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

Percentage Accurate: 68.1% → 90.7%

Time: 19.0s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% 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: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-306) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (+ (* (- y x) a) (* z (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((((y - x) * 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) * (t - z)) / (a - t))
    if ((t_1 <= (-2d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((((y - x) * 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) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-306) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((((y - x) * 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(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-306) || !(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(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-306) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((((y - x) * 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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-306], 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[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $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))) < -2.00000000000000006e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 67.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   if -2.00000000000000006e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

      1. associate-/l* 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in t around -inf 99.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-306} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 2: 82.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-306)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 5e+304) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-306:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 5e+304:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-306], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 27.6%

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

      1. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in x around 0 18.8%

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

      1. associate-*r/ 58.8%

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

   6. Simplified 58.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000006e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 95.2%

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

   if -2.00000000000000006e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

      1. associate-/l* 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 3: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-306) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-2d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-306) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-306) || !(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(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-306) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-306], 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[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000006e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 67.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   if -2.00000000000000006e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

      1. associate-/l* 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-306} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 4: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+149}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= a -1.2e+149)
     (+ x (* z (/ y a)))
     (if (<= a -2.05e+51)
       t_1
       (if (<= a -7e+20)
         (* x (- 1.0 (/ z a)))
         (if (<= a -1.1e-134)
           t_1
           (if (<= a 2.1e-301)
             t_2
             (if (<= a 1.4e-72)
               t_1
               (if (<= a 4.6e+53) t_2 (- x (/ y (/ a t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -1.2e+149) {
		tmp = x + (z * (y / a));
	} else if (a <= -2.05e+51) {
		tmp = t_1;
	} else if (a <= -7e+20) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -1.1e-134) {
		tmp = t_1;
	} else if (a <= 2.1e-301) {
		tmp = t_2;
	} else if (a <= 1.4e-72) {
		tmp = t_1;
	} else if (a <= 4.6e+53) {
		tmp = t_2;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (a <= (-1.2d+149)) then
        tmp = x + (z * (y / a))
    else if (a <= (-2.05d+51)) then
        tmp = t_1
    else if (a <= (-7d+20)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= (-1.1d-134)) then
        tmp = t_1
    else if (a <= 2.1d-301) then
        tmp = t_2
    else if (a <= 1.4d-72) then
        tmp = t_1
    else if (a <= 4.6d+53) then
        tmp = t_2
    else
        tmp = x - (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -1.2e+149) {
		tmp = x + (z * (y / a));
	} else if (a <= -2.05e+51) {
		tmp = t_1;
	} else if (a <= -7e+20) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -1.1e-134) {
		tmp = t_1;
	} else if (a <= 2.1e-301) {
		tmp = t_2;
	} else if (a <= 1.4e-72) {
		tmp = t_1;
	} else if (a <= 4.6e+53) {
		tmp = t_2;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -1.2e+149:
		tmp = x + (z * (y / a))
	elif a <= -2.05e+51:
		tmp = t_1
	elif a <= -7e+20:
		tmp = x * (1.0 - (z / a))
	elif a <= -1.1e-134:
		tmp = t_1
	elif a <= 2.1e-301:
		tmp = t_2
	elif a <= 1.4e-72:
		tmp = t_1
	elif a <= 4.6e+53:
		tmp = t_2
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.2e+149)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (a <= -2.05e+51)
		tmp = t_1;
	elseif (a <= -7e+20)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= -1.1e-134)
		tmp = t_1;
	elseif (a <= 2.1e-301)
		tmp = t_2;
	elseif (a <= 1.4e-72)
		tmp = t_1;
	elseif (a <= 4.6e+53)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -1.2e+149)
		tmp = x + (z * (y / a));
	elseif (a <= -2.05e+51)
		tmp = t_1;
	elseif (a <= -7e+20)
		tmp = x * (1.0 - (z / a));
	elseif (a <= -1.1e-134)
		tmp = t_1;
	elseif (a <= 2.1e-301)
		tmp = t_2;
	elseif (a <= 1.4e-72)
		tmp = t_1;
	elseif (a <= 4.6e+53)
		tmp = t_2;
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+149], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e+51], t$95$1, If[LessEqual[a, -7e+20], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-134], t$95$1, If[LessEqual[a, 2.1e-301], t$95$2, If[LessEqual[a, 1.4e-72], t$95$1, If[LessEqual[a, 4.6e+53], t$95$2, N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.20000000000000006e149

