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

Percentage Accurate: 67.6% → 90.5%

Time: 15.9s

Alternatives: 17

Speedup: 0.9×

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: 67.6% 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: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-286} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -4e-286) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (- y (/ (* (- a z) (- x y)) 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 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((a - z) * (x - y)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-4d-286)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y - (((a - z) * (x - y)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((a - z) * (x - y)) / 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 <= -4e-286) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y - (((a - z) * (x - y)) / 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 <= -4e-286) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / 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 <= -4e-286) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y - (((a - z) * (x - y)) / 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, -4e-286], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $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))) < -4.0000000000000002e-286 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 70.2%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   if -4.0000000000000002e-286 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.6%

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

   2. Taylor expanded in t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. div-sub 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. distribute-rgt-out-- 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-286} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 2: 83.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-279}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a - z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -1e+306)
     (+ y (/ (- x y) (/ t z)))
     (if (<= t_1 -4e-286)
       t_1
       (if (<= t_1 1e-279)
         (- y (/ (* (- a z) (- x y)) t))
         (if (<= t_1 5e+304) t_1 (- y (/ (- a z) (/ t x)))))))))

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 <= -1e+306) {
		tmp = y + ((x - y) / (t / z));
	} else if (t_1 <= -4e-286) {
		tmp = t_1;
	} else if (t_1 <= 1e-279) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = y - ((a - z) / (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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t_1 <= (-1d+306)) then
        tmp = y + ((x - y) / (t / z))
    else if (t_1 <= (-4d-286)) then
        tmp = t_1
    else if (t_1 <= 1d-279) then
        tmp = y - (((a - z) * (x - y)) / t)
    else if (t_1 <= 5d+304) then
        tmp = t_1
    else
        tmp = y - ((a - z) / (t / x))
    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 <= -1e+306) {
		tmp = y + ((x - y) / (t / z));
	} else if (t_1 <= -4e-286) {
		tmp = t_1;
	} else if (t_1 <= 1e-279) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = y - ((a - z) / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -1e+306:
		tmp = y + ((x - y) / (t / z))
	elif t_1 <= -4e-286:
		tmp = t_1
	elif t_1 <= 1e-279:
		tmp = y - (((a - z) * (x - y)) / t)
	elif t_1 <= 5e+304:
		tmp = t_1
	else:
		tmp = y - ((a - z) / (t / x))
	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 <= -1e+306)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t_1 <= -4e-286)
		tmp = t_1;
	elseif (t_1 <= 1e-279)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	elseif (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(Float64(a - z) / Float64(t / x)));
	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 <= -1e+306)
		tmp = y + ((x - y) / (t / z));
	elseif (t_1 <= -4e-286)
		tmp = t_1;
	elseif (t_1 <= 1e-279)
		tmp = y - (((a - z) * (x - y)) / t);
	elseif (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = y - ((a - z) / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-286], t$95$1, If[LessEqual[t$95$1, 1e-279], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+304], t$95$1, N[(y - N[(N[(a - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000002e306

   1. Initial program 46.7%

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

   2. Taylor expanded in t around inf 44.9%

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

      1. sub-neg 44.9%

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

      2. +-commutative 44.9%

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

      3. mul-1-neg 44.9%

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

      4. unsub-neg 44.9%

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

      5. *-commutative 44.9%

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

      6. associate-/l* 54.7%

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

      7. mul-1-neg 54.7%

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

      8. remove-double-neg 54.7%

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

      9. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in a around 0 53.3%

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

      1. associate-*l/ 66.1%

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

      2. *-commutative 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in z around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

   if -1.00000000000000002e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.0000000000000002e-286 or 1.00000000000000006e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 97.4%

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

   if -4.0000000000000002e-286 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.00000000000000006e-279

   1. Initial program 4.7%

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

   2. Taylor expanded in t around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. div-sub 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. distribute-rgt-out-- 99.9%

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

   4. Simplified 99.9%

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

   if 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 25.8%

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

   2. Taylor expanded in t around -inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. div-sub 50.5%

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

      4. *-commutative 50.5%

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

      5. div-sub 52.2%

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

      6. distribute-rgt-out-- 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{+306}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{-279}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a - z}{\frac{t}{x}}\\ \end{array} \]

