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

Percentage Accurate: 67.0% → 88.3%

Time: 19.0s

Alternatives: 24

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.0% 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: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-236} \lor \neg \left(t_1 \leq 10^{-169}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-236) (not (<= t_1 1e-169)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-236) || !(t_1 <= 1e-169)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-5d-236)) .or. (.not. (t_1 <= 1d-169))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = y + (((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 t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-236) || !(t_1 <= 1e-169)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-236) or not (t_1 <= 1e-169):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-236) || !(t_1 <= 1e-169))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-236) || ~((t_1 <= 1e-169)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-236], N[Not[LessEqual[t$95$1, 1e-169]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.9999999999999998e-236 or 1.00000000000000002e-169 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.0%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   if -4.9999999999999998e-236 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.00000000000000002e-169

   1. Initial program 13.6%

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

      1. associate-/l* 13.6%

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

   3. Simplified 13.6%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-sub 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-236} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{-169}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 2: 45.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.2e+152)
     y
     (if (<= t -4e+38)
       (* z (/ x t))
       (if (<= t -1.5e-162)
         t_1
         (if (<= t -3.8e-185)
           (/ (* y z) a)
           (if (<= t -8.5e-301)
             t_1
             (if (<= t 1.06e-35)
               (* z (/ (- y x) a))
               (if (<= t 3.2e+91) t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.2e+152) {
		tmp = y;
	} else if (t <= -4e+38) {
		tmp = z * (x / t);
	} else if (t <= -1.5e-162) {
		tmp = t_1;
	} else if (t <= -3.8e-185) {
		tmp = (y * z) / a;
	} else if (t <= -8.5e-301) {
		tmp = t_1;
	} else if (t <= 1.06e-35) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.2e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-7.2d+152)) then
        tmp = y
    else if (t <= (-4d+38)) then
        tmp = z * (x / t)
    else if (t <= (-1.5d-162)) then
        tmp = t_1
    else if (t <= (-3.8d-185)) then
        tmp = (y * z) / a
    else if (t <= (-8.5d-301)) then
        tmp = t_1
    else if (t <= 1.06d-35) then
        tmp = z * ((y - x) / a)
    else if (t <= 3.2d+91) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.2e+152) {
		tmp = y;
	} else if (t <= -4e+38) {
		tmp = z * (x / t);
	} else if (t <= -1.5e-162) {
		tmp = t_1;
	} else if (t <= -3.8e-185) {
		tmp = (y * z) / a;
	} else if (t <= -8.5e-301) {
		tmp = t_1;
	} else if (t <= 1.06e-35) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.2e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -7.2e+152:
		tmp = y
	elif t <= -4e+38:
		tmp = z * (x / t)
	elif t <= -1.5e-162:
		tmp = t_1
	elif t <= -3.8e-185:
		tmp = (y * z) / a
	elif t <= -8.5e-301:
		tmp = t_1
	elif t <= 1.06e-35:
		tmp = z * ((y - x) / a)
	elif t <= 3.2e+91:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -7.2e+152)
		tmp = y;
	elseif (t <= -4e+38)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -1.5e-162)
		tmp = t_1;
	elseif (t <= -3.8e-185)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= -8.5e-301)
		tmp = t_1;
	elseif (t <= 1.06e-35)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 3.2e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -7.2e+152)
		tmp = y;
	elseif (t <= -4e+38)
		tmp = z * (x / t);
	elseif (t <= -1.5e-162)
		tmp = t_1;
	elseif (t <= -3.8e-185)
		tmp = (y * z) / a;
	elseif (t <= -8.5e-301)
		tmp = t_1;
	elseif (t <= 1.06e-35)
		tmp = z * ((y - x) / a);
	elseif (t <= 3.2e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+152], y, If[LessEqual[t, -4e+38], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-162], t$95$1, If[LessEqual[t, -3.8e-185], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, -8.5e-301], t$95$1, If[LessEqual[t, 1.06e-35], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+91], t$95$1, y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.1999999999999998e152 or 3.19999999999999989e91 < t

   1. Initial program 30.5%

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

      1. associate-/l* 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -7.1999999999999998e152 < t < -3.99999999999999991e38

   1. Initial program 50.6%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. div-sub 57.7%

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

      2. associate-*r/ 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 37.9%

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

      3. distribute-neg-frac 37.9%

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

   9. Simplified 37.9%

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

   10. Taylor expanded in a around 0 38.1%

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

       1. *-commutative 38.1%

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

       2. *-rgt-identity 38.1%

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

       3. times-frac 38.3%

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

       4. /-rgt-identity 38.3%

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

   12. Simplified 38.3%

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

   if -3.99999999999999991e38 < t < -1.49999999999999999e-162 or -3.7999999999999999e-185 < t < -8.50000000000000046e-301 or 1.06e-35 < t < 3.19999999999999989e91

   1. Initial program 84.2%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around 0 55.1%

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

      1. +-commutative 55.1%

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

      2. *-commutative 55.1%

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

      3. associate-/l* 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in x around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

   9. Simplified 50.6%

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

   if -1.49999999999999999e-162 < t < -3.7999999999999999e-185

   1. Initial program 87.8%

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

      1. associate-/l* 76.1%

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

   3. Simplified 76.1%

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

      1. associate-/l* 87.8%

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

      2. clear-num 87.2%

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

      3. inv-pow 87.2%

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

   5. Applied egg-rr 87.2%

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

      1. unpow-1 87.2%

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

      2. associate-/r* 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in x around 0 63.6%

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

      1. associate-/l* 63.6%

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

   10. Simplified 63.6%

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

   11. Taylor expanded in t around 0 54.3%

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

   if -8.50000000000000046e-301 < t < 1.06e-35

   1. Initial program 93.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in z around inf 61.4%

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

      1. div-sub 61.4%

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

   9. Simplified 61.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+151}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -3.8e+151)
     y
     (if (<= t -5e+39)
       (* z (/ x t))
       (if (<= t -1.1e+26)
         t_1
         (if (<= t -2.6e-19)
           (* x (- 1.0 (/ z a)))
           (if (<= t 1.95e-171)
             t_1
             (if (<= t 6.2e-28)
               (* z (/ (- y x) a))
               (if (<= t 5.3e+91) t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -3.8e+151) {
		tmp = y;
	} else if (t <= -5e+39) {
		tmp = z * (x / t);
	} else if (t <= -1.1e+26) {
		tmp = t_1;
	} else if (t <= -2.6e-19) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.95e-171) {
		tmp = t_1;
	} else if (t <= 6.2e-28) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.3e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-3.8d+151)) then
        tmp = y
    else if (t <= (-5d+39)) then
        tmp = z * (x / t)
    else if (t <= (-1.1d+26)) then
        tmp = t_1
    else if (t <= (-2.6d-19)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.95d-171) then
        tmp = t_1
    else if (t <= 6.2d-28) then
        tmp = z * ((y - x) / a)
    else if (t <= 5.3d+91) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -3.8e+151) {
		tmp = y;
	} else if (t <= -5e+39) {
		tmp = z * (x / t);
	} else if (t <= -1.1e+26) {
		tmp = t_1;
	} else if (t <= -2.6e-19) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.95e-171) {
		tmp = t_1;
	} else if (t <= 6.2e-28) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.3e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -3.8e+151:
		tmp = y
	elif t <= -5e+39:
		tmp = z * (x / t)
	elif t <= -1.1e+26:
		tmp = t_1
	elif t <= -2.6e-19:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.95e-171:
		tmp = t_1
	elif t <= 6.2e-28:
		tmp = z * ((y - x) / a)
	elif t <= 5.3e+91:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -3.8e+151)
		tmp = y;
	elseif (t <= -5e+39)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -1.1e+26)
		tmp = t_1;
	elseif (t <= -2.6e-19)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.95e-171)
		tmp = t_1;
	elseif (t <= 6.2e-28)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 5.3e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -3.8e+151)
		tmp = y;
	elseif (t <= -5e+39)
		tmp = z * (x / t);
	elseif (t <= -1.1e+26)
		tmp = t_1;
	elseif (t <= -2.6e-19)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.95e-171)
		tmp = t_1;
	elseif (t <= 6.2e-28)
		tmp = z * ((y - x) / a);
	elseif (t <= 5.3e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+151], y, If[LessEqual[t, -5e+39], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e+26], t$95$1, If[LessEqual[t, -2.6e-19], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-171], t$95$1, If[LessEqual[t, 6.2e-28], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+91], t$95$1, y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.8e151 or 5.29999999999999997e91 < t