   1. Initial program 62.7%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 82.5%

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

   5. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 75.7%

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

      2. associate-/r/ 75.7%

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

   7. Simplified 75.7%

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

   if -1.20000000000000006e149 < a < -2.05000000000000005e51 or -7e20 < a < -1.1e-134 or 2.0999999999999999e-301 < a < 1.3999999999999999e-72

   1. Initial program 55.6%

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

      1. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   if -2.05000000000000005e51 < a < -7e20

   1. Initial program 76.5%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around 0 76.4%

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

   5. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   7. Simplified 76.4%

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

   if -1.1e-134 < a < 2.0999999999999999e-301 or 1.3999999999999999e-72 < a < 4.60000000000000039e53

   1. Initial program 57.4%

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

      1. associate-/l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in z around inf 65.4%

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

      1. div-sub 67.0%

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

   6. Simplified 67.0%

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

   if 4.60000000000000039e53 < a

   1. Initial program 72.1%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 64.7%

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

      1. fma-def 64.7%

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

      2. associate-*r/ 77.3%

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

      3. fma-def 77.3%

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

      4. neg-mul-1 77.3%

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

      5. +-commutative 77.3%

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

      6. unsub-neg 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in y around inf 77.0%

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

   8. Taylor expanded in t around 0 64.6%

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

      1. associate-/l* 68.0%

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

   10. Simplified 68.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+149}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+200}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -5.2e+200)
     y
     (if (<= t -5e+140)
       (+ x y)
       (if (<= t -2.5e+38)
         (* z (/ x t))
         (if (<= t -2.4e-249)
           t_1
           (if (<= t 7.2e-124)
             (* x (- 1.0 (/ z a)))
             (if (<= t 2.65e+31)
               t_1
               (if (<= t 6e+213)
                 (- x (* t (/ y a)))
                 (+ y (/ (* y a) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -5.2e+200) {
		tmp = y;
	} else if (t <= -5e+140) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = z * (x / t);
	} else if (t <= -2.4e-249) {
		tmp = t_1;
	} else if (t <= 7.2e-124) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.65e+31) {
		tmp = t_1;
	} else if (t <= 6e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-5.2d+200)) then
        tmp = y
    else if (t <= (-5d+140)) then
        tmp = x + y
    else if (t <= (-2.5d+38)) then
        tmp = z * (x / t)
    else if (t <= (-2.4d-249)) then
        tmp = t_1
    else if (t <= 7.2d-124) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2.65d+31) then
        tmp = t_1
    else if (t <= 6d+213) then
        tmp = x - (t * (y / a))
    else
        tmp = y + ((y * a) / 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 + (z * (y / a));
	double tmp;
	if (t <= -5.2e+200) {
		tmp = y;
	} else if (t <= -5e+140) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = z * (x / t);
	} else if (t <= -2.4e-249) {
		tmp = t_1;
	} else if (t <= 7.2e-124) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.65e+31) {
		tmp = t_1;
	} else if (t <= 6e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -5.2e+200:
		tmp = y
	elif t <= -5e+140:
		tmp = x + y
	elif t <= -2.5e+38:
		tmp = z * (x / t)
	elif t <= -2.4e-249:
		tmp = t_1
	elif t <= 7.2e-124:
		tmp = x * (1.0 - (z / a))
	elif t <= 2.65e+31:
		tmp = t_1
	elif t <= 6e+213:
		tmp = x - (t * (y / a))
	else:
		tmp = y + ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -5.2e+200)
		tmp = y;
	elseif (t <= -5e+140)
		tmp = Float64(x + y);
	elseif (t <= -2.5e+38)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -2.4e-249)
		tmp = t_1;
	elseif (t <= 7.2e-124)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2.65e+31)
		tmp = t_1;
	elseif (t <= 6e+213)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -5.2e+200)
		tmp = y;
	elseif (t <= -5e+140)
		tmp = x + y;
	elseif (t <= -2.5e+38)
		tmp = z * (x / t);
	elseif (t <= -2.4e-249)
		tmp = t_1;
	elseif (t <= 7.2e-124)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2.65e+31)
		tmp = t_1;
	elseif (t <= 6e+213)
		tmp = x - (t * (y / a));
	else
		tmp = y + ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+200], y, If[LessEqual[t, -5e+140], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.5e+38], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-249], t$95$1, If[LessEqual[t, 7.2e-124], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+31], t$95$1, If[LessEqual[t, 6e+213], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.2000000000000003e200