Alternative 3: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ y (* z (/ x t)))))
   (if (<= t -5e+194)
     t_2
     (if (<= t -5.4e-22)
       t_1
       (if (<= t -1.35e-79)
         (+ x (/ y (/ a z)))
         (if (<= t -5e-173)
           (* z (/ (- y x) (- a t)))
           (if (<= t 1.2e-7)
             (+ x (/ z (/ a (- y x))))
             (if (<= t 5.2e+113) 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 = y + (z * (x / t));
	double tmp;
	if (t <= -5e+194) {
		tmp = t_2;
	} else if (t <= -5.4e-22) {
		tmp = t_1;
	} else if (t <= -1.35e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= -5e-173) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.2e-7) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 5.2e+113) {
		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 = y + (z * (x / t))
    if (t <= (-5d+194)) then
        tmp = t_2
    else if (t <= (-5.4d-22)) then
        tmp = t_1
    else if (t <= (-1.35d-79)) then
        tmp = x + (y / (a / z))
    else if (t <= (-5d-173)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.2d-7) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 5.2d+113) 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 = y + (z * (x / t));
	double tmp;
	if (t <= -5e+194) {
		tmp = t_2;
	} else if (t <= -5.4e-22) {
		tmp = t_1;
	} else if (t <= -1.35e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= -5e-173) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.2e-7) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 5.2e+113) {
		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 = y + (z * (x / t))
	tmp = 0
	if t <= -5e+194:
		tmp = t_2
	elif t <= -5.4e-22:
		tmp = t_1
	elif t <= -1.35e-79:
		tmp = x + (y / (a / z))
	elif t <= -5e-173:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.2e-7:
		tmp = x + (z / (a / (y - x)))
	elif t <= 5.2e+113:
		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(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -5e+194)
		tmp = t_2;
	elseif (t <= -5.4e-22)
		tmp = t_1;
	elseif (t <= -1.35e-79)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -5e-173)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.2e-7)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 5.2e+113)
		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 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -5e+194)
		tmp = t_2;
	elseif (t <= -5.4e-22)
		tmp = t_1;
	elseif (t <= -1.35e-79)
		tmp = x + (y / (a / z));
	elseif (t <= -5e-173)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.2e-7)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 5.2e+113)
		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[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+194], t$95$2, If[LessEqual[t, -5.4e-22], t$95$1, If[LessEqual[t, -1.35e-79], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-173], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-7], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+113], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.99999999999999989e194 or 5.1999999999999998e113 < t

   1. Initial program 30.0%

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

   2. Taylor expanded in t around inf 58.8%

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

      1. sub-neg 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. associate-/l* 70.6%

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

      7. mul-1-neg 70.6%

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

      8. remove-double-neg 70.6%

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

      9. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in a around 0 59.8%

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

      1. associate-*l/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-*r/ 73.0%

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

      3. *-commutative 73.0%

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

      4. distribute-rgt-neg-in 73.0%

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

   10. Simplified 73.0%

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

   if -4.99999999999999989e194 < t < -5.4000000000000004e-22 or 1.19999999999999989e-7 < t < 5.1999999999999998e113

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

      1. clear-num 81.3%

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

      2. inv-pow 81.3%

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

   5. Applied egg-rr 81.3%

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

      1. unpow-1 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

      2. *-commutative 64.0%

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

   10. Simplified 64.0%

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

   if -5.4000000000000004e-22 < t < -1.3500000000000001e-79

   1. Initial program 80.2%

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

   2. Taylor expanded in t around 0 66.2%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if -1.3500000000000001e-79 < t < -5.0000000000000002e-173

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around inf 85.6%

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

      1. div-sub 85.6%

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

   10. Simplified 85.6%

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

   if -5.0000000000000002e-173 < t < 1.19999999999999989e-7

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0 69.0%

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

      1. associate-/l* 75.1%

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

   4. Simplified 75.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+194}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 4: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ y (* z (/ x t)))))
   (if (<= t -4.3e+194)
     t_2
     (if (<= t -1.02e-22)
       t_1
       (if (<= t -1.45e-79)
         (+ x (/ y (/ a z)))
         (if (<= t -8.6e-173)
           (* z (/ (- y x) (- a t)))
           (if (<= t 6e+22)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t 8.4e+114) 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 = y + (z * (x / t));
	double tmp;
	if (t <= -4.3e+194) {
		tmp = t_2;
	} else if (t <= -1.02e-22) {
		tmp = t_1;
	} else if (t <= -1.45e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= -8.6e-173) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 6e+22) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 8.4e+114) {
		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 = y + (z * (x / t))
    if (t <= (-4.3d+194)) then
        tmp = t_2
    else if (t <= (-1.02d-22)) then
        tmp = t_1
    else if (t <= (-1.45d-79)) then
        tmp = x + (y / (a / z))
    else if (t <= (-8.6d-173)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 6d+22) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 8.4d+114) 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 = y + (z * (x / t));
	double tmp;
	if (t <= -4.3e+194) {
		tmp = t_2;
	} else if (t <= -1.02e-22) {
		tmp = t_1;
	} else if (t <= -1.45e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= -8.6e-173) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 6e+22) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 8.4e+114) {
		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 = y + (z * (x / t))
	tmp = 0
	if t <= -4.3e+194:
		tmp = t_2
	elif t <= -1.02e-22:
		tmp = t_1
	elif t <= -1.45e-79:
		tmp = x + (y / (a / z))
	elif t <= -8.6e-173:
		tmp = z * ((y - x) / (a - t))
	elif t <= 6e+22:
		tmp = x + ((y - x) / (a / z))
	elif t <= 8.4e+114:
		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(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -4.3e+194)
		tmp = t_2;
	elseif (t <= -1.02e-22)
		tmp = t_1;
	elseif (t <= -1.45e-79)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -8.6e-173)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 6e+22)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 8.4e+114)
		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 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -4.3e+194)
		tmp = t_2;
	elseif (t <= -1.02e-22)
		tmp = t_1;
	elseif (t <= -1.45e-79)
		tmp = x + (y / (a / z));
	elseif (t <= -8.6e-173)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 6e+22)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 8.4e+114)
		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[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+194], t$95$2, If[LessEqual[t, -1.02e-22], t$95$1, If[LessEqual[t, -1.45e-79], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.6e-173], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+22], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+114], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.29999999999999994e194 or 8.4000000000000001e114 < t