   1. Initial program 30.5%

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

      1. associate-/l* 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -3.8e151 < t < -5.00000000000000015e39

   1. Initial program 50.6%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. div-sub 57.7%

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

      2. associate-*r/ 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 37.9%

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

      3. distribute-neg-frac 37.9%

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

   9. Simplified 37.9%

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

   10. Taylor expanded in a around 0 38.1%

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

       1. *-commutative 38.1%

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

       2. *-rgt-identity 38.1%

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

       3. times-frac 38.3%

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

       4. /-rgt-identity 38.3%

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

   12. Simplified 38.3%

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

   if -5.00000000000000015e39 < t < -1.10000000000000004e26 or -2.60000000000000013e-19 < t < 1.9499999999999999e-171 or 6.19999999999999984e-28 < t < 5.29999999999999997e91

   1. Initial program 88.1%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 60.7%

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

      1. +-commutative 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around inf 54.0%

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

      1. associate-/l* 57.2%

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

   9. Simplified 57.2%

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

   if -1.10000000000000004e26 < t < -2.60000000000000013e-19

   1. Initial program 61.4%

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

      1. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in t around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. *-commutative 48.9%

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

      3. associate-/l* 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. mul-1-neg 58.9%

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

      3. unsub-neg 58.9%

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

   9. Simplified 58.9%

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

   if 1.9499999999999999e-171 < t < 6.19999999999999984e-28

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

   9. Simplified 65.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+151}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -2.7e+147)
     y
     (if (<= t -1.4e+38)
       (* z (/ x t))
       (if (<= t -2.1e+24)
         t_1
         (if (<= t -2.6e-19)
           (* x (- 1.0 (/ z a)))
           (if (<= t 1e-168)
             t_1
             (if (<= t 2.8e-30)
               (* z (/ (- y x) a))
               (if (<= t 3.6e+91) (+ x (/ z (/ a y))) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -2.7e+147) {
		tmp = y;
	} else if (t <= -1.4e+38) {
		tmp = z * (x / t);
	} else if (t <= -2.1e+24) {
		tmp = t_1;
	} else if (t <= -2.6e-19) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1e-168) {
		tmp = t_1;
	} else if (t <= 2.8e-30) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.6e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-2.7d+147)) then
        tmp = y
    else if (t <= (-1.4d+38)) then
        tmp = z * (x / t)
    else if (t <= (-2.1d+24)) then
        tmp = t_1
    else if (t <= (-2.6d-19)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1d-168) then
        tmp = t_1
    else if (t <= 2.8d-30) then
        tmp = z * ((y - x) / a)
    else if (t <= 3.6d+91) then
        tmp = x + (z / (a / y))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -2.7e+147) {
		tmp = y;
	} else if (t <= -1.4e+38) {
		tmp = z * (x / t);
	} else if (t <= -2.1e+24) {
		tmp = t_1;
	} else if (t <= -2.6e-19) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1e-168) {
		tmp = t_1;
	} else if (t <= 2.8e-30) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.6e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -2.7e+147:
		tmp = y
	elif t <= -1.4e+38:
		tmp = z * (x / t)
	elif t <= -2.1e+24:
		tmp = t_1
	elif t <= -2.6e-19:
		tmp = x * (1.0 - (z / a))
	elif t <= 1e-168:
		tmp = t_1
	elif t <= 2.8e-30:
		tmp = z * ((y - x) / a)
	elif t <= 3.6e+91:
		tmp = x + (z / (a / y))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -2.7e+147)
		tmp = y;
	elseif (t <= -1.4e+38)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -2.1e+24)
		tmp = t_1;
	elseif (t <= -2.6e-19)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1e-168)
		tmp = t_1;
	elseif (t <= 2.8e-30)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 3.6e+91)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -2.7e+147)
		tmp = y;
	elseif (t <= -1.4e+38)
		tmp = z * (x / t);
	elseif (t <= -2.1e+24)
		tmp = t_1;
	elseif (t <= -2.6e-19)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1e-168)
		tmp = t_1;
	elseif (t <= 2.8e-30)
		tmp = z * ((y - x) / a);
	elseif (t <= 3.6e+91)
		tmp = x + (z / (a / y));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+147], y, If[LessEqual[t, -1.4e+38], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e+24], t$95$1, If[LessEqual[t, -2.6e-19], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-168], t$95$1, If[LessEqual[t, 2.8e-30], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+91], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.69999999999999998e147 or 3.6e91 < t

   1. Initial program 30.5%

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

      1. associate-/l* 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -2.69999999999999998e147 < t < -1.4e38

   1. Initial program 50.6%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. div-sub 57.7%

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

      2. associate-*r/ 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 37.9%

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

      3. distribute-neg-frac 37.9%

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

   9. Simplified 37.9%

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

   10. Taylor expanded in a around 0 38.1%

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

       1. *-commutative 38.1%

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

       2. *-rgt-identity 38.1%

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

       3. times-frac 38.3%

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

       4. /-rgt-identity 38.3%

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

   12. Simplified 38.3%

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

   if -1.4e38 < t < -2.1000000000000001e24 or -2.60000000000000013e-19 < t < 1e-168

   1. Initial program 91.2%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around 0 67.7%

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

      1. +-commutative 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-/l* 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in y around inf 58.5%

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

      1. associate-/l* 62.9%

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

   9. Simplified 62.9%

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

   if -2.1000000000000001e24 < t < -2.60000000000000013e-19

   1. Initial program 61.4%

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

      1. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in t around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. *-commutative 48.9%

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

      3. associate-/l* 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. mul-1-neg 58.9%

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

      3. unsub-neg 58.9%

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

   9. Simplified 58.9%

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

   if 1e-168 < t < 2.79999999999999988e-30

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

   9. Simplified 65.8%

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

   if 2.79999999999999988e-30 < t < 3.6e91

   1. Initial program 79.0%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in t around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 40.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 10^{-168}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -5.6e+107)
     t_1
     (if (<= t -7.5e+55)
       (/ (* z (- x y)) t)
       (if (<= t -1.7e-43)
         t_1
         (if (<= t 1.06e-168)
           (+ x (/ y (/ a z)))
           (if (<= t 4e-29)
             (* z (/ (- y x) a))
             (if (<= t 2.95e+91)
               (+ x (/ z (/ a y)))
               (* y (/ (- t z) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -5.6e+107) {
		tmp = t_1;
	} else if (t <= -7.5e+55) {
		tmp = (z * (x - y)) / t;
	} else if (t <= -1.7e-43) {
		tmp = t_1;
	} else if (t <= 1.06e-168) {
		tmp = x + (y / (a / z));
	} else if (t <= 4e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.95e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * ((t - 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) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y / t))
    if (t <= (-5.6d+107)) then
        tmp = t_1
    else if (t <= (-7.5d+55)) then
        tmp = (z * (x - y)) / t
    else if (t <= (-1.7d-43)) then
        tmp = t_1
    else if (t <= 1.06d-168) then
        tmp = x + (y / (a / z))
    else if (t <= 4d-29) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.95d+91) then
        tmp = x + (z / (a / y))
    else
        tmp = y * ((t - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -5.6e+107) {
		tmp = t_1;
	} else if (t <= -7.5e+55) {
		tmp = (z * (x - y)) / t;
	} else if (t <= -1.7e-43) {
		tmp = t_1;
	} else if (t <= 1.06e-168) {
		tmp = x + (y / (a / z));
	} else if (t <= 4e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.95e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -5.6e+107:
		tmp = t_1
	elif t <= -7.5e+55:
		tmp = (z * (x - y)) / t
	elif t <= -1.7e-43:
		tmp = t_1
	elif t <= 1.06e-168:
		tmp = x + (y / (a / z))
	elif t <= 4e-29:
		tmp = z * ((y - x) / a)
	elif t <= 2.95e+91:
		tmp = x + (z / (a / y))
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -5.6e+107)
		tmp = t_1;
	elseif (t <= -7.5e+55)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (t <= -1.7e-43)
		tmp = t_1;
	elseif (t <= 1.06e-168)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4e-29)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.95e+91)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -5.6e+107)
		tmp = t_1;
	elseif (t <= -7.5e+55)
		tmp = (z * (x - y)) / t;
	elseif (t <= -1.7e-43)
		tmp = t_1;
	elseif (t <= 1.06e-168)
		tmp = x + (y / (a / z));
	elseif (t <= 4e-29)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.95e+91)
		tmp = x + (z / (a / y));
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+107], t$95$1, If[LessEqual[t, -7.5e+55], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.7e-43], t$95$1, If[LessEqual[t, 1.06e-168], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-29], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+91], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.59999999999999969e107 or -7.50000000000000014e55 < t < -1.7e-43