   1. Initial program 22.2%

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

      1. associate-/l* 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -5.2000000000000003e200 < t < -5.00000000000000008e140

   1. Initial program 45.0%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 38.2%

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

      1. fma-def 38.2%

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

      2. associate-*r/ 59.6%

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

      3. fma-def 59.6%

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

      4. neg-mul-1 59.6%

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

      5. +-commutative 59.6%

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

      6. unsub-neg 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in y around inf 57.4%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   10. Simplified 59.2%

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

   if -5.00000000000000008e140 < t < -2.49999999999999985e38

   1. Initial program 44.7%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in a around 0 36.9%

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

      1. associate-/l* 37.1%

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

   9. Simplified 37.1%

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

   10. Taylor expanded in z around 0 36.9%

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

       1. associate-*r/ 37.2%

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

   12. Simplified 37.2%

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

   if -2.49999999999999985e38 < t < -2.40000000000000013e-249 or 7.20000000000000019e-124 < t < 2.6500000000000002e31

   1. Initial program 82.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around inf 60.9%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.3%

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

   7. Simplified 64.3%

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

   if -2.40000000000000013e-249 < t < 7.20000000000000019e-124

   1. Initial program 85.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 86.5%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   7. Simplified 67.9%

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

   if 2.6500000000000002e31 < t < 6.0000000000000002e213

   1. Initial program 45.8%

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

      1. associate-/l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around 0 32.6%

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

      1. fma-def 32.6%

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

      2. associate-*r/ 53.4%

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

      3. fma-def 53.4%

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

      4. neg-mul-1 53.4%

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

      5. +-commutative 53.4%

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

      6. unsub-neg 53.4%

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

   6. Simplified 53.4%

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

   7. Taylor expanded in y around inf 52.9%

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

   8. Taylor expanded in a around inf 39.8%

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

   if 6.0000000000000002e213 < t

   1. Initial program 23.4%

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

      1. associate-/l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around 0 30.3%

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

   5. Taylor expanded in z around 0 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-*r/ 30.3%

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

      3. neg-mul-1 30.3%

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

      4. distribute-rgt-neg-in 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in a around 0 67.5%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+200}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-249}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \]

Alternative 6: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+214}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -8.5e+214)
     y
     (if (<= t -1.5e+140)
       (+ x y)
       (if (<= t -2.5e+38)
         (/ (* x (- z a)) t)
         (if (<= t -2.2e-245)
           t_1
           (if (<= t 2.5e-126)
             (* x (- 1.0 (/ z a)))
             (if (<= t 3.5e+28)
               t_1
               (if (<= t 6e+213)
                 (- x (* t (/ y a)))
                 (+ y (/ (* y a) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -8.5e+214) {
		tmp = y;
	} else if (t <= -1.5e+140) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = (x * (z - a)) / t;
	} else if (t <= -2.2e-245) {
		tmp = t_1;
	} else if (t <= 2.5e-126) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3.5e+28) {
		tmp = t_1;
	} else if (t <= 6e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-8.5d+214)) then
        tmp = y
    else if (t <= (-1.5d+140)) then
        tmp = x + y
    else if (t <= (-2.5d+38)) then
        tmp = (x * (z - a)) / t
    else if (t <= (-2.2d-245)) then
        tmp = t_1
    else if (t <= 2.5d-126) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 3.5d+28) then
        tmp = t_1
    else if (t <= 6d+213) then
        tmp = x - (t * (y / a))
    else
        tmp = y + ((y * a) / 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 + (z * (y / a));
	double tmp;
	if (t <= -8.5e+214) {
		tmp = y;
	} else if (t <= -1.5e+140) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = (x * (z - a)) / t;
	} else if (t <= -2.2e-245) {
		tmp = t_1;
	} else if (t <= 2.5e-126) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3.5e+28) {
		tmp = t_1;
	} else if (t <= 6e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -8.5e+214:
		tmp = y
	elif t <= -1.5e+140:
		tmp = x + y
	elif t <= -2.5e+38:
		tmp = (x * (z - a)) / t
	elif t <= -2.2e-245:
		tmp = t_1
	elif t <= 2.5e-126:
		tmp = x * (1.0 - (z / a))
	elif t <= 3.5e+28:
		tmp = t_1
	elif t <= 6e+213:
		tmp = x - (t * (y / a))
	else:
		tmp = y + ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -8.5e+214)
		tmp = y;
	elseif (t <= -1.5e+140)
		tmp = Float64(x + y);
	elseif (t <= -2.5e+38)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (t <= -2.2e-245)
		tmp = t_1;
	elseif (t <= 2.5e-126)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 3.5e+28)
		tmp = t_1;
	elseif (t <= 6e+213)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -8.5e+214)
		tmp = y;
	elseif (t <= -1.5e+140)
		tmp = x + y;
	elseif (t <= -2.5e+38)
		tmp = (x * (z - a)) / t;
	elseif (t <= -2.2e-245)
		tmp = t_1;
	elseif (t <= 2.5e-126)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 3.5e+28)
		tmp = t_1;
	elseif (t <= 6e+213)
		tmp = x - (t * (y / a));
	else
		tmp = y + ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+214], y, If[LessEqual[t, -1.5e+140], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.5e+38], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -2.2e-245], t$95$1, If[LessEqual[t, 2.5e-126], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+28], t$95$1, If[LessEqual[t, 6e+213], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -8.50000000000000045e214

