%

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

      1. add0 39.5%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 53.2%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 53.2%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 39.5%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 39.5%

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

       3. *-commutative 39.5%

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

       4. associate-*r/ 55.8%

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

   12. Simplified 55.8%

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

   if -8.0000000000000003e121 < x < -4.10000000000000001e80 or 6 < x

   1. Initial program 64.7%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in t around 0 65.1%

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

   6. Taylor expanded in x around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. sub-neg 59.9%

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

   8. Simplified 59.9%

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

   if -4.10000000000000001e80 < x < -1.40000000000000006e-18

   1. Initial program 73.6%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 55.4%

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

      1. div-sub 55.4%

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

   7. Simplified 55.4%

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

   if -1.40000000000000006e-18 < x < 6

   1. Initial program 79.3%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. associate-*r/ 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 6:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= a -6e+52)
     t_2
     (if (<= a 6.6e-238)
       t_1
       (if (<= a 4.4e-29)
         (* z (/ (- y x) (- a t)))
         (if (<= a 2.9e+150) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6e+52) {
		tmp = t_2;
	} else if (a <= 6.6e-238) {
		tmp = t_1;
	} else if (a <= 4.4e-29) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.9e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (z * ((y - x) / a))
    if (a <= (-6d+52)) then
        tmp = t_2
    else if (a <= 6.6d-238) then
        tmp = t_1
    else if (a <= 4.4d-29) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 2.9d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -6e+52) {
		tmp = t_2;
	} else if (a <= 6.6e-238) {
		tmp = t_1;
	} else if (a <= 4.4e-29) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.9e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -6e+52:
		tmp = t_2
	elif a <= 6.6e-238:
		tmp = t_1
	elif a <= 4.4e-29:
		tmp = z * ((y - x) / (a - t))
	elif a <= 2.9e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -6e+52)
		tmp = t_2;
	elseif (a <= 6.6e-238)
		tmp = t_1;
	elseif (a <= 4.4e-29)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 2.9e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -6e+52)
		tmp = t_2;
	elseif (a <= 6.6e-238)
		tmp = t_1;
	elseif (a <= 4.4e-29)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 2.9e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+52], t$95$2, If[LessEqual[a, 6.6e-238], t$95$1, If[LessEqual[a, 4.4e-29], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+150], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e52 or 2.90000000000000011e150 < a

   1. Initial program 68.4%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t around 0 62.5%

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

      1. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

   if -6e52 < a < 6.59999999999999939e-238 or 4.39999999999999981e-29 < a < 2.90000000000000011e150

   1. Initial program 72.2%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. associate-*r/ 67.0%

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

   7. Simplified 67.0%

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

   if 6.59999999999999939e-238 < a < 4.39999999999999981e-29

   1. Initial program 64.3%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. div-sub 71.5%

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

   7. Simplified 71.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.5e+121)
   (* (- z a) (/ x t))
   (if (<= x -2.6e+80)
     (* x (- 1.0 (/ z a)))
     (if (<= x -4.8e-16)
       (* z (/ (- y x) (- a t)))
       (if (<= x 6e-5) (* y (/ (- z t) (- a t))) (+ x (* (- y x) (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.5e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -2.6e+80) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= -4.8e-16) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 6e-5) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) * (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 (x <= (-1.5d+121)) then
        tmp = (z - a) * (x / t)
    else if (x <= (-2.6d+80)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= (-4.8d-16)) then
        tmp = z * ((y - x) / (a - t))
    else if (x <= 6d-5) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) * (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 (x <= -1.5e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -2.6e+80) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= -4.8e-16) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 6e-5) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.5e+121:
		tmp = (z - a) * (x / t)
	elif x <= -2.6e+80:
		tmp = x * (1.0 - (z / a))
	elif x <= -4.8e-16:
		tmp = z * ((y - x) / (a - t))
	elif x <= 6e-5:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.5e+121)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (x <= -2.6e+80)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= -4.8e-16)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (x <= 6e-5)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.5e+121)
		tmp = (z - a) * (x / t);
	elseif (x <= -2.6e+80)
		tmp = x * (1.0 - (z / a));
	elseif (x <= -4.8e-16)
		tmp = z * ((y - x) / (a - t));
	elseif (x <= 6e-5)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.5e+121], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e+80], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-16], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-5], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.5000000000000001e121