   1. Initial program 46.0%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

      1. associate-/l* 46.0%

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

      2. clear-num 45.7%

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

      3. inv-pow 45.7%

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

   5. Applied egg-rr 45.7%

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

      1. unpow-1 45.7%

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

      2. associate-/r* 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in x around 0 48.8%

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

      1. associate-/l* 63.9%

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

   10. Simplified 63.9%

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

   11. Taylor expanded in a around 0 42.8%

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

       1. associate-*r/ 42.8%

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

       2. associate-*r* 42.8%

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

       3. neg-mul-1 42.8%

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

   13. Simplified 42.8%

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

   14. Taylor expanded in z around 0 50.8%

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

       1. +-commutative 50.8%

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

       2. mul-1-neg 50.8%

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

       3. unsub-neg 50.8%

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

       4. associate-/l* 56.5%

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

       5. associate-/r/ 56.5%

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

   16. Simplified 56.5%

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

   if -5.59999999999999969e107 < t < -7.50000000000000014e55

   1. Initial program 67.5%

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

      1. associate-/l* 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in z around inf 76.5%

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

      1. div-sub 76.5%

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

      2. associate-*r/ 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in a around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. *-commutative 76.3%

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

      4. distribute-rgt-neg-in 76.3%

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

   9. Simplified 76.3%

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

   if -1.7e-43 < t < 1.06e-168

   1. Initial program 91.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around inf 61.4%

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

      1. associate-/l* 65.0%

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

   9. Simplified 65.0%

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

   if 1.06e-168 < t < 3.99999999999999977e-29

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

   9. Simplified 65.8%

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

   if 3.99999999999999977e-29 < t < 2.9500000000000001e91

   1. Initial program 79.0%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in t around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 40.8%

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

   if 2.9500000000000001e91 < t

   1. Initial program 27.5%

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

      1. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

      1. associate-/l* 27.5%

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

      2. clear-num 27.4%

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

      3. inv-pow 27.4%

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

   5. Applied egg-rr 27.4%

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

      1. unpow-1 27.4%

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

      2. associate-/r* 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in x around 0 33.2%

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

      1. associate-/l* 70.8%

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

   10. Simplified 70.8%

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

   11. Taylor expanded in a around 0 33.3%

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

       1. associate-*r/ 33.3%

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

       2. associate-*r* 33.3%

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

       3. neg-mul-1 33.3%

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

   13. Simplified 33.3%

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

   14. Taylor expanded in y around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-*l/ 65.1%

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

       3. distribute-rgt-neg-in 65.1%

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

   16. Simplified 65.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+107}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-43}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]

Alternative 6: 48.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+147}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.75e+147)
     y
     (if (<= t -8e+39)
       (* z (/ x t))
       (if (<= t -1.55e-162)
         t_1
         (if (<= t -3.8e-185) (/ (* y z) a) (if (<= t 3.6e+91) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.75e+147) {
		tmp = y;
	} else if (t <= -8e+39) {
		tmp = z * (x / t);
	} else if (t <= -1.55e-162) {
		tmp = t_1;
	} else if (t <= -3.8e-185) {
		tmp = (y * z) / a;
	} else if (t <= 3.6e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-2.75d+147)) then
        tmp = y
    else if (t <= (-8d+39)) then
        tmp = z * (x / t)
    else if (t <= (-1.55d-162)) then
        tmp = t_1
    else if (t <= (-3.8d-185)) then
        tmp = (y * z) / a
    else if (t <= 3.6d+91) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.75e+147) {
		tmp = y;
	} else if (t <= -8e+39) {
		tmp = z * (x / t);
	} else if (t <= -1.55e-162) {
		tmp = t_1;
	} else if (t <= -3.8e-185) {
		tmp = (y * z) / a;
	} else if (t <= 3.6e+91) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.75e+147:
		tmp = y
	elif t <= -8e+39:
		tmp = z * (x / t)
	elif t <= -1.55e-162:
		tmp = t_1
	elif t <= -3.8e-185:
		tmp = (y * z) / a
	elif t <= 3.6e+91:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -2.75e+147)
		tmp = y;
	elseif (t <= -8e+39)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -1.55e-162)
		tmp = t_1;
	elseif (t <= -3.8e-185)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 3.6e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -2.75e+147)
		tmp = y;
	elseif (t <= -8e+39)
		tmp = z * (x / t);
	elseif (t <= -1.55e-162)
		tmp = t_1;
	elseif (t <= -3.8e-185)
		tmp = (y * z) / a;
	elseif (t <= 3.6e+91)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e+147], y, If[LessEqual[t, -8e+39], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.55e-162], t$95$1, If[LessEqual[t, -3.8e-185], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3.6e+91], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7499999999999999e147 or 3.6e91 < t

   1. Initial program 30.5%

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

      1. associate-/l* 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -2.7499999999999999e147 < t < -7.99999999999999952e39

   1. Initial program 50.6%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. div-sub 57.7%

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

      2. associate-*r/ 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 37.9%

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

      3. distribute-neg-frac 37.9%

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

   9. Simplified 37.9%

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

   10. Taylor expanded in a around 0 38.1%

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

       1. *-commutative 38.1%

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

       2. *-rgt-identity 38.1%

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

       3. times-frac 38.3%

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

       4. /-rgt-identity 38.3%

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

   12. Simplified 38.3%

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

   if -7.99999999999999952e39 < t < -1.5499999999999999e-162 or -3.7999999999999999e-185 < t < 3.6e91

   1. Initial program 87.0%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in x around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

   9. Simplified 50.6%

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

   if -1.5499999999999999e-162 < t < -3.7999999999999999e-185

   1. Initial program 87.8%

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

      1. associate-/l* 76.1%

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

   3. Simplified 76.1%

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

      1. associate-/l* 87.8%

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

      2. clear-num 87.2%

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

      3. inv-pow 87.2%

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

   5. Applied egg-rr 87.2%

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

      1. unpow-1 87.2%

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

      2. associate-/r* 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in x around 0 63.6%

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

      1. associate-/l* 63.6%

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

   10. Simplified 63.6%

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

   11. Taylor expanded in t around 0 54.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+147}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -5.4e+23)
     t_2
     (if (<= z 2.2)
       t_1
       (if (<= z 3.7e+30) (+ x (/ y (/ a z))) (if (<= z 4e+115) 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 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.4e+23) {
		tmp = t_2;
	} else if (z <= 2.2) {
		tmp = t_1;
	} else if (z <= 3.7e+30) {
		tmp = x + (y / (a / z));
	} else if (z <= 4e+115) {
		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 = z * ((y - x) / (a - t))
    if (z <= (-5.4d+23)) then
        tmp = t_2
    else if (z <= 2.2d0) then
        tmp = t_1
    else if (z <= 3.7d+30) then
        tmp = x + (y / (a / z))
    else if (z <= 4d+115) 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 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -5.4e+23) {
		tmp = t_2;
	} else if (z <= 2.2) {
		tmp = t_1;
	} else if (z <= 3.7e+30) {
		tmp = x + (y / (a / z));
	} else if (z <= 4e+115) {
		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 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -5.4e+23:
		tmp = t_2
	elif z <= 2.2:
		tmp = t_1
	elif z <= 3.7e+30:
		tmp = x + (y / (a / z))
	elif z <= 4e+115:
		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(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -5.4e+23)
		tmp = t_2;
	elseif (z <= 2.2)
		tmp = t_1;
	elseif (z <= 3.7e+30)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (z <= 4e+115)
		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 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -5.4e+23)
		tmp = t_2;
	elseif (z <= 2.2)
		tmp = t_1;
	elseif (z <= 3.7e+30)
		tmp = x + (y / (a / z));
	elseif (z <= 4e+115)
		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[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+23], t$95$2, If[LessEqual[z, 2.2], t$95$1, If[LessEqual[z, 3.7e+30], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+115], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3999999999999997e23 or 4.0000000000000001e115 < z