   1. Initial program 22.2%

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

      1. associate-/l* 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -8.50000000000000045e214 < t < -1.49999999999999998e140

   1. Initial program 45.0%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 38.2%

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

      1. fma-def 38.2%

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

      2. associate-*r/ 59.6%

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

      3. fma-def 59.6%

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

      4. neg-mul-1 59.6%

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

      5. +-commutative 59.6%

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

      6. unsub-neg 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in y around inf 57.4%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   10. Simplified 59.2%

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

   if -1.49999999999999998e140 < t < -2.49999999999999985e38

   1. Initial program 44.7%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in t around -inf 41.9%

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

   if -2.49999999999999985e38 < t < -2.19999999999999993e-245 or 2.50000000000000003e-126 < t < 3.5e28

   1. Initial program 82.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around inf 60.9%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.3%

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

   7. Simplified 64.3%

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

   if -2.19999999999999993e-245 < t < 2.50000000000000003e-126

   1. Initial program 85.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 86.5%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   7. Simplified 67.9%

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

   if 3.5e28 < t < 6.0000000000000002e213

   1. Initial program 45.8%

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

      1. associate-/l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around 0 32.6%

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

      1. fma-def 32.6%

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

      2. associate-*r/ 53.4%

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

      3. fma-def 53.4%

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

      4. neg-mul-1 53.4%

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

      5. +-commutative 53.4%

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

      6. unsub-neg 53.4%

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

   6. Simplified 53.4%

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

   7. Taylor expanded in y around inf 52.9%

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

   8. Taylor expanded in a around inf 39.8%

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

   if 6.0000000000000002e213 < t

   1. Initial program 23.4%

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

      1. associate-/l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around 0 30.3%

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

   5. Taylor expanded in z around 0 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-*r/ 30.3%

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

      3. neg-mul-1 30.3%

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

      4. distribute-rgt-neg-in 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in a around 0 67.5%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+214}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-245}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \]