   1. Initial program 30.0%

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

   2. Taylor expanded in t around inf 58.8%

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

      1. sub-neg 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. associate-/l* 70.6%

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

      7. mul-1-neg 70.6%

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

      8. remove-double-neg 70.6%

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

      9. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in a around 0 59.8%

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

      1. associate-*l/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-*r/ 73.0%

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

      3. *-commutative 73.0%

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

      4. distribute-rgt-neg-in 73.0%

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

   10. Simplified 73.0%

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

   if -4.29999999999999994e194 < t < -1.02000000000000002e-22 or 6e22 < t < 8.4000000000000001e114

   1. Initial program 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

   5. Applied egg-rr 79.9%

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

      1. unpow-1 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.2%

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

      2. *-commutative 65.2%

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

   10. Simplified 65.2%

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

   if -1.02000000000000002e-22 < t < -1.45e-79

   1. Initial program 80.2%

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

   2. Taylor expanded in t around 0 66.2%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   if -1.45e-79 < t < -8.6000000000000006e-173

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around inf 85.6%

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

      1. div-sub 85.6%

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

   10. Simplified 85.6%

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

   if -8.6000000000000006e-173 < t < 6e22

   1. Initial program 89.8%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 73.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+194}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 5: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 33000000000:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -1.4e+140)
     t_1
     (if (<= a -1.8e+117)
       (+ y (* z (/ x t)))
       (if (<= a -2.5e-103)
         t_2
         (if (<= a 33000000000.0)
           (- y (* z (/ (- y x) t)))
           (if (<= a 1.4e+110)
             t_1
             (if (<= a 4.5e+196) (* y (/ (- z t) (- a t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -1.8e+117) {
		tmp = y + (z * (x / t));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 33000000000.0) {
		tmp = y - (z * ((y - x) / t));
	} else if (a <= 1.4e+110) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = x + ((y - x) / (a / z))
    if (a <= (-1.4d+140)) then
        tmp = t_1
    else if (a <= (-1.8d+117)) then
        tmp = y + (z * (x / t))
    else if (a <= (-2.5d-103)) then
        tmp = t_2
    else if (a <= 33000000000.0d0) then
        tmp = y - (z * ((y - x) / t))
    else if (a <= 1.4d+110) then
        tmp = t_1
    else if (a <= 4.5d+196) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -1.8e+117) {
		tmp = y + (z * (x / t));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 33000000000.0) {
		tmp = y - (z * ((y - x) / t));
	} else if (a <= 1.4e+110) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -1.4e+140:
		tmp = t_1
	elif a <= -1.8e+117:
		tmp = y + (z * (x / t))
	elif a <= -2.5e-103:
		tmp = t_2
	elif a <= 33000000000.0:
		tmp = y - (z * ((y - x) / t))
	elif a <= 1.4e+110:
		tmp = t_1
	elif a <= 4.5e+196:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -1.8e+117)
		tmp = Float64(y + Float64(z * Float64(x / t)));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 33000000000.0)
		tmp = Float64(y - Float64(z * Float64(Float64(y - x) / t)));
	elseif (a <= 1.4e+110)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -1.8e+117)
		tmp = y + (z * (x / t));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 33000000000.0)
		tmp = y - (z * ((y - x) / t));
	elseif (a <= 1.4e+110)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+140], t$95$1, If[LessEqual[a, -1.8e+117], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-103], t$95$2, If[LessEqual[a, 33000000000.0], N[(y - N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+110], t$95$1, If[LessEqual[a, 4.5e+196], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999991e140 or 3.3e10 < a < 1.39999999999999993e110

   1. Initial program 64.0%

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

   2. Taylor expanded in t around 0 67.2%

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

      1. associate-/l* 75.5%

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

   4. Simplified 75.5%

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

   if -1.39999999999999991e140 < a < -1.80000000000000006e117

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf 83.8%

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

      1. sub-neg 83.8%

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

      2. +-commutative 83.8%

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

      3. mul-1-neg 83.8%

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

      4. unsub-neg 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-/l* 99.2%

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

      7. mul-1-neg 99.2%

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

      8. remove-double-neg 99.2%

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

      9. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in a around 0 83.8%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -1.80000000000000006e117 < a < -2.49999999999999983e-103 or 4.49999999999999978e196 < a

   1. Initial program 71.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 71.8%

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

   if -2.49999999999999983e-103 < a < 3.3e10

   1. Initial program 60.7%

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

   2. Taylor expanded in t around inf 83.9%

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

      1. sub-neg 83.9%

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

      2. +-commutative 83.9%

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

      3. mul-1-neg 83.9%

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

      4. unsub-neg 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-/l* 90.3%

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

      7. mul-1-neg 90.3%

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

      8. remove-double-neg 90.3%

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

      9. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in a around 0 80.3%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   if 1.39999999999999993e110 < a < 4.49999999999999978e196