   1. Initial program 69.4%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 81.8%

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

      1. div-sub 81.8%

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

   6. Simplified 81.8%

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

   if -5.3999999999999997e23 < z < 2.2000000000000002 or 3.70000000000000016e30 < z < 4.0000000000000001e115

   1. Initial program 60.8%

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

      1. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 46.5%

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

      1. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   if 2.2000000000000002 < z < 3.70000000000000016e30

   1. Initial program 75.7%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in t around 0 72.2%

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

      1. +-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y around inf 71.9%

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

      1. associate-/l* 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 8: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+48}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ a (- y x))))))
   (if (<= a -5.6e+125)
     t_1
     (if (<= a -5.9e+26)
       (/ y (/ (- a t) (- z t)))
       (if (<= a 6.2e+48) (- y (* (- a z) (/ (- x y) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -5.6e+125) {
		tmp = t_1;
	} else if (a <= -5.9e+26) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 6.2e+48) {
		tmp = y - ((a - z) * ((x - y) / 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 + ((z - t) / (a / (y - x)))
    if (a <= (-5.6d+125)) then
        tmp = t_1
    else if (a <= (-5.9d+26)) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 6.2d+48) then
        tmp = y - ((a - z) * ((x - y) / 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 + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -5.6e+125) {
		tmp = t_1;
	} else if (a <= -5.9e+26) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 6.2e+48) {
		tmp = y - ((a - z) * ((x - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / (a / (y - x)))
	tmp = 0
	if a <= -5.6e+125:
		tmp = t_1
	elif a <= -5.9e+26:
		tmp = y / ((a - t) / (z - t))
	elif a <= 6.2e+48:
		tmp = y - ((a - z) * ((x - y) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -5.6e+125)
		tmp = t_1;
	elseif (a <= -5.9e+26)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 6.2e+48)
		tmp = Float64(y - Float64(Float64(a - z) * Float64(Float64(x - y) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / (a / (y - x)));
	tmp = 0.0;
	if (a <= -5.6e+125)
		tmp = t_1;
	elseif (a <= -5.9e+26)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 6.2e+48)
		tmp = y - ((a - z) * ((x - y) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+125], t$95$1, If[LessEqual[a, -5.9e+26], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+48], N[(y - N[(N[(a - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6000000000000002e125 or 6.20000000000000011e48 < a

   1. Initial program 67.3%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-/l* 82.3%

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

   6. Simplified 82.3%

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

   if -5.6000000000000002e125 < a < -5.9000000000000003e26

   1. Initial program 60.7%

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

      1. associate-/l* 71.6%

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

   3. Simplified 71.6%

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

      1. associate-/l* 60.7%

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

      2. clear-num 60.3%

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

      3. inv-pow 60.3%

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

   5. Applied egg-rr 60.3%

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

      1. unpow-1 60.3%

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

      2. associate-/r* 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in x around 0 57.6%

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

      1. associate-/l* 76.4%

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

   10. Simplified 76.4%

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

   if -5.9000000000000003e26 < a < 6.20000000000000011e48

   1. Initial program 63.8%

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

      1. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. unsub-neg 73.7%

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

      3. div-sub 72.4%

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

      4. *-commutative 72.4%

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

      5. div-sub 73.7%

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

      6. distribute-rgt-out-- 73.7%

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

   6. Simplified 73.7%

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

      1. *-commutative 73.7%

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

      2. *-un-lft-identity 73.7%

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

      3. times-frac 79.1%

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

   8. Applied egg-rr 79.1%

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

   9. Taylor expanded in z around 0 77.6%

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

       1. mul-1-neg 77.6%

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

       2. unsub-neg 77.6%

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

       3. div-sub 77.7%

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

       4. *-commutative 77.7%

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

       5. associate-*r/ 72.4%

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

       6. associate-/l* 77.8%

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

       7. associate-/l* 77.1%

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

       8. div-sub 79.1%

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

       9. associate-/l* 73.7%

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

       10. associate-*r/ 79.1%

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

   11. Simplified 79.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+48}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 9: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-7} \lor \neg \left(t \leq 1.28 \cdot 10^{+110}\right):\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e-7) (not (<= t 1.28e+110)))
   (- y (* (- a z) (/ (- x y) t)))
   (+ x (/ (* (- y x) (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e-7) || !(t <= 1.28e+110)) {
		tmp = y - ((a - z) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.35d-7)) .or. (.not. (t <= 1.28d+110))) then
        tmp = y - ((a - z) * ((x - y) / t))
    else
        tmp = x + (((y - x) * (z - t)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e-7) || !(t <= 1.28e+110)) {
		tmp = y - ((a - z) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e-7) or not (t <= 1.28e+110):
		tmp = y - ((a - z) * ((x - y) / t))
	else:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e-7) || !(t <= 1.28e+110))
		tmp = Float64(y - Float64(Float64(a - z) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e-7) || ~((t <= 1.28e+110)))
		tmp = y - ((a - z) * ((x - y) / t));
	else
		tmp = x + (((y - x) * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e-7], N[Not[LessEqual[t, 1.28e+110]], $MachinePrecision]], N[(y - N[(N[(a - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000004e-7 or 1.28e110 < t

   1. Initial program 36.2%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in t around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. div-sub 67.5%

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

      4. *-commutative 67.5%

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

      5. div-sub 67.5%

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

      6. distribute-rgt-out-- 68.5%

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

   6. Simplified 68.5%

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

      1. *-commutative 68.5%

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

      2. *-un-lft-identity 68.5%

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

      3. times-frac 85.2%

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

   8. Applied egg-rr 85.2%

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

   9. Taylor expanded in z around 0 77.1%

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

       1. mul-1-neg 77.1%

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

       2. unsub-neg 77.1%

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

       3. div-sub 77.1%

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

       4. *-commutative 77.1%

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

       5. associate-*r/ 67.5%

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

       6. associate-/l* 77.1%

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

       7. associate-/l* 84.3%

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

       8. div-sub 85.2%

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

       9. associate-/l* 68.5%

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

       10. associate-*r/ 85.2%

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

   11. Simplified 85.2%

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

   if -1.35000000000000004e-7 < t < 1.28e110

   1. Initial program 89.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-7} \lor \neg \left(t \leq 1.28 \cdot 10^{+110}\right):\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 10: 53.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -6.5e-43)
     t_1
     (if (<= t 7.5e-169)
       (+ x (/ y (/ a z)))
       (if (<= t 1.02e-29)
         (* z (/ (- y x) a))
         (if (<= t 2.9e+91) (+ x (/ z (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -6.5e-43) {
		tmp = t_1;
	} else if (t <= 7.5e-169) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.02e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.9e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y / t))
    if (t <= (-6.5d-43)) then
        tmp = t_1
    else if (t <= 7.5d-169) then
        tmp = x + (y / (a / z))
    else if (t <= 1.02d-29) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.9d+91) then
        tmp = x + (z / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -6.5e-43) {
		tmp = t_1;
	} else if (t <= 7.5e-169) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.02e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.9e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -6.5e-43:
		tmp = t_1
	elif t <= 7.5e-169:
		tmp = x + (y / (a / z))
	elif t <= 1.02e-29:
		tmp = z * ((y - x) / a)
	elif t <= 2.9e+91:
		tmp = x + (z / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -6.5e-43)
		tmp = t_1;
	elseif (t <= 7.5e-169)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.02e-29)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.9e+91)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -6.5e-43)
		tmp = t_1;
	elseif (t <= 7.5e-169)
		tmp = x + (y / (a / z));
	elseif (t <= 1.02e-29)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.9e+91)
		tmp = x + (z / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-43], t$95$1, If[LessEqual[t, 7.5e-169], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-29], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+91], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.50000000000000001e-43 or 2.90000000000000014e91 < t