Alternative 7: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+217}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -6e+219)
     y
     (if (<= t -9e+142)
       (+ x y)
       (if (<= t -2.5e+38)
         (/ (- z a) (/ t x))
         (if (<= t -1.1e-248)
           t_1
           (if (<= t 1.3e-126)
             (* x (- 1.0 (/ z a)))
             (if (<= t 8.6e+41)
               t_1
               (if (<= t 1.02e+217)
                 (- x (* t (/ y a)))
                 (+ y (/ (* y a) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -6e+219) {
		tmp = y;
	} else if (t <= -9e+142) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = (z - a) / (t / x);
	} else if (t <= -1.1e-248) {
		tmp = t_1;
	} else if (t <= 1.3e-126) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8.6e+41) {
		tmp = t_1;
	} else if (t <= 1.02e+217) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-6d+219)) then
        tmp = y
    else if (t <= (-9d+142)) then
        tmp = x + y
    else if (t <= (-2.5d+38)) then
        tmp = (z - a) / (t / x)
    else if (t <= (-1.1d-248)) then
        tmp = t_1
    else if (t <= 1.3d-126) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 8.6d+41) then
        tmp = t_1
    else if (t <= 1.02d+217) then
        tmp = x - (t * (y / a))
    else
        tmp = y + ((y * a) / 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 + (z * (y / a));
	double tmp;
	if (t <= -6e+219) {
		tmp = y;
	} else if (t <= -9e+142) {
		tmp = x + y;
	} else if (t <= -2.5e+38) {
		tmp = (z - a) / (t / x);
	} else if (t <= -1.1e-248) {
		tmp = t_1;
	} else if (t <= 1.3e-126) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8.6e+41) {
		tmp = t_1;
	} else if (t <= 1.02e+217) {
		tmp = x - (t * (y / a));
	} else {
		tmp = y + ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -6e+219:
		tmp = y
	elif t <= -9e+142:
		tmp = x + y
	elif t <= -2.5e+38:
		tmp = (z - a) / (t / x)
	elif t <= -1.1e-248:
		tmp = t_1
	elif t <= 1.3e-126:
		tmp = x * (1.0 - (z / a))
	elif t <= 8.6e+41:
		tmp = t_1
	elif t <= 1.02e+217:
		tmp = x - (t * (y / a))
	else:
		tmp = y + ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -6e+219)
		tmp = y;
	elseif (t <= -9e+142)
		tmp = Float64(x + y);
	elseif (t <= -2.5e+38)
		tmp = Float64(Float64(z - a) / Float64(t / x));
	elseif (t <= -1.1e-248)
		tmp = t_1;
	elseif (t <= 1.3e-126)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 8.6e+41)
		tmp = t_1;
	elseif (t <= 1.02e+217)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -6e+219)
		tmp = y;
	elseif (t <= -9e+142)
		tmp = x + y;
	elseif (t <= -2.5e+38)
		tmp = (z - a) / (t / x);
	elseif (t <= -1.1e-248)
		tmp = t_1;
	elseif (t <= 1.3e-126)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 8.6e+41)
		tmp = t_1;
	elseif (t <= 1.02e+217)
		tmp = x - (t * (y / a));
	else
		tmp = y + ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+219], y, If[LessEqual[t, -9e+142], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.5e+38], N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e-248], t$95$1, If[LessEqual[t, 1.3e-126], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+41], t$95$1, If[LessEqual[t, 1.02e+217], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.9999999999999995e219

   1. Initial program 22.2%

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

      1. associate-/l* 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -5.9999999999999995e219 < t < -8.9999999999999998e142

   1. Initial program 45.0%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 38.2%

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

      1. fma-def 38.2%

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

      2. associate-*r/ 59.6%

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

      3. fma-def 59.6%

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

      4. neg-mul-1 59.6%

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

      5. +-commutative 59.6%

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

      6. unsub-neg 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in y around inf 57.4%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   10. Simplified 59.2%

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

   if -8.9999999999999998e142 < t < -2.49999999999999985e38

   1. Initial program 44.7%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in t around -inf 41.9%

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

      1. associate-/l* 42.1%

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

   9. Simplified 42.1%

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

   if -2.49999999999999985e38 < t < -1.1e-248 or 1.3e-126 < t < 8.60000000000000048e41

   1. Initial program 82.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around inf 60.9%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.3%

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

   7. Simplified 64.3%

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

   if -1.1e-248 < t < 1.3e-126

   1. Initial program 85.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 86.5%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   7. Simplified 67.9%

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

   if 8.60000000000000048e41 < t < 1.02e217

   1. Initial program 45.8%

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

      1. associate-/l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around 0 32.6%

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

      1. fma-def 32.6%

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

      2. associate-*r/ 53.4%

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

      3. fma-def 53.4%

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

      4. neg-mul-1 53.4%

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

      5. +-commutative 53.4%

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

      6. unsub-neg 53.4%

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

   6. Simplified 53.4%

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

   7. Taylor expanded in y around inf 52.9%

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

   8. Taylor expanded in a around inf 39.8%

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

   if 1.02e217 < t

   1. Initial program 23.4%

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

      1. associate-/l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around 0 30.3%