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.8%

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

      2. inv-pow 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. unpow-1 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.3%

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

      2. *-commutative 69.3%

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

   10. Simplified 69.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 33000000000:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+110}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 820000000000:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -1.4e+140)
     t_1
     (if (<= a -3.6e+118)
       (+ y (* z (/ x t)))
       (if (<= a -2.5e-103)
         t_2
         (if (<= a 820000000000.0)
           (+ y (/ (- x y) (/ t z)))
           (if (<= a 3.9e+108)
             t_1
             (if (<= a 4.5e+196) (* y (/ (- z t) (- a t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -3.6e+118) {
		tmp = y + (z * (x / t));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 820000000000.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 3.9e+108) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = x + ((y - x) / (a / z))
    if (a <= (-1.4d+140)) then
        tmp = t_1
    else if (a <= (-3.6d+118)) then
        tmp = y + (z * (x / t))
    else if (a <= (-2.5d-103)) then
        tmp = t_2
    else if (a <= 820000000000.0d0) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 3.9d+108) then
        tmp = t_1
    else if (a <= 4.5d+196) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -3.6e+118) {
		tmp = y + (z * (x / t));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 820000000000.0) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 3.9e+108) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -1.4e+140:
		tmp = t_1
	elif a <= -3.6e+118:
		tmp = y + (z * (x / t))
	elif a <= -2.5e-103:
		tmp = t_2
	elif a <= 820000000000.0:
		tmp = y + ((x - y) / (t / z))
	elif a <= 3.9e+108:
		tmp = t_1
	elif a <= 4.5e+196:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -3.6e+118)
		tmp = Float64(y + Float64(z * Float64(x / t)));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 820000000000.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 3.9e+108)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -3.6e+118)
		tmp = y + (z * (x / t));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 820000000000.0)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 3.9e+108)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+140], t$95$1, If[LessEqual[a, -3.6e+118], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-103], t$95$2, If[LessEqual[a, 820000000000.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+108], t$95$1, If[LessEqual[a, 4.5e+196], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999991e140 or 8.2e11 < a < 3.89999999999999985e108

   1. Initial program 64.0%

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

   2. Taylor expanded in t around 0 67.2%

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

      1. associate-/l* 75.5%

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

   4. Simplified 75.5%

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

   if -1.39999999999999991e140 < a < -3.6e118

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf 83.8%

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

      1. sub-neg 83.8%

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

      2. +-commutative 83.8%

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

      3. mul-1-neg 83.8%

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

      4. unsub-neg 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-/l* 99.2%

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

      7. mul-1-neg 99.2%

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

      8. remove-double-neg 99.2%

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

      9. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in a around 0 83.8%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -3.6e118 < a < -2.49999999999999983e-103 or 4.49999999999999978e196 < a

   1. Initial program 71.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 71.8%

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

   if -2.49999999999999983e-103 < a < 8.2e11

   1. Initial program 60.7%

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

   2. Taylor expanded in t around inf 83.9%

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

      1. sub-neg 83.9%

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

      2. +-commutative 83.9%

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

      3. mul-1-neg 83.9%

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

      4. unsub-neg 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-/l* 90.3%

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

      7. mul-1-neg 90.3%

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

      8. remove-double-neg 90.3%

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

      9. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in a around 0 80.3%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 86.7%

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

   10. Simplified 86.7%

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

   if 3.89999999999999985e108 < a < 4.49999999999999978e196

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.8%

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

      2. inv-pow 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. unpow-1 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.3%

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

      2. *-commutative 69.3%

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

   10. Simplified 69.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 820000000000:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{+110}:\\ \;\;\;\;y - \frac{a - z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+20}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -1.4e+140)
     t_1
     (if (<= a -2.55e+110)
       (- y (/ (- a z) (/ t x)))
       (if (<= a -2.5e-103)
         t_2
         (if (<= a 3.7e+20)
           (+ y (/ (- x y) (/ t z)))
           (if (<= a 4.5e+110)
             t_1
             (if (<= a 4.5e+196) (* y (/ (- z t) (- a t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -2.55e+110) {
		tmp = y - ((a - z) / (t / x));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 3.7e+20) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 4.5e+110) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = x + ((y - x) / (a / z))
    if (a <= (-1.4d+140)) then
        tmp = t_1
    else if (a <= (-2.55d+110)) then
        tmp = y - ((a - z) / (t / x))
    else if (a <= (-2.5d-103)) then
        tmp = t_2
    else if (a <= 3.7d+20) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 4.5d+110) then
        tmp = t_1
    else if (a <= 4.5d+196) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_1;
	} else if (a <= -2.55e+110) {
		tmp = y - ((a - z) / (t / x));
	} else if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 3.7e+20) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 4.5e+110) {
		tmp = t_1;
	} else if (a <= 4.5e+196) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -1.4e+140:
		tmp = t_1
	elif a <= -2.55e+110:
		tmp = y - ((a - z) / (t / x))
	elif a <= -2.5e-103:
		tmp = t_2
	elif a <= 3.7e+20:
		tmp = y + ((x - y) / (t / z))
	elif a <= 4.5e+110:
		tmp = t_1
	elif a <= 4.5e+196:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -2.55e+110)
		tmp = Float64(y - Float64(Float64(a - z) / Float64(t / x)));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 3.7e+20)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 4.5e+110)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -1.4e+140)
		tmp = t_1;
	elseif (a <= -2.55e+110)
		tmp = y - ((a - z) / (t / x));
	elseif (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 3.7e+20)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 4.5e+110)
		tmp = t_1;
	elseif (a <= 4.5e+196)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+140], t$95$1, If[LessEqual[a, -2.55e+110], N[(y - N[(N[(a - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-103], t$95$2, If[LessEqual[a, 3.7e+20], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+110], t$95$1, If[LessEqual[a, 4.5e+196], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999991e140 or 3.7e20 < a < 4.5000000000000003e110