   1. Initial program 40.9%

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

      1. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

      1. associate-/l* 40.9%

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

      2. clear-num 40.7%

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

      3. inv-pow 40.7%

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

   5. Applied egg-rr 40.7%

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

      1. unpow-1 40.7%

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

      2. associate-/r* 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in x around 0 43.1%

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

      1. associate-/l* 64.7%

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

   10. Simplified 64.7%

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

   11. Taylor expanded in a around 0 39.2%

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

       1. associate-*r/ 39.2%

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

       2. associate-*r* 39.2%

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

       3. neg-mul-1 39.2%

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

   13. Simplified 39.2%

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

   14. Taylor expanded in z around 0 52.8%

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

       1. +-commutative 52.8%

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

       2. mul-1-neg 52.8%

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

       3. unsub-neg 52.8%

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

       4. associate-/l* 57.9%

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

       5. associate-/r/ 57.9%

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

   16. Simplified 57.9%

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

   if -6.50000000000000001e-43 < t < 7.49999999999999978e-169

   1. Initial program 91.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around inf 61.4%

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

      1. associate-/l* 65.0%

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

   9. Simplified 65.0%

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

   if 7.49999999999999978e-169 < t < 1.01999999999999994e-29

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

   9. Simplified 65.8%

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

   if 1.01999999999999994e-29 < t < 2.90000000000000014e91

   1. Initial program 79.0%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in t around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 40.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-43}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-43}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e-43)
   (- y (* z (/ y t)))
   (if (<= t 8.2e-169)
     (+ x (/ y (/ a z)))
     (if (<= t 4.2e-29)
       (* z (/ (- y x) a))
       (if (<= t 3e+91) (+ x (/ z (/ a y))) (* y (/ (- t z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e-43) {
		tmp = y - (z * (y / t));
	} else if (t <= 8.2e-169) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.2e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * ((t - 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 <= (-3.1d-43)) then
        tmp = y - (z * (y / t))
    else if (t <= 8.2d-169) then
        tmp = x + (y / (a / z))
    else if (t <= 4.2d-29) then
        tmp = z * ((y - x) / a)
    else if (t <= 3d+91) then
        tmp = x + (z / (a / y))
    else
        tmp = y * ((t - 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 <= -3.1e-43) {
		tmp = y - (z * (y / t));
	} else if (t <= 8.2e-169) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.2e-29) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3e+91) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e-43:
		tmp = y - (z * (y / t))
	elif t <= 8.2e-169:
		tmp = x + (y / (a / z))
	elif t <= 4.2e-29:
		tmp = z * ((y - x) / a)
	elif t <= 3e+91:
		tmp = x + (z / (a / y))
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e-43)
		tmp = Float64(y - Float64(z * Float64(y / t)));
	elseif (t <= 8.2e-169)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.2e-29)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 3e+91)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e-43)
		tmp = y - (z * (y / t));
	elseif (t <= 8.2e-169)
		tmp = x + (y / (a / z));
	elseif (t <= 4.2e-29)
		tmp = z * ((y - x) / a);
	elseif (t <= 3e+91)
		tmp = x + (z / (a / y));
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e-43], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-169], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-29], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+91], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.0999999999999999e-43

   1. Initial program 49.2%

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

      1. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

      1. associate-/l* 49.2%

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

      2. clear-num 49.0%

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

      3. inv-pow 49.0%

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

   5. Applied egg-rr 49.0%

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

      1. unpow-1 49.0%

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

      2. associate-/r* 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in x around 0 49.2%

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

      1. associate-/l* 60.9%

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

   10. Simplified 60.9%

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

   11. Taylor expanded in a around 0 42.9%

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

       1. associate-*r/ 42.9%

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

       2. associate-*r* 42.9%

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

       3. neg-mul-1 42.9%

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

   13. Simplified 42.9%

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

   14. Taylor expanded in z around 0 49.7%

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

       1. +-commutative 49.7%

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

       2. mul-1-neg 49.7%

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

       3. unsub-neg 49.7%

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

       4. associate-/l* 53.4%

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

       5. associate-/r/ 53.4%

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

   16. Simplified 53.4%

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

   if -3.0999999999999999e-43 < t < 8.1999999999999996e-169

   1. Initial program 91.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around inf 61.4%

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

      1. associate-/l* 65.0%

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

   9. Simplified 65.0%

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

   if 8.1999999999999996e-169 < t < 4.19999999999999979e-29

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

   9. Simplified 65.8%

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

   if 4.19999999999999979e-29 < t < 3.00000000000000006e91

   1. Initial program 79.0%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in t around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 40.8%

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

   if 3.00000000000000006e91 < t

   1. Initial program 27.5%

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

      1. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

      1. associate-/l* 27.5%

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

      2. clear-num 27.4%

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

      3. inv-pow 27.4%

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

   5. Applied egg-rr 27.4%

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

      1. unpow-1 27.4%

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

      2. associate-/r* 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in x around 0 33.2%

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

      1. associate-/l* 70.8%

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

   10. Simplified 70.8%

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

   11. Taylor expanded in a around 0 33.3%

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

       1. associate-*r/ 33.3%

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

       2. associate-*r* 33.3%

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

       3. neg-mul-1 33.3%

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

   13. Simplified 33.3%

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

   14. Taylor expanded in y around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-*l/ 65.1%

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

       3. distribute-rgt-neg-in 65.1%

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

   16. Simplified 65.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-43}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]

Alternative 12: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq 4.2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-64}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a 4.2e-157)
     t_1
     (if (<= a 9e-64)
       (/ (- z) (/ (- a t) x))
       (if (<= a 2.25e+98) t_1 (+ x (/ z (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= 4.2e-157) {
		tmp = t_1;
	} else if (a <= 9e-64) {
		tmp = -z / ((a - t) / x);
	} else if (a <= 2.25e+98) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= 4.2d-157) then
        tmp = t_1
    else if (a <= 9d-64) then
        tmp = -z / ((a - t) / x)
    else if (a <= 2.25d+98) then
        tmp = t_1
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= 4.2e-157) {
		tmp = t_1;
	} else if (a <= 9e-64) {
		tmp = -z / ((a - t) / x);
	} else if (a <= 2.25e+98) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= 4.2e-157:
		tmp = t_1
	elif a <= 9e-64:
		tmp = -z / ((a - t) / x)
	elif a <= 2.25e+98:
		tmp = t_1
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= 4.2e-157)
		tmp = t_1;
	elseif (a <= 9e-64)
		tmp = Float64(Float64(-z) / Float64(Float64(a - t) / x));
	elseif (a <= 2.25e+98)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= 4.2e-157)
		tmp = t_1;
	elseif (a <= 9e-64)
		tmp = -z / ((a - t) / x);
	elseif (a <= 2.25e+98)
		tmp = t_1;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4.2e-157], t$95$1, If[LessEqual[a, 9e-64], N[((-z) / N[(N[(a - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+98], t$95$1, N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 4.2e-157 or 9.00000000000000019e-64 < a < 2.2500000000000001e98

   1. Initial program 63.6%

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

      1. associate-/l* 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 61.3%

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

   6. Simplified 61.3%

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

   if 4.2e-157 < a < 9.00000000000000019e-64

   1. Initial program 70.4%

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

      1. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 67.7%

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

      1. div-sub 67.7%

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

      2. associate-*r/ 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in y around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. associate-/l* 57.8%