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

   5. Taylor expanded in z around 0 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-*r/ 30.3%

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

      3. neg-mul-1 30.3%

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

      4. distribute-rgt-neg-in 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in a around 0 67.5%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-248}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+217}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \end{array} \]

Alternative 8: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -3.8e+17)
     (+ x (/ (- y x) (/ a z)))
     (if (<= a -1.75e-122)
       t_1
       (if (<= a 1.7e-299)
         (/ (* (- y x) z) (- a t))
         (if (<= a 1.55e-71)
           t_1
           (if (<= a 3.3e+24)
             (* z (/ (- y x) (- a t)))
             (+ x (* t (/ (- x y) (- a t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -3.8e+17) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -1.75e-122) {
		tmp = t_1;
	} else if (a <= 1.7e-299) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 1.55e-71) {
		tmp = t_1;
	} else if (a <= 3.3e+24) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (t * ((x - y) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-3.8d+17)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= (-1.75d-122)) then
        tmp = t_1
    else if (a <= 1.7d-299) then
        tmp = ((y - x) * z) / (a - t)
    else if (a <= 1.55d-71) then
        tmp = t_1
    else if (a <= 3.3d+24) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (t * ((x - y) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -3.8e+17) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -1.75e-122) {
		tmp = t_1;
	} else if (a <= 1.7e-299) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 1.55e-71) {
		tmp = t_1;
	} else if (a <= 3.3e+24) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (t * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -3.8e+17:
		tmp = x + ((y - x) / (a / z))
	elif a <= -1.75e-122:
		tmp = t_1
	elif a <= 1.7e-299:
		tmp = ((y - x) * z) / (a - t)
	elif a <= 1.55e-71:
		tmp = t_1
	elif a <= 3.3e+24:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (t * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.8e+17)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= -1.75e-122)
		tmp = t_1;
	elseif (a <= 1.7e-299)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 1.55e-71)
		tmp = t_1;
	elseif (a <= 3.3e+24)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -3.8e+17)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= -1.75e-122)
		tmp = t_1;
	elseif (a <= 1.7e-299)
		tmp = ((y - x) * z) / (a - t);
	elseif (a <= 1.55e-71)
		tmp = t_1;
	elseif (a <= 3.3e+24)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (t * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+17], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.75e-122], t$95$1, If[LessEqual[a, 1.7e-299], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-71], t$95$1, If[LessEqual[a, 3.3e+24], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.8e17

   1. Initial program 63.0%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 72.7%

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

   if -3.8e17 < a < -1.7500000000000001e-122 or 1.6999999999999999e-299 < a < 1.55000000000000001e-71