   1. Initial program 45.0%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. associate-*r/ 50.5%

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

      3. associate-*r/ 50.5%

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

      4. div-sub 50.5%

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

      5. distribute-lft-out-- 50.5%

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

      6. associate-*r/ 50.5%

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

      7. mul-1-neg 50.5%

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

      8. unsub-neg 50.5%

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

      9. div-sub 50.5%

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

      10. associate-/l* 52.7%

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

      11. associate-/l* 65.9%

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

      12. distribute-rgt-out-- 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in y around 0 39.5%

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

      1. add0 39.5%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 53.2%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 53.2%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 39.5%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 39.5%

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

       3. *-commutative 39.5%

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

       4. associate-*r/ 55.8%

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

   12. Simplified 55.8%

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

   if -1.5000000000000001e121 < x < -2.59999999999999982e80

   1. Initial program 65.3%

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

      1. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around 0 71.7%

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

   6. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. sub-neg 71.7%

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

   8. Simplified 71.7%

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

   if -2.59999999999999982e80 < x < -4.8000000000000001e-16

   1. Initial program 73.6%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 55.4%

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

      1. div-sub 55.4%

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

   7. Simplified 55.4%

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

   if -4.8000000000000001e-16 < x < 6.00000000000000015e-5

   1. Initial program 79.3%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. associate-*r/ 77.9%

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

   7. Simplified 77.9%

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

   if 6.00000000000000015e-5 < x

   1. Initial program 64.6%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 64.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-45}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot x}{t}\\ \mathbf{elif}\;x \leq 0.0024:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.7e+121)
   (* (- z a) (/ x t))
   (if (<= x -8.5e+82)
     (* x (- 1.0 (/ z a)))
     (if (<= x -7.2e-45)
       (+ y (/ (* (- z a) x) t))
       (if (<= x 0.0024)
         (* y (/ (- z t) (- a t)))
         (+ x (* (- y x) (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.7e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -8.5e+82) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= -7.2e-45) {
		tmp = y + (((z - a) * x) / t);
	} else if (x <= 0.0024) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) * (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 (x <= (-3.7d+121)) then
        tmp = (z - a) * (x / t)
    else if (x <= (-8.5d+82)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= (-7.2d-45)) then
        tmp = y + (((z - a) * x) / t)
    else if (x <= 0.0024d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) * (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 (x <= -3.7e+121) {
		tmp = (z - a) * (x / t);
	} else if (x <= -8.5e+82) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= -7.2e-45) {
		tmp = y + (((z - a) * x) / t);
	} else if (x <= 0.0024) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.7e+121:
		tmp = (z - a) * (x / t)
	elif x <= -8.5e+82:
		tmp = x * (1.0 - (z / a))
	elif x <= -7.2e-45:
		tmp = y + (((z - a) * x) / t)
	elif x <= 0.0024:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.7e+121)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (x <= -8.5e+82)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= -7.2e-45)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * x) / t));
	elseif (x <= 0.0024)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.7e+121)
		tmp = (z - a) * (x / t);
	elseif (x <= -8.5e+82)
		tmp = x * (1.0 - (z / a));
	elseif (x <= -7.2e-45)
		tmp = y + (((z - a) * x) / t);
	elseif (x <= 0.0024)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.7e+121], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e+82], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-45], N[(y + N[(N[(N[(z - a), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0024], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.70000000000000013e121

   1. Initial program 45.0%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. associate-*r/ 50.5%

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

      3. associate-*r/ 50.5%

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

      4. div-sub 50.5%

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

      5. distribute-lft-out-- 50.5%

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

      6. associate-*r/ 50.5%

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

      7. mul-1-neg 50.5%

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

      8. unsub-neg 50.5%

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

      9. div-sub 50.5%

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

      10. associate-/l* 52.7%

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

      11. associate-/l* 65.9%

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

      12. distribute-rgt-out-- 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in y around 0 39.5%