   1. Initial program 64.0%

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

   2. Taylor expanded in t around 0 67.2%

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

      1. associate-/l* 75.5%

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

   4. Simplified 75.5%

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

   if -1.39999999999999991e140 < a < -2.5500000000000001e110

   1. Initial program 71.9%

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

   2. Taylor expanded in t around -inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

      3. div-sub 72.7%

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

      4. *-commutative 72.7%

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

      5. div-sub 72.7%

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

      6. distribute-rgt-out-- 72.7%

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

   4. Simplified 72.7%

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

   5. Taylor expanded in y around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   if -2.5500000000000001e110 < a < -2.49999999999999983e-103 or 4.49999999999999978e196 < a

   1. Initial program 72.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 73.1%

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

   if -2.49999999999999983e-103 < a < 3.7e20

   1. Initial program 60.7%

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

   2. Taylor expanded in t around inf 83.9%

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

      1. sub-neg 83.9%

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

      2. +-commutative 83.9%

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

      3. mul-1-neg 83.9%

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

      4. unsub-neg 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-/l* 90.3%

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

      7. mul-1-neg 90.3%

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

      8. remove-double-neg 90.3%

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

      9. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in a around 0 80.3%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 86.7%

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

   10. Simplified 86.7%

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

   if 4.5000000000000003e110 < a < 4.49999999999999978e196

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.8%

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

      2. inv-pow 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. unpow-1 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.3%

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

      2. *-commutative 69.3%

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

   10. Simplified 69.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{+110}:\\ \;\;\;\;y - \frac{a - z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+20}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+110}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -2.5e-103)
     t_2
     (if (<= a 1.56e-201)
       t_1
       (if (<= a 8e-195) (/ (* x (- z a)) t) (if (<= a 7.1e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 1.56e-201) {
		tmp = t_1;
	} else if (a <= 8e-195) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 7.1e+45) {
		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 * (1.0d0 - (z / t))
    t_2 = x + (y / (a / z))
    if (a <= (-2.5d-103)) then
        tmp = t_2
    else if (a <= 1.56d-201) then
        tmp = t_1
    else if (a <= 8d-195) then
        tmp = (x * (z - a)) / t
    else if (a <= 7.1d+45) 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 * (1.0 - (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.5e-103) {
		tmp = t_2;
	} else if (a <= 1.56e-201) {
		tmp = t_1;
	} else if (a <= 8e-195) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 7.1e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -2.5e-103:
		tmp = t_2
	elif a <= 1.56e-201:
		tmp = t_1
	elif a <= 8e-195:
		tmp = (x * (z - a)) / t
	elif a <= 7.1e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 1.56e-201)
		tmp = t_1;
	elseif (a <= 8e-195)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (a <= 7.1e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2.5e-103)
		tmp = t_2;
	elseif (a <= 1.56e-201)
		tmp = t_1;
	elseif (a <= 8e-195)
		tmp = (x * (z - a)) / t;
	elseif (a <= 7.1e+45)
		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[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-103], t$95$2, If[LessEqual[a, 1.56e-201], t$95$1, If[LessEqual[a, 8e-195], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 7.1e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.49999999999999983e-103 or 7.1e45 < a

   1. Initial program 67.4%

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

   2. Taylor expanded in t around 0 57.9%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   if -2.49999999999999983e-103 < a < 1.56e-201 or 8.0000000000000007e-195 < a < 7.1e45

   1. Initial program 62.1%

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

   2. Taylor expanded in t around inf 80.4%

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

      1. sub-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. mul-1-neg 80.4%

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

      4. unsub-neg 80.4%

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

      5. *-commutative 80.4%

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

      6. associate-/l* 86.9%

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

      7. mul-1-neg 86.9%

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

      8. remove-double-neg 86.9%

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

      9. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in a around 0 78.5%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in y around inf 63.0%

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

   if 1.56e-201 < a < 8.0000000000000007e-195

   1. Initial program 41.7%

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

   2. Taylor expanded in y around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*r/ 42.0%

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

      4. distribute-rgt-neg-in 42.0%

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

      5. mul-1-neg 42.0%

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

      6. metadata-eval 42.0%

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

      7. times-frac 42.0%

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

      8. *-lft-identity 42.0%

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

      9. neg-mul-1 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in t around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. distribute-lft1-in 99.4%