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

      3. distribute-neg-frac 57.8%

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

   9. Simplified 57.8%

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

   if 2.2500000000000001e98 < a

   1. Initial program 65.7%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in y around inf 73.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-64}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 70.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 0.00072:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e-42)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t 0.00072)
     (+ x (/ (- z t) (/ a (- y x))))
     (+ y (/ (- z a) (/ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e-42) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 0.00072) {
		tmp = x + ((z - t) / (a / (y - x)));
	} else {
		tmp = y + ((z - a) / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d-42)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 0.00072d0) then
        tmp = x + ((z - t) / (a / (y - x)))
    else
        tmp = y + ((z - a) / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e-42) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 0.00072) {
		tmp = x + ((z - t) / (a / (y - x)));
	} else {
		tmp = y + ((z - a) / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e-42:
		tmp = y + ((x - y) / (t / z))
	elif t <= 0.00072:
		tmp = x + ((z - t) / (a / (y - x)))
	else:
		tmp = y + ((z - a) / (t / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e-42)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 0.00072)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))));
	else
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e-42)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 0.00072)
		tmp = x + ((z - t) / (a / (y - x)));
	else
		tmp = y + ((z - a) / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e-42], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00072], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000001e-42

   1. Initial program 49.2%

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

      1. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around -inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. div-sub 67.4%

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

      4. *-commutative 67.4%

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

      5. div-sub 67.4%

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

      6. distribute-rgt-out-- 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. associate-/l* 72.1%

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

   9. Simplified 72.1%

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

   if -1.25000000000000001e-42 < t < 7.20000000000000045e-4

   1. Initial program 91.4%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 77.4%

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

   6. Simplified 77.4%

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

   if 7.20000000000000045e-4 < t

   1. Initial program 41.3%

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

      1. associate-/l* 69.4%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in t around -inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

      3. div-sub 66.6%

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

      4. *-commutative 66.6%

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

      5. div-sub 66.6%

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

      6. distribute-rgt-out-- 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-/l* 76.9%

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

   9. Simplified 76.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 0.00072:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \end{array} \]

Alternative 14: 31.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+215)
   (* (/ z a) (- x))
   (if (<= z -4.4e+26)
     (/ z (/ t x))
     (if (<= z 2.65e+60)
       y
       (if (<= z 2.3e+216) (* z (/ x t)) (/ (- y) (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+215) {
		tmp = (z / a) * -x;
	} else if (z <= -4.4e+26) {
		tmp = z / (t / x);
	} else if (z <= 2.65e+60) {
		tmp = y;
	} else if (z <= 2.3e+216) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+215)) then
        tmp = (z / a) * -x
    else if (z <= (-4.4d+26)) then
        tmp = z / (t / x)
    else if (z <= 2.65d+60) then
        tmp = y
    else if (z <= 2.3d+216) then
        tmp = z * (x / t)
    else
        tmp = -y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+215) {
		tmp = (z / a) * -x;
	} else if (z <= -4.4e+26) {
		tmp = z / (t / x);
	} else if (z <= 2.65e+60) {
		tmp = y;
	} else if (z <= 2.3e+216) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+215:
		tmp = (z / a) * -x
	elif z <= -4.4e+26:
		tmp = z / (t / x)
	elif z <= 2.65e+60:
		tmp = y
	elif z <= 2.3e+216:
		tmp = z * (x / t)
	else:
		tmp = -y / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+215)
		tmp = Float64(Float64(z / a) * Float64(-x));
	elseif (z <= -4.4e+26)
		tmp = Float64(z / Float64(t / x));
	elseif (z <= 2.65e+60)
		tmp = y;
	elseif (z <= 2.3e+216)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = Float64(Float64(-y) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+215)
		tmp = (z / a) * -x;
	elseif (z <= -4.4e+26)
		tmp = z / (t / x);
	elseif (z <= 2.65e+60)
		tmp = y;
	elseif (z <= 2.3e+216)
		tmp = z * (x / t);
	else
		tmp = -y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+215], N[(N[(z / a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, -4.4e+26], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+60], y, If[LessEqual[z, 2.3e+216], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.49999999999999977e215

   1. Initial program 55.4%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 45.2%

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

      1. +-commutative 45.2%

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

      2. *-commutative 45.2%

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

      3. associate-/l* 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in x around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in z around inf 35.6%

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

       1. mul-1-neg 35.6%

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

       2. associate-*l/ 43.9%

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

       3. *-commutative 43.9%

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

       4. distribute-rgt-neg-in 43.9%

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

   12. Simplified 43.9%

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

   if -3.49999999999999977e215 < z < -4.40000000000000014e26

   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* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. div-sub 79.1%

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

      2. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. associate-/l* 53.1%

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

      3. distribute-neg-frac 53.1%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in a around 0 39.6%

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

       1. associate-/l* 44.8%

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

   12. Simplified 44.8%

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

   if -4.40000000000000014e26 < z < 2.6499999999999998e60

   1. Initial program 61.1%

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

      1. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around inf 42.9%

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

   if 2.6499999999999998e60 < z < 2.29999999999999996e216

   1. Initial program 75.3%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in z around inf 69.8%

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

      1. div-sub 69.7%

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

      2. associate-*r/ 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in y around 0 29.4%

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

      1. mul-1-neg 29.4%

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

      2. associate-/l* 43.0%

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

      3. distribute-neg-frac 43.0%

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

   9. Simplified 43.0%

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

   10. Taylor expanded in a around 0 26.8%

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

       1. *-commutative 26.8%

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

       2. *-rgt-identity 26.8%

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

       3. times-frac 40.4%

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

       4. /-rgt-identity 40.4%

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

   12. Simplified 40.4%

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

   if 2.29999999999999996e216 < z

   1. Initial program 72.1%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/l* 72.1%

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

      2. clear-num 72.1%

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

      3. inv-pow 72.1%

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

   5. Applied egg-rr 72.1%

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

      1. unpow-1 72.1%

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

      2. associate-/r* 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in x around 0 43.5%

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

      1. associate-/l* 59.2%

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

   10. Simplified 59.2%

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

   11. Taylor expanded in a around 0 39.4%

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

       1. associate-*r/ 39.4%

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

       2. associate-*r* 39.4%

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

       3. neg-mul-1 39.4%

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

   13. Simplified 39.4%

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

   14. Taylor expanded in z around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-/l* 50.6%

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

   16. Simplified 50.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \]

Alternative 15: 31.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+215}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+215)
   (* (- z) (/ x a))
   (if (<= z -7.2e+26)
     (/ z (/ t x))
     (if (<= z 1.8e+60)
       y
       (if (<= z 4.6e+214) (* z (/ x t)) (/ (- y) (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+215) {
		tmp = -z * (x / a);
	} else if (z <= -7.2e+26) {
		tmp = z / (t / x);
	} else if (z <= 1.8e+60) {
		tmp = y;
	} else if (z <= 4.6e+214) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.6d+215)) then
        tmp = -z * (x / a)
    else if (z <= (-7.2d+26)) then
        tmp = z / (t / x)
    else if (z <= 1.8d+60) then
        tmp = y
    else if (z <= 4.6d+214) then
        tmp = z * (x / t)
    else
        tmp = -y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+215) {
		tmp = -z * (x / a);
	} else if (z <= -7.2e+26) {
		tmp = z / (t / x);
	} else if (z <= 1.8e+60) {
		tmp = y;
	} else if (z <= 4.6e+214) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+215:
		tmp = -z * (x / a)
	elif z <= -7.2e+26:
		tmp = z / (t / x)
	elif z <= 1.8e+60:
		tmp = y
	elif z <= 4.6e+214:
		tmp = z * (x / t)
	else:
		tmp = -y / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+215)
		tmp = Float64(Float64(-z) * Float64(x / a));
	elseif (z <= -7.2e+26)
		tmp = Float64(z / Float64(t / x));
	elseif (z <= 1.8e+60)
		tmp = y;
	elseif (z <= 4.6e+214)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = Float64(Float64(-y) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+215)
		tmp = -z * (x / a);
	elseif (z <= -7.2e+26)
		tmp = z / (t / x);
	elseif (z <= 1.8e+60)
		tmp = y;
	elseif (z <= 4.6e+214)
		tmp = z * (x / t);
	else
		tmp = -y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+215], N[((-z) * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e+26], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+60], y, If[LessEqual[z, 4.6e+214], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.5999999999999999e215