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

      1. add0 39.5%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 53.2%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 53.2%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 39.5%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 39.5%

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

       3. *-commutative 39.5%

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

       4. associate-*r/ 55.8%

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

   12. Simplified 55.8%

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

   if -3.70000000000000013e121 < x < -8.4999999999999995e82

   1. Initial program 65.3%

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

      1. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around 0 71.7%

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

   6. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. sub-neg 71.7%

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

   8. Simplified 71.7%

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

   if -8.4999999999999995e82 < x < -7.20000000000000001e-45

   1. Initial program 71.8%

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

      1. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. associate-*r/ 62.9%

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

      3. associate-*r/ 62.9%

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

      4. div-sub 63.0%

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

      5. distribute-lft-out-- 63.0%

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

      6. associate-*r/ 63.0%

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

      7. mul-1-neg 63.0%

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

      8. unsub-neg 63.0%

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

      9. div-sub 62.9%

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

      10. associate-/l* 63.1%

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

      11. associate-/l* 63.4%

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

      12. distribute-rgt-out-- 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in y around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-/l* 56.2%

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

   10. Simplified 56.2%

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

   11. Taylor expanded in y around 0 55.2%

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

   if -7.20000000000000001e-45 < x < 0.00239999999999999979

   1. Initial program 79.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   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-*r/ 78.3%

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

   7. Simplified 78.3%

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

   if 0.00239999999999999979 < x

   1. Initial program 64.6%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 64.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+121}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-45}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot x}{t}\\ \mathbf{elif}\;x \leq 0.0024:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+52)
   x
   (if (<= a -2e-186) y (if (<= a 4.8e-30) (* x (/ (- z a) t)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+52) {
		tmp = x;
	} else if (a <= -2e-186) {
		tmp = y;
	} else if (a <= 4.8e-30) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+52)) then
        tmp = x
    else if (a <= (-2d-186)) then
        tmp = y
    else if (a <= 4.8d-30) then
        tmp = x * ((z - a) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+52) {
		tmp = x;
	} else if (a <= -2e-186) {
		tmp = y;
	} else if (a <= 4.8e-30) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+52:
		tmp = x
	elif a <= -2e-186:
		tmp = y
	elif a <= 4.8e-30:
		tmp = x * ((z - a) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+52)
		tmp = x;
	elseif (a <= -2e-186)
		tmp = y;
	elseif (a <= 4.8e-30)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+52)
		tmp = x;
	elseif (a <= -2e-186)
		tmp = y;
	elseif (a <= 4.8e-30)
		tmp = x * ((z - a) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+52], x, If[LessEqual[a, -2e-186], y, If[LessEqual[a, 4.8e-30], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2e52 or 4.7999999999999997e-30 < a

   1. Initial program 69.2%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 43.3%

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

   if -6.2e52 < a < -1.9999999999999998e-186

   1. Initial program 76.2%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around inf 42.7%

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

   if -1.9999999999999998e-186 < a < 4.7999999999999997e-30

   1. Initial program 66.5%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. associate-*r/ 79.4%

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

      3. associate-*r/ 79.4%

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

      4. div-sub 80.8%

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

      5. distribute-lft-out-- 80.8%

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

      6. associate-*r/ 80.8%

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

      7. mul-1-neg 80.8%

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

      8. unsub-neg 80.8%

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

      9. div-sub 79.4%

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

      10. associate-/l* 75.9%

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

      11. associate-/l* 81.8%

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

      12. distribute-rgt-out-- 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 43.6%