   1. Initial program 55.1%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 50.6%

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

      1. associate-*r/ 70.8%

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

   6. Simplified 70.8%

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

   if -1.7500000000000001e-122 < a < 1.6999999999999999e-299

   1. Initial program 54.7%

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

      1. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. div-sub 71.3%

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

      2. associate-*r/ 74.1%

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

   6. Simplified 74.1%

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

   if 1.55000000000000001e-71 < a < 3.2999999999999999e24

   1. Initial program 59.6%

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

      1. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 70.1%

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

      1. div-sub 70.1%

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

   6. Simplified 70.1%

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

   if 3.2999999999999999e24 < a

   1. Initial program 71.2%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 60.1%

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

      1. fma-def 60.1%

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

      2. associate-*r/ 74.3%

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

      3. fma-def 74.3%

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

      4. neg-mul-1 74.3%

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

      5. +-commutative 74.3%

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

      6. unsub-neg 74.3%

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

   6. Simplified 74.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{x - y}{a - t}\\ \end{array} \]

Alternative 9: 39.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-126}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= a -2.4e+113)
     x
     (if (<= a -1.3e+70)
       (* y (/ z a))
       (if (<= a -1.55e+21)
         (+ x y)
         (if (<= a -8.8e-126)
           y
           (if (<= a 1.65e-302)
             t_1
             (if (<= a 6.6e-71)
               y
               (if (<= a 1.25e-34) t_1 (if (<= a 4.1e+132) (+ x y) x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -2.4e+113) {
		tmp = x;
	} else if (a <= -1.3e+70) {
		tmp = y * (z / a);
	} else if (a <= -1.55e+21) {
		tmp = x + y;
	} else if (a <= -8.8e-126) {
		tmp = y;
	} else if (a <= 1.65e-302) {
		tmp = t_1;
	} else if (a <= 6.6e-71) {
		tmp = y;
	} else if (a <= 1.25e-34) {
		tmp = t_1;
	} else if (a <= 4.1e+132) {
		tmp = x + 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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (a <= (-2.4d+113)) then
        tmp = x
    else if (a <= (-1.3d+70)) then
        tmp = y * (z / a)
    else if (a <= (-1.55d+21)) then
        tmp = x + y
    else if (a <= (-8.8d-126)) then
        tmp = y
    else if (a <= 1.65d-302) then
        tmp = t_1
    else if (a <= 6.6d-71) then
        tmp = y
    else if (a <= 1.25d-34) then
        tmp = t_1
    else if (a <= 4.1d+132) then
        tmp = x + 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 t_1 = x * (z / t);
	double tmp;
	if (a <= -2.4e+113) {
		tmp = x;
	} else if (a <= -1.3e+70) {
		tmp = y * (z / a);
	} else if (a <= -1.55e+21) {
		tmp = x + y;
	} else if (a <= -8.8e-126) {
		tmp = y;
	} else if (a <= 1.65e-302) {
		tmp = t_1;
	} else if (a <= 6.6e-71) {
		tmp = y;
	} else if (a <= 1.25e-34) {
		tmp = t_1;
	} else if (a <= 4.1e+132) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if a <= -2.4e+113:
		tmp = x
	elif a <= -1.3e+70:
		tmp = y * (z / a)
	elif a <= -1.55e+21:
		tmp = x + y
	elif a <= -8.8e-126:
		tmp = y
	elif a <= 1.65e-302:
		tmp = t_1
	elif a <= 6.6e-71:
		tmp = y
	elif a <= 1.25e-34:
		tmp = t_1
	elif a <= 4.1e+132:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (a <= -2.4e+113)
		tmp = x;
	elseif (a <= -1.3e+70)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -1.55e+21)
		tmp = Float64(x + y);
	elseif (a <= -8.8e-126)
		tmp = y;
	elseif (a <= 1.65e-302)
		tmp = t_1;
	elseif (a <= 6.6e-71)
		tmp = y;
	elseif (a <= 1.25e-34)
		tmp = t_1;
	elseif (a <= 4.1e+132)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (a <= -2.4e+113)
		tmp = x;
	elseif (a <= -1.3e+70)
		tmp = y * (z / a);
	elseif (a <= -1.55e+21)
		tmp = x + y;
	elseif (a <= -8.8e-126)
		tmp = y;
	elseif (a <= 1.65e-302)
		tmp = t_1;
	elseif (a <= 6.6e-71)
		tmp = y;
	elseif (a <= 1.25e-34)
		tmp = t_1;
	elseif (a <= 4.1e+132)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+113], x, If[LessEqual[a, -1.3e+70], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e+21], N[(x + y), $MachinePrecision], If[LessEqual[a, -8.8e-126], y, If[LessEqual[a, 1.65e-302], t$95$1, If[LessEqual[a, 6.6e-71], y, If[LessEqual[a, 1.25e-34], t$95$1, If[LessEqual[a, 4.1e+132], N[(x + y), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.39999999999999983e113 or 4.09999999999999992e132 < a

   1. Initial program 64.2%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 59.5%

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

   if -2.39999999999999983e113 < a < -1.3e70

   1. Initial program 59.6%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in y around inf 44.8%

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

   6. Taylor expanded in x around 0 45.4%

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

      1. associate-*r/ 58.8%

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

   8. Simplified 58.8%

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

   if -1.3e70 < a < -1.55e21 or 1.2500000000000001e-34 < a < 4.09999999999999992e132

   1. Initial program 69.6%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 49.0%

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

      1. fma-def 49.0%

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

      2. associate-*r/ 59.3%

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

      3. fma-def 59.3%

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

      4. neg-mul-1 59.3%

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

      5. +-commutative 59.3%

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

      6. unsub-neg 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around inf 57.9%