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

      3. metadata-eval 99.4%

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

      4. mul0-lft 99.4%

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

      5. neg-sub0 99.4%

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

      6. sub-neg 99.4%

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

      7. div-sub 99.4%

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

      8. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 55.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -1.4e+140)
     t_2
     (if (<= a -1.28e+14)
       t_1
       (if (<= a -2.5e-103)
         (/ (* (- y x) z) a)
         (if (<= a 1.05e+48) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_2;
	} else if (a <= -1.28e+14) {
		tmp = t_1;
	} else if (a <= -2.5e-103) {
		tmp = ((y - x) * z) / a;
	} else if (a <= 1.05e+48) {
		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 * (x / t))
    t_2 = x + (y / (a / z))
    if (a <= (-1.4d+140)) then
        tmp = t_2
    else if (a <= (-1.28d+14)) then
        tmp = t_1
    else if (a <= (-2.5d-103)) then
        tmp = ((y - x) * z) / a
    else if (a <= 1.05d+48) 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 * (x / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.4e+140) {
		tmp = t_2;
	} else if (a <= -1.28e+14) {
		tmp = t_1;
	} else if (a <= -2.5e-103) {
		tmp = ((y - x) * z) / a;
	} else if (a <= 1.05e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -1.4e+140:
		tmp = t_2
	elif a <= -1.28e+14:
		tmp = t_1
	elif a <= -2.5e-103:
		tmp = ((y - x) * z) / a
	elif a <= 1.05e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.4e+140)
		tmp = t_2;
	elseif (a <= -1.28e+14)
		tmp = t_1;
	elseif (a <= -2.5e-103)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= 1.05e+48)
		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 * (x / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -1.4e+140)
		tmp = t_2;
	elseif (a <= -1.28e+14)
		tmp = t_1;
	elseif (a <= -2.5e-103)
		tmp = ((y - x) * z) / a;
	elseif (a <= 1.05e+48)
		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[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+140], t$95$2, If[LessEqual[a, -1.28e+14], t$95$1, If[LessEqual[a, -2.5e-103], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1.05e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999991e140 or 1.0499999999999999e48 < a

   1. Initial program 63.8%

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

   2. Taylor expanded in t around 0 58.4%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. associate-/l* 64.5%

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

   5. Simplified 64.5%

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

   if -1.39999999999999991e140 < a < -1.28e14 or -2.49999999999999983e-103 < a < 1.0499999999999999e48

   1. Initial program 63.2%

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

   2. Taylor expanded in t around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. mul-1-neg 73.9%

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

      4. unsub-neg 73.9%

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

      5. *-commutative 73.9%

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

      6. associate-/l* 81.1%

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

      7. mul-1-neg 81.1%

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

      8. remove-double-neg 81.1%

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

      9. associate-/l* 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in a around 0 72.5%

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

      1. associate-*l/ 79.1%

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

      2. *-commutative 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in y around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r/ 67.2%

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

      3. *-commutative 67.2%

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

      4. distribute-rgt-neg-in 67.2%

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

   10. Simplified 67.2%

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

   if -1.28e14 < a < -2.49999999999999983e-103

   1. Initial program 84.8%

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

   2. Taylor expanded in t around 0 69.7%

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

   3. Taylor expanded in a around 0 62.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{+14}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.5e+91)
   (+ y (* z (/ x t)))
   (if (<= x -3.1e+41)
     (+ x (/ y (/ a z)))
     (if (<= x 2.8e+105) (* y (/ (- z t) (- a t))) (- x (/ z (/ a x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.5e+91) {
		tmp = y + (z * (x / t));
	} else if (x <= -3.1e+41) {
		tmp = x + (y / (a / z));
	} else if (x <= 2.8e+105) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z / (a / 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 (x <= (-1.5d+91)) then
        tmp = y + (z * (x / t))
    else if (x <= (-3.1d+41)) then
        tmp = x + (y / (a / z))
    else if (x <= 2.8d+105) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (z / (a / 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 (x <= -1.5e+91) {
		tmp = y + (z * (x / t));
	} else if (x <= -3.1e+41) {
		tmp = x + (y / (a / z));
	} else if (x <= 2.8e+105) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z / (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.5e+91:
		tmp = y + (z * (x / t))
	elif x <= -3.1e+41:
		tmp = x + (y / (a / z))
	elif x <= 2.8e+105:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (z / (a / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.5e+91)
		tmp = Float64(y + Float64(z * Float64(x / t)));
	elseif (x <= -3.1e+41)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (x <= 2.8e+105)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(z / Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.5e+91)
		tmp = y + (z * (x / t));
	elseif (x <= -3.1e+41)
		tmp = x + (y / (a / z));
	elseif (x <= 2.8e+105)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (z / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.5e+91], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e+41], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+105], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.50000000000000003e91

   1. Initial program 45.9%

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

   2. Taylor expanded in t around inf 53.0%

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

      1. sub-neg 53.0%

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

      2. +-commutative 53.0%

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

      3. mul-1-neg 53.0%

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

      4. unsub-neg 53.0%

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

      5. *-commutative 53.0%

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

      6. associate-/l* 63.4%

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

      7. mul-1-neg 63.4%

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

      8. remove-double-neg 63.4%

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

      9. associate-/l* 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in a around 0 49.2%