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

      1. associate-/l* 47.3%

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

   10. Simplified 47.3%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -2.15e+52)
     t_1
     (if (<= a -1.75e-186) y (if (<= a 2.5e-31) (* x (/ (- z a) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.15e+52) {
		tmp = t_1;
	} else if (a <= -1.75e-186) {
		tmp = y;
	} else if (a <= 2.5e-31) {
		tmp = x * ((z - 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 = x * (1.0d0 - (z / a))
    if (a <= (-2.15d+52)) then
        tmp = t_1
    else if (a <= (-1.75d-186)) then
        tmp = y
    else if (a <= 2.5d-31) then
        tmp = x * ((z - 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 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.15e+52) {
		tmp = t_1;
	} else if (a <= -1.75e-186) {
		tmp = y;
	} else if (a <= 2.5e-31) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -2.15e+52:
		tmp = t_1
	elif a <= -1.75e-186:
		tmp = y
	elif a <= 2.5e-31:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -2.15e+52)
		tmp = t_1;
	elseif (a <= -1.75e-186)
		tmp = y;
	elseif (a <= 2.5e-31)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	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 (a <= -2.15e+52)
		tmp = t_1;
	elseif (a <= -1.75e-186)
		tmp = y;
	elseif (a <= 2.5e-31)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	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[a, -2.15e+52], t$95$1, If[LessEqual[a, -1.75e-186], y, If[LessEqual[a, 2.5e-31], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.15e52 or 2.5e-31 < a

   1. Initial program 69.2%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around 0 61.7%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. sub-neg 50.4%

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

   8. Simplified 50.4%

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

   if -2.15e52 < a < -1.74999999999999995e-186

   1. Initial program 76.2%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around inf 42.7%

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

   if -1.74999999999999995e-186 < a < 2.5e-31

   1. Initial program 66.5%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. associate-*r/ 79.4%

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

      3. associate-*r/ 79.4%

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

      4. div-sub 80.8%

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

      5. distribute-lft-out-- 80.8%

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

      6. associate-*r/ 80.8%

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

      7. mul-1-neg 80.8%

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

      8. unsub-neg 80.8%

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

      9. div-sub 79.4%

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

      10. associate-/l* 75.9%

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

      11. associate-/l* 81.8%

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

      12. distribute-rgt-out-- 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 43.6%

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

      1. associate-/l* 47.3%

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

   10. Simplified 47.3%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -2.4e+52)
     t_1
     (if (<= a -1.5e-186) y (if (<= a 1.02e-32) (* (- z a) (/ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.4e+52) {
		tmp = t_1;
	} else if (a <= -1.5e-186) {
		tmp = y;
	} else if (a <= 1.02e-32) {
		tmp = (z - a) * (x / 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 = x * (1.0d0 - (z / a))
    if (a <= (-2.4d+52)) then
        tmp = t_1
    else if (a <= (-1.5d-186)) then
        tmp = y
    else if (a <= 1.02d-32) then
        tmp = (z - a) * (x / 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 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.4e+52) {
		tmp = t_1;
	} else if (a <= -1.5e-186) {
		tmp = y;
	} else if (a <= 1.02e-32) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -2.4e+52:
		tmp = t_1
	elif a <= -1.5e-186:
		tmp = y
	elif a <= 1.02e-32:
		tmp = (z - a) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -2.4e+52)
		tmp = t_1;
	elseif (a <= -1.5e-186)
		tmp = y;
	elseif (a <= 1.02e-32)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	else
		tmp = t_1;
	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 (a <= -2.4e+52)
		tmp = t_1;
	elseif (a <= -1.5e-186)
		tmp = y;
	elseif (a <= 1.02e-32)
		tmp = (z - a) * (x / t);
	else
		tmp = t_1;
	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[a, -2.4e+52], t$95$1, If[LessEqual[a, -1.5e-186], y, If[LessEqual[a, 1.02e-32], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4e52 or 1.02000000000000002e-32 < a

   1. Initial program 69.2%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around 0 61.7%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. sub-neg 50.4%

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

   8. Simplified 50.4%

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

   if -2.4e52 < a < -1.5000000000000001e-186

   1. Initial program 76.2%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around inf 42.7%

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

   if -1.5000000000000001e-186 < a < 1.02000000000000002e-32

   1. Initial program 66.5%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. associate-*r/ 79.4%

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

      3. associate-*r/ 79.4%

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

      4. div-sub 80.8%

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

      5. distribute-lft-out-- 80.8%

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

      6. associate-*r/ 80.8%

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

      7. mul-1-neg 80.8%

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

      8. unsub-neg 80.8%

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

      9. div-sub 79.4%

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

      10. associate-/l* 75.9%

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

      11. associate-/l* 81.8%

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

      12. distribute-rgt-out-- 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 43.6%