   1. Initial program 55.4%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 45.2%

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

      1. +-commutative 45.2%

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

      2. *-commutative 45.2%

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

      3. associate-/l* 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in x around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in z around inf 35.6%

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

       1. associate-/l* 44.4%

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

       2. associate-*r/ 44.4%

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

       3. associate-*l/ 44.4%

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

       4. metadata-eval 44.4%

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

       5. distribute-neg-frac 44.4%

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

       6. distribute-lft-neg-in 44.4%

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

       7. *-commutative 44.4%

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

       8. distribute-rgt-neg-in 44.4%

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

       9. associate-/r/ 44.4%

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

       10. associate-*l/ 44.5%

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

       11. *-lft-identity 44.5%

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

   12. Simplified 44.5%

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

   if -5.5999999999999999e215 < z < -7.20000000000000048e26

   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* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. div-sub 79.1%

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

      2. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. associate-/l* 53.1%

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

      3. distribute-neg-frac 53.1%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in a around 0 39.6%

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

       1. associate-/l* 44.8%

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

   12. Simplified 44.8%

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

   if -7.20000000000000048e26 < z < 1.79999999999999984e60

   1. Initial program 61.1%

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

      1. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around inf 42.9%

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

   if 1.79999999999999984e60 < z < 4.5999999999999998e214

   1. Initial program 75.3%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in z around inf 69.8%

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

      1. div-sub 69.7%

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

      2. associate-*r/ 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in y around 0 29.4%

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

      1. mul-1-neg 29.4%

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

      2. associate-/l* 43.0%

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

      3. distribute-neg-frac 43.0%

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

   9. Simplified 43.0%

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

   10. Taylor expanded in a around 0 26.8%

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

       1. *-commutative 26.8%

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

       2. *-rgt-identity 26.8%

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

       3. times-frac 40.4%

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

       4. /-rgt-identity 40.4%

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

   12. Simplified 40.4%

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

   if 4.5999999999999998e214 < z

   1. Initial program 72.1%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/l* 72.1%

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

      2. clear-num 72.1%

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

      3. inv-pow 72.1%

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

   5. Applied egg-rr 72.1%

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

      1. unpow-1 72.1%

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

      2. associate-/r* 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in x around 0 43.5%

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

      1. associate-/l* 59.2%

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

   10. Simplified 59.2%

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

   11. Taylor expanded in a around 0 39.4%

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

       1. associate-*r/ 39.4%

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

       2. associate-*r* 39.4%

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

       3. neg-mul-1 39.4%

          \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot \left(z - t\right)}{t} \]

   13. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(z - t\right)}{t}} \]

   14. Taylor expanded in z around inf 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   15. Step-by-step derivation

       1. mul-1-neg 39.4%

          \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

       2. associate-/l* 50.6%

          \[\leadsto -\color{blue}{\frac{y}{\frac{t}{z}}} \]

   16. Simplified 50.6%

       \[\leadsto \color{blue}{-\frac{y}{\frac{t}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+215}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \]

Alternative 16: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-42} \lor \neg \left(t \leq 9600000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.18e-42) (not (<= t 9600000000000.0)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.18e-42) || !(t <= 9600000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.18d-42)) .or. (.not. (t <= 9600000000000.0d0))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.18e-42) || !(t <= 9600000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.18e-42) or not (t <= 9600000000000.0):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.18e-42) || !(t <= 9600000000000.0))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.18e-42) || ~((t <= 9600000000000.0)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.18e-42], N[Not[LessEqual[t, 9600000000000.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.17999999999999995e-42 or 9.6e12 < t

   1. Initial program 44.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 67.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in x around 0 42.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 61.7%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 61.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.17999999999999995e-42 < t < 9.6e12

   1. Initial program 90.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 68.6%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 68.6%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 68.6%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 72.3%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-42} \lor \neg \left(t \leq 9600000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 17: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-43} \lor \neg \left(t \leq 3900000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.1e-43) (not (<= t 3900000000000.0)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.1e-43) || !(t <= 3900000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.1d-43)) .or. (.not. (t <= 3900000000000.0d0))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.1e-43) || !(t <= 3900000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.1e-43) or not (t <= 3900000000000.0):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.1e-43) || !(t <= 3900000000000.0))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.1e-43) || ~((t <= 3900000000000.0)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.1e-43], N[Not[LessEqual[t, 3900000000000.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.10000000000000037e-43 or 3.9e12 < t

   1. Initial program 44.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 67.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in x around 0 42.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 61.7%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 61.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -6.10000000000000037e-43 < t < 3.9e12

   1. Initial program 90.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 74.7%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-43} \lor \neg \left(t \leq 3900000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 18: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-43} \lor \neg \left(t \leq 1.85 \cdot 10^{-24}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e-43) (not (<= t 1.85e-24)))
   (+ y (/ (- x y) (/ t z)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-43) || !(t <= 1.85e-24)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3d-43)) .or. (.not. (t <= 1.85d-24))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-43) || !(t <= 1.85e-24)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e-43) or not (t <= 1.85e-24):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e-43) || !(t <= 1.85e-24))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e-43) || ~((t <= 1.85e-24)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e-43], N[Not[LessEqual[t, 1.85e-24]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000003e-43 or 1.8499999999999999e-24 < t

   1. Initial program 47.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 68.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 66.0%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.0%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 66.0%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 66.0%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 66.0%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 66.0%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 66.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 66.7%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 62.6%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 62.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 72.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 72.8%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   if -3.00000000000000003e-43 < t < 1.8499999999999999e-24

   1. Initial program 91.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 78.6%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-43} \lor \neg \left(t \leq 1.85 \cdot 10^{-24}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 19: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-43}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 0.009:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e-43)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t 0.009) (+ x (/ (- y x) (/ a z))) (+ y (/ (- z a) (/ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e-43) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 0.009) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y + ((z - a) / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.2d-43)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 0.009d0) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y + ((z - a) / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e-43) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 0.009) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y + ((z - a) / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e-43:
		tmp = y + ((x - y) / (t / z))
	elif t <= 0.009:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y + ((z - a) / (t / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e-43)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 0.009)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e-43)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 0.009)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y + ((z - a) / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e-43], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.009], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999995e-43

   1. Initial program 49.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 66.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 67.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 67.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 67.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 67.4%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 67.4%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 67.4%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 68.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 68.6%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 64.8%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 72.1%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 72.1%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   if -9.1999999999999995e-43 < t < 0.00899999999999999932

   1. Initial program 91.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 76.3%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a}{z}}} \]

   if 0.00899999999999999932 < t

   1. Initial program 41.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 69.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 66.6%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.6%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 66.6%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 66.6%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 66.6%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 66.6%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 66.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 66.8%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in y around 0 67.4%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{\left(z - a\right) \cdot x}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 67.4%

         \[\leadsto y - \color{blue}{\left(-\frac{\left(z - a\right) \cdot x}{t}\right)} \]

      2. associate-/l* 76.9%

         \[\leadsto y - \left(-\color{blue}{\frac{z - a}{\frac{t}{x}}}\right) \]

   9. Simplified 76.9%

      \[\leadsto y - \color{blue}{\left(-\frac{z - a}{\frac{t}{x}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-43}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 0.009:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \end{array} \]