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

      1. associate-*l/ 57.9%

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

      2. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in y around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. associate-*r/ 56.0%

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

      3. *-commutative 56.0%

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

      4. distribute-rgt-neg-in 56.0%

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

   10. Simplified 56.0%

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

   if -1.50000000000000003e91 < x < -3.1e41

   1. Initial program 74.3%

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

   2. Taylor expanded in t around 0 73.6%

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

   3. Taylor expanded in y around inf 73.1%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -3.1e41 < x < 2.8000000000000001e105

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

      1. clear-num 83.2%

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

      2. inv-pow 83.2%

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

   5. Applied egg-rr 83.2%

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

      1. unpow-1 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in y around inf 69.4%

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

      1. div-sub 69.4%

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

      2. *-commutative 69.4%

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

   10. Simplified 69.4%

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

   if 2.8000000000000001e105 < x

   1. Initial program 55.3%

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

   2. Taylor expanded in t around 0 52.0%

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

   3. Taylor expanded in y around 0 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. sub-neg 51.9%

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

      4. associate-/l* 59.0%

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

   5. Simplified 59.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 11: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-108} \lor \neg \left(a \leq 1.85 \cdot 10^{-42}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.8e-108) (not (<= a 1.85e-42)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.8e-108) || !(a <= 1.85e-42)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.8d-108)) .or. (.not. (a <= 1.85d-42))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.8e-108) || !(a <= 1.85e-42)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.8e-108) or not (a <= 1.85e-42):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.8e-108) || !(a <= 1.85e-42))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.8e-108) || ~((a <= 1.85e-42)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.8e-108], N[Not[LessEqual[a, 1.85e-42]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.80000000000000004e-108 or 1.8500000000000001e-42 < a

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 64.1%

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

      1. associate-*r/ 77.1%

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

   4. Simplified 77.1%

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

   if -6.80000000000000004e-108 < a < 1.8500000000000001e-42

   1. Initial program 60.9%

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

   2. Taylor expanded in t around inf 88.1%

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

      1. sub-neg 88.1%

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

      2. +-commutative 88.1%

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

      3. mul-1-neg 88.1%

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

      4. unsub-neg 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-/l* 93.5%

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

      7. mul-1-neg 93.5%

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

      8. remove-double-neg 93.5%

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

      9. associate-/l* 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in a around 0 84.9%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in z around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 90.2%

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

   10. Simplified 90.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-108} \lor \neg \left(a \leq 1.85 \cdot 10^{-42}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 12: 55.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-103} \lor \neg \left(a \leq 3.8 \cdot 10^{+41}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e-103) (not (<= a 3.8e+41)))
   (+ x (/ y (/ a z)))
   (* y (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-103) || !(a <= 3.8e+41)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * (1.0 - (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 ((a <= (-2.3d-103)) .or. (.not. (a <= 3.8d+41))) then
        tmp = x + (y / (a / z))
    else
        tmp = y * (1.0d0 - (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 ((a <= -2.3e-103) || !(a <= 3.8e+41)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e-103) or not (a <= 3.8e+41):
		tmp = x + (y / (a / z))
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e-103) || !(a <= 3.8e+41))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e-103) || ~((a <= 3.8e+41)))
		tmp = x + (y / (a / z));
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e-103], N[Not[LessEqual[a, 3.8e+41]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3000000000000001e-103 or 3.8000000000000001e41 < a

   1. Initial program 67.4%

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

   2. Taylor expanded in t around 0 57.9%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   if -2.3000000000000001e-103 < a < 3.8000000000000001e41

   1. Initial program 61.3%

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

   2. Taylor expanded in t around inf 81.2%

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

      1. sub-neg 81.2%

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

      2. +-commutative 81.2%

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

      3. mul-1-neg 81.2%

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

      4. unsub-neg 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-/l* 87.4%

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

      7. mul-1-neg 87.4%

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

      8. remove-double-neg 87.4%

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

      9. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in a around 0 78.6%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-103} \lor \neg \left(a \leq 3.8 \cdot 10^{+41}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 13: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.55e+140) x (if (<= a 3.1e+47) (* y (- 1.0 (/ z t))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e+140) {
		tmp = x;
	} else if (a <= 3.1e+47) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.55d+140)) then
        tmp = x
    else if (a <= 3.1d+47) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e+140) {
		tmp = x;
	} else if (a <= 3.1e+47) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.55e+140:
		tmp = x
	elif a <= 3.1e+47:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.55e+140)
		tmp = x;
	elseif (a <= 3.1e+47)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.55e+140)
		tmp = x;
	elseif (a <= 3.1e+47)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.55e+140], x, If[LessEqual[a, 3.1e+47], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e140 or 3.1000000000000001e47 < a

   1. Initial program 63.8%

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

   2. Taylor expanded in a around inf 53.2%

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

   if -1.55e140 < a < 3.1000000000000001e47

   1. Initial program 65.1%

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

   2. Taylor expanded in t around inf 71.1%

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

      1. sub-neg 71.1%

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

      2. +-commutative 71.1%

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

      3. mul-1-neg 71.1%

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

      4. unsub-neg 71.1%

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

      5. *-commutative 71.1%

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

      6. associate-/l* 77.7%

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

      7. mul-1-neg 77.7%

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

      8. remove-double-neg 77.7%

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

      9. associate-/l* 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in a around 0 68.6%