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

      1. add0 43.6%

         \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t} + 0} \]

      2. associate-/l* 47.3%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} + 0 \]

   10. Applied egg-rr 47.3%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t} + 0} \]
   11. Step-by-step derivation

       1. associate-*r/ 43.6%

          \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} + 0 \]

       2. add0 43.6%

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

       3. *-commutative 43.6%

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

       4. associate-*r/ 49.4%

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

   12. Simplified 49.4%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-186}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-29} \lor \neg \left(t \leq 3.2 \cdot 10^{+33}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.85e-29) (not (<= t 3.2e+33)))
   (+ y (* (- z a) (/ (- x y) t)))
   (+ x (* (- y x) (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-29) || !(t <= 3.2e+33)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + ((y - x) * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.85d-29)) .or. (.not. (t <= 3.2d+33))) then
        tmp = y + ((z - a) * ((x - y) / t))
    else
        tmp = x + ((y - x) * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-29) || !(t <= 3.2e+33)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + ((y - x) * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.85e-29) or not (t <= 3.2e+33):
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x + ((y - x) * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.85e-29) || !(t <= 3.2e+33))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.85e-29) || ~((t <= 3.2e+33)))
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x + ((y - x) * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.85e-29], N[Not[LessEqual[t, 3.2e+33]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8499999999999999e-29 or 3.20000000000000017e33 < t

   1. Initial program 52.7%

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

      1. associate-/l* 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in t around inf 62.0%

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

      1. associate--l+ 62.0%

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

      2. associate-*r/ 62.0%

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

      3. associate-*r/ 62.0%

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

      4. div-sub 62.0%

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

      5. distribute-lft-out-- 62.0%

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

      6. associate-*r/ 62.0%

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

      7. mul-1-neg 62.0%

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

      8. unsub-neg 62.0%

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

      9. div-sub 62.0%

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

      10. associate-/l* 71.1%

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

      11. associate-/l* 79.7%

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

      12. distribute-rgt-out-- 79.7%

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

   7. Simplified 79.7%

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

   if -1.8499999999999999e-29 < t < 3.20000000000000017e33

   1. Initial program 88.3%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-29} \lor \neg \left(t \leq 3.2 \cdot 10^{+33}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-30}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e-30)
   (+ y (/ (- a z) (/ t (- y x))))
   (if (<= t 3.5e+32)
     (+ x (* (- y x) (/ (- z t) a)))
     (+ y (* (- z a) (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e-30) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else if (t <= 3.5e+32) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = y + ((z - a) * ((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 (t <= (-7d-30)) then
        tmp = y + ((a - z) / (t / (y - x)))
    else if (t <= 3.5d+32) then
        tmp = x + ((y - x) * ((z - t) / a))
    else
        tmp = y + ((z - a) * ((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 (t <= -7e-30) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else if (t <= 3.5e+32) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e-30:
		tmp = y + ((a - z) / (t / (y - x)))
	elif t <= 3.5e+32:
		tmp = x + ((y - x) * ((z - t) / a))
	else:
		tmp = y + ((z - a) * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e-30)
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	elseif (t <= 3.5e+32)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e-30)
		tmp = y + ((a - z) / (t / (y - x)));
	elseif (t <= 3.5e+32)
		tmp = x + ((y - x) * ((z - t) / a));
	else
		tmp = y + ((z - a) * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e-30], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+32], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000006e-30