Alternative 20: 31.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+26)
   (/ z (/ t x))
   (if (<= z 1.35e+60)
     y
     (if (<= z 2.5e+215) (* z (/ x t)) (/ (- y) (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+26) {
		tmp = z / (t / x);
	} else if (z <= 1.35e+60) {
		tmp = y;
	} else if (z <= 2.5e+215) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.4d+26)) then
        tmp = z / (t / x)
    else if (z <= 1.35d+60) then
        tmp = y
    else if (z <= 2.5d+215) then
        tmp = z * (x / t)
    else
        tmp = -y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+26) {
		tmp = z / (t / x);
	} else if (z <= 1.35e+60) {
		tmp = y;
	} else if (z <= 2.5e+215) {
		tmp = z * (x / t);
	} else {
		tmp = -y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+26:
		tmp = z / (t / x)
	elif z <= 1.35e+60:
		tmp = y
	elif z <= 2.5e+215:
		tmp = z * (x / t)
	else:
		tmp = -y / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+26)
		tmp = Float64(z / Float64(t / x));
	elseif (z <= 1.35e+60)
		tmp = y;
	elseif (z <= 2.5e+215)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = Float64(Float64(-y) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+26)
		tmp = z / (t / x);
	elseif (z <= 1.35e+60)
		tmp = y;
	elseif (z <= 2.5e+215)
		tmp = z * (x / t);
	else
		tmp = -y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+26], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+60], y, If[LessEqual[z, 2.5e+215], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4000000000000003e26

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 86.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 78.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 65.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 45.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{a - t}} \]

      2. associate-/l* 51.6%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a - t}{x}}} \]

      3. distribute-neg-frac 51.6%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   9. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   10. Taylor expanded in a around 0 32.7%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 35.8%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if -3.4000000000000003e26 < z < 1.35e60

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 73.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{y} \]

   if 1.35e60 < z < 2.5000000000000001e215

   1. Initial program 75.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 82.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 69.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 69.7%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 29.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 29.4%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{a - t}} \]

      2. associate-/l* 43.0%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a - t}{x}}} \]

      3. distribute-neg-frac 43.0%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   9. Simplified 43.0%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   10. Taylor expanded in a around 0 26.8%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. *-commutative 26.8%

          \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]

       2. *-rgt-identity 26.8%

          \[\leadsto \frac{x \cdot z}{\color{blue}{t \cdot 1}} \]

       3. times-frac 40.4%

          \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{z}{1}} \]

       4. /-rgt-identity 40.4%

          \[\leadsto \frac{x}{t} \cdot \color{blue}{z} \]

   12. Simplified 40.4%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot z} \]

   if 2.5000000000000001e215 < z

   1. Initial program 72.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.1%

         \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]

      2. clear-num 72.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      3. inv-pow 72.1%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}\right)}^{-1}} \]

   5. Applied egg-rr 72.1%

      \[\leadsto x + \color{blue}{{\left(\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 72.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      2. associate-/r* 96.9%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a - t}{y - x}}{z - t}}} \]

   7. Simplified 96.9%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{y - x}}{z - t}}} \]

   8. Taylor expanded in x around 0 43.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   9. Step-by-step derivation

      1. associate-/l* 59.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   10. Simplified 59.2%

       \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   11. Taylor expanded in a around 0 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-*r/ 39.4%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot \left(z - t\right)\right)}{t}} \]

       2. associate-*r* 39.4%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(z - t\right)}}{t} \]

       3. neg-mul-1 39.4%

          \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot \left(z - t\right)}{t} \]

   13. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(z - t\right)}{t}} \]

   14. Taylor expanded in z around inf 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   15. Step-by-step derivation

       1. mul-1-neg 39.4%

          \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

       2. associate-/l* 50.6%

          \[\leadsto -\color{blue}{\frac{y}{\frac{t}{z}}} \]

   16. Simplified 50.6%

       \[\leadsto \color{blue}{-\frac{y}{\frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \end{array} \]

Alternative 21: 31.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+26} \lor \neg \left(z \leq 1.52 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.55e+26) (not (<= z 1.52e+60))) (* z (/ x t)) y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+26) || !(z <= 1.52e+60)) {
		tmp = z * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.55d+26)) .or. (.not. (z <= 1.52d+60))) then
        tmp = z * (x / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+26) || !(z <= 1.52e+60)) {
		tmp = z * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.55e+26) or not (z <= 1.52e+60):
		tmp = z * (x / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.55e+26) || !(z <= 1.52e+60))
		tmp = Float64(z * Float64(x / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.55e+26) || ~((z <= 1.52e+60)))
		tmp = z * (x / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.55e+26], N[Not[LessEqual[z, 1.52e+60]], $MachinePrecision]], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e26 or 1.52e60 < z

   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* 88.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 78.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 62.6%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 62.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 38.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{a - t}} \]

      2. associate-/l* 46.8%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a - t}{x}}} \]

      3. distribute-neg-frac 46.8%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   9. Simplified 46.8%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   10. Taylor expanded in a around 0 28.9%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. *-commutative 28.9%

          \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]

       2. *-rgt-identity 28.9%

          \[\leadsto \frac{x \cdot z}{\color{blue}{t \cdot 1}} \]

       3. times-frac 34.9%

          \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{z}{1}} \]

       4. /-rgt-identity 34.9%

          \[\leadsto \frac{x}{t} \cdot \color{blue}{z} \]

   12. Simplified 34.9%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot z} \]

   if -2.5499999999999999e26 < z < 1.52e60

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 73.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+26} \lor \neg \left(z \leq 1.52 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22: 31.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e+26) (/ z (/ t x)) (if (<= z 2.65e+60) y (* z (/ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+26) {
		tmp = z / (t / x);
	} else if (z <= 2.65e+60) {
		tmp = y;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.1d+26)) then
        tmp = z / (t / x)
    else if (z <= 2.65d+60) then
        tmp = y
    else
        tmp = z * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+26) {
		tmp = z / (t / x);
	} else if (z <= 2.65e+60) {
		tmp = y;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e+26:
		tmp = z / (t / x)
	elif z <= 2.65e+60:
		tmp = y
	else:
		tmp = z * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e+26)
		tmp = Float64(z / Float64(t / x));
	elseif (z <= 2.65e+60)
		tmp = y;
	else
		tmp = Float64(z * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e+26)
		tmp = z / (t / x);
	elseif (z <= 2.65e+60)
		tmp = y;
	else
		tmp = z * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e+26], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+60], y, N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.09999999999999983e26

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 86.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 78.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 65.1%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 45.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{a - t}} \]

      2. associate-/l* 51.6%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a - t}{x}}} \]

      3. distribute-neg-frac 51.6%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   9. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   10. Taylor expanded in a around 0 32.7%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 35.8%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if -4.09999999999999983e26 < z < 2.6499999999999998e60

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 73.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{y} \]

   if 2.6499999999999998e60 < z

   1. Initial program 73.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 78.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. associate-*r/ 60.0%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   7. Taylor expanded in y around 0 32.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 32.2%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{a - t}} \]

      2. associate-/l* 41.7%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a - t}{x}}} \]

      3. distribute-neg-frac 41.7%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   9. Simplified 41.7%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a - t}{x}}} \]

   10. Taylor expanded in a around 0 24.8%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. *-commutative 24.8%

          \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]

       2. *-rgt-identity 24.8%

          \[\leadsto \frac{x \cdot z}{\color{blue}{t \cdot 1}} \]

       3. times-frac 34.0%

          \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{z}{1}} \]

       4. /-rgt-identity 34.0%

          \[\leadsto \frac{x}{t} \cdot \color{blue}{z} \]

   12. Simplified 34.0%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 23: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+126) x (if (<= a 7.6e+94) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+126) {
		tmp = x;
	} else if (a <= 7.6e+94) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+126)) then
        tmp = x
    else if (a <= 7.6d+94) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+126) {
		tmp = x;
	} else if (a <= 7.6e+94) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+126:
		tmp = x
	elif a <= 7.6e+94:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+126)
		tmp = x;
	elseif (a <= 7.6e+94)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+126)
		tmp = x;
	elseif (a <= 7.6e+94)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+126], x, If[LessEqual[a, 7.6e+94], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999925e125 or 7.5999999999999993e94 < a

   1. Initial program 65.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 51.3%

      \[\leadsto \color{blue}{x} \]

   if -9.99999999999999925e125 < a < 7.5999999999999993e94

   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* 74.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 34.8%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 25.4% 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 64.5%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 79.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Simplified 79.7%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

4. Taylor expanded in a around inf 20.2%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 20.2%

   \[\leadsto x \]

Developer target: 86.3% accurate, 0.7× 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 2023224 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))