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

      1. associate-*l/ 74.6%

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

      2. *-commutative 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around inf 53.0%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 37.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+30)
   x
   (if (<= a -3.6e-101)
     (/ (* x (- z)) a)
     (if (<= a -1.9e-103) x (if (<= a 1.1e+43) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+30) {
		tmp = x;
	} else if (a <= -3.6e-101) {
		tmp = (x * -z) / a;
	} else if (a <= -1.9e-103) {
		tmp = x;
	} else if (a <= 1.1e+43) {
		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 <= (-3.4d+30)) then
        tmp = x
    else if (a <= (-3.6d-101)) then
        tmp = (x * -z) / a
    else if (a <= (-1.9d-103)) then
        tmp = x
    else if (a <= 1.1d+43) 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 <= -3.4e+30) {
		tmp = x;
	} else if (a <= -3.6e-101) {
		tmp = (x * -z) / a;
	} else if (a <= -1.9e-103) {
		tmp = x;
	} else if (a <= 1.1e+43) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+30:
		tmp = x
	elif a <= -3.6e-101:
		tmp = (x * -z) / a
	elif a <= -1.9e-103:
		tmp = x
	elif a <= 1.1e+43:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+30)
		tmp = x;
	elseif (a <= -3.6e-101)
		tmp = Float64(Float64(x * Float64(-z)) / a);
	elseif (a <= -1.9e-103)
		tmp = x;
	elseif (a <= 1.1e+43)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+30)
		tmp = x;
	elseif (a <= -3.6e-101)
		tmp = (x * -z) / a;
	elseif (a <= -1.9e-103)
		tmp = x;
	elseif (a <= 1.1e+43)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+30], x, If[LessEqual[a, -3.6e-101], N[(N[(x * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.9e-103], x, If[LessEqual[a, 1.1e+43], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4000000000000002e30 or -3.6e-101 < a < -1.9e-103 or 1.1e43 < a

   1. Initial program 66.0%

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

   2. Taylor expanded in a around inf 49.5%

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

   if -3.4000000000000002e30 < a < -3.6e-101

   1. Initial program 79.3%

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

   2. Taylor expanded in x around inf 44.6%

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

      1. *-commutative 44.6%

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

      2. distribute-lft-in 44.6%

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

      3. *-rgt-identity 44.6%

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

      4. mul-1-neg 44.6%

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

      5. distribute-rgt-neg-in 44.6%

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

      6. unsub-neg 44.6%

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

      7. associate-*r/ 38.1%

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

      8. *-commutative 38.1%

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

      9. associate-/l* 44.6%

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

   4. Simplified 44.6%

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

   5. Taylor expanded in t around 0 37.9%

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

   6. Taylor expanded in z around inf 38.1%

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

      1. associate-*r/ 38.1%

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

      2. neg-mul-1 38.1%

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

      3. distribute-rgt-neg-in 38.1%

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

   8. Simplified 38.1%

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

   if -1.9e-103 < a < 1.1e43

   1. Initial program 61.3%

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

   2. Taylor expanded in t around inf 43.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+31) x (if (<= a 1.12e+42) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+31) {
		tmp = x;
	} else if (a <= 1.12e+42) {
		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 <= (-2.1d+31)) then
        tmp = x
    else if (a <= 1.12d+42) 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 <= -2.1e+31) {
		tmp = x;
	} else if (a <= 1.12e+42) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+31:
		tmp = x
	elif a <= 1.12e+42:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+31)
		tmp = x;
	elseif (a <= 1.12e+42)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+31)
		tmp = x;
	elseif (a <= 1.12e+42)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+31], x, If[LessEqual[a, 1.12e+42], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.09999999999999979e31 or 1.12e42 < a

   1. Initial program 65.7%

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

   2. Taylor expanded in a around inf 49.1%

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

   if -2.09999999999999979e31 < a < 1.12e42

   1. Initial program 63.5%

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

   2. Taylor expanded in t around inf 39.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 64.5%

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

2. Taylor expanded in y around 0 37.8%

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

   1. mul-1-neg 37.8%

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

   2. *-commutative 37.8%

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

   3. associate-*r/ 45.9%

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

   4. distribute-rgt-neg-in 45.9%

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

   5. mul-1-neg 45.9%

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

   6. metadata-eval 45.9%

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

   7. times-frac 45.9%

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

   8. *-lft-identity 45.9%

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

   9. neg-mul-1 45.9%

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

4. Simplified 45.9%

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

5. Taylor expanded in t around inf 2.8%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
6. Step-by-step derivation

   1. distribute-lft1-in 2.8%

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

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

7. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 2.8%

   \[\leadsto 0 \]

Alternative 17: 25.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.5%

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

2. Taylor expanded in a around inf 26.7%

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

3. Final simplification 26.7%

   \[\leadsto x \]

Developer target: 86.4% 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 2023199 
(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))))