   1. Initial program 58.1%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in t around inf 59.8%

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

      1. associate--l+ 59.8%

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

      2. associate-*r/ 59.8%

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

      3. associate-*r/ 59.8%

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

      4. div-sub 59.8%

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

      5. distribute-lft-out-- 59.8%

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

      6. associate-*r/ 59.8%

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

      7. mul-1-neg 59.8%

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

      8. unsub-neg 59.8%

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

      9. div-sub 59.8%

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

      10. associate-/l* 67.0%

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

      11. associate-/l* 74.0%

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

      12. distribute-rgt-out-- 74.0%

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

   7. Simplified 74.0%

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

      1. *-commutative 74.0%

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

      2. clear-num 74.0%

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

      3. un-div-inv 74.1%

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

   9. Applied egg-rr 74.1%

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

   if -7.0000000000000006e-30 < t < 3.5000000000000001e32

   1. Initial program 88.3%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   if 3.5000000000000001e32 < t

   1. Initial program 47.2%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in t around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-*r/ 64.3%

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

      3. associate-*r/ 64.3%

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

      4. div-sub 64.3%

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

      5. distribute-lft-out-- 64.3%

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

      6. associate-*r/ 64.3%

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

      7. mul-1-neg 64.3%

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

      8. unsub-neg 64.3%

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

      9. div-sub 64.3%

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

      10. associate-/l* 75.3%

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

      11. associate-/l* 85.5%

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

      12. distribute-rgt-out-- 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-30}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+52)
   x
   (if (<= a -4.5e-193) y (if (<= a 3.8e-29) (* x (/ z t)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+52) {
		tmp = x;
	} else if (a <= -4.5e-193) {
		tmp = y;
	} else if (a <= 3.8e-29) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+52)) then
        tmp = x
    else if (a <= (-4.5d-193)) then
        tmp = y
    else if (a <= 3.8d-29) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+52) {
		tmp = x;
	} else if (a <= -4.5e-193) {
		tmp = y;
	} else if (a <= 3.8e-29) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+52:
		tmp = x
	elif a <= -4.5e-193:
		tmp = y
	elif a <= 3.8e-29:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+52)
		tmp = x;
	elseif (a <= -4.5e-193)
		tmp = y;
	elseif (a <= 3.8e-29)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+52)
		tmp = x;
	elseif (a <= -4.5e-193)
		tmp = y;
	elseif (a <= 3.8e-29)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+52], x, If[LessEqual[a, -4.5e-193], y, If[LessEqual[a, 3.8e-29], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5e52 or 3.79999999999999976e-29 < a

   1. Initial program 69.2%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 43.3%

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

   if -2.5e52 < a < -4.4999999999999999e-193

   1. Initial program 74.9%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around inf 41.3%

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

   if -4.4999999999999999e-193 < a < 3.79999999999999976e-29

   1. Initial program 66.9%

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

      1. associate-/l* 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. associate-*r/ 79.4%

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

      3. associate-*r/ 79.4%

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

      4. div-sub 79.5%

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

      5. distribute-lft-out-- 79.5%

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

      6. associate-*r/ 79.5%

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

      7. mul-1-neg 79.5%

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

      8. unsub-neg 79.5%

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

      9. div-sub 79.4%

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

      10. associate-/l* 77.0%

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

      11. associate-/l* 83.2%

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

      12. distribute-rgt-out-- 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in y around 0 43.8%

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

   9. Taylor expanded in z around inf 38.7%

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

       1. associate-/l* 43.8%

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

   11. Simplified 43.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+96) y (if (<= t 1.02e+43) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+96) {
		tmp = y;
	} else if (t <= 1.02e+43) {
		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 <= (-1.3d+96)) then
        tmp = y
    else if (t <= 1.02d+43) 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 <= -1.3e+96) {
		tmp = y;
	} else if (t <= 1.02e+43) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+96:
		tmp = y
	elif t <= 1.02e+43:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+96)
		tmp = y;
	elseif (t <= 1.02e+43)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+96)
		tmp = y;
	elseif (t <= 1.02e+43)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+96], y, If[LessEqual[t, 1.02e+43], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e96 or 1.02e43 < t

   1. Initial program 42.9%

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

      1. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in t around inf 46.0%

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

   if -1.3e96 < t < 1.02e43

   1. Initial program 87.6%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 34.4%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.6% 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 69.8%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 82.7%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

3. Simplified 82.7%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z - t}{a - t}} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 24.7%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 24.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024046 
(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))))