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

   8. Taylor expanded in t around inf 47.2%

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

      1. neg-mul-1 47.2%

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

   10. Simplified 47.2%

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

   if -1.55e21 < a < -8.80000000000000058e-126 or 1.6500000000000001e-302 < a < 6.6000000000000003e-71

   1. Initial program 55.6%

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

      1. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around inf 46.2%

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

   if -8.80000000000000058e-126 < a < 1.6500000000000001e-302 or 6.6000000000000003e-71 < a < 1.2500000000000001e-34

   1. Initial program 57.0%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in x around -inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-in 53.4%

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

   6. Simplified 53.4%

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

   7. Taylor expanded in a around 0 48.1%

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

      1. associate-/l* 45.9%

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

   9. Simplified 45.9%

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

       1. associate-/r/ 54.7%

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

   11. Applied egg-rr 54.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-126}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 39.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-133}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-67}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+113)
   x
   (if (<= a -6e+71)
     (* y (/ z a))
     (if (<= a -1.55e+21)
       (+ x y)
       (if (<= a -2.1e-133)
         y
         (if (<= a 5.4e-303)
           (* x (/ z t))
           (if (<= a 7.2e-67)
             y
             (if (<= a 5.7e-36)
               (/ (* x z) t)
               (if (<= a 1.25e+137) (+ x y) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+113) {
		tmp = x;
	} else if (a <= -6e+71) {
		tmp = y * (z / a);
	} else if (a <= -1.55e+21) {
		tmp = x + y;
	} else if (a <= -2.1e-133) {
		tmp = y;
	} else if (a <= 5.4e-303) {
		tmp = x * (z / t);
	} else if (a <= 7.2e-67) {
		tmp = y;
	} else if (a <= 5.7e-36) {
		tmp = (x * z) / t;
	} else if (a <= 1.25e+137) {
		tmp = x + 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 <= (-1.1d+113)) then
        tmp = x
    else if (a <= (-6d+71)) then
        tmp = y * (z / a)
    else if (a <= (-1.55d+21)) then
        tmp = x + y
    else if (a <= (-2.1d-133)) then
        tmp = y
    else if (a <= 5.4d-303) then
        tmp = x * (z / t)
    else if (a <= 7.2d-67) then
        tmp = y
    else if (a <= 5.7d-36) then
        tmp = (x * z) / t
    else if (a <= 1.25d+137) then
        tmp = x + 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 <= -1.1e+113) {
		tmp = x;
	} else if (a <= -6e+71) {
		tmp = y * (z / a);
	} else if (a <= -1.55e+21) {
		tmp = x + y;
	} else if (a <= -2.1e-133) {
		tmp = y;
	} else if (a <= 5.4e-303) {
		tmp = x * (z / t);
	} else if (a <= 7.2e-67) {
		tmp = y;
	} else if (a <= 5.7e-36) {
		tmp = (x * z) / t;
	} else if (a <= 1.25e+137) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+113:
		tmp = x
	elif a <= -6e+71:
		tmp = y * (z / a)
	elif a <= -1.55e+21:
		tmp = x + y
	elif a <= -2.1e-133:
		tmp = y
	elif a <= 5.4e-303:
		tmp = x * (z / t)
	elif a <= 7.2e-67:
		tmp = y
	elif a <= 5.7e-36:
		tmp = (x * z) / t
	elif a <= 1.25e+137:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+113)
		tmp = x;
	elseif (a <= -6e+71)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -1.55e+21)
		tmp = Float64(x + y);
	elseif (a <= -2.1e-133)
		tmp = y;
	elseif (a <= 5.4e-303)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 7.2e-67)
		tmp = y;
	elseif (a <= 5.7e-36)
		tmp = Float64(Float64(x * z) / t);
	elseif (a <= 1.25e+137)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+113)
		tmp = x;
	elseif (a <= -6e+71)
		tmp = y * (z / a);
	elseif (a <= -1.55e+21)
		tmp = x + y;
	elseif (a <= -2.1e-133)
		tmp = y;
	elseif (a <= 5.4e-303)
		tmp = x * (z / t);
	elseif (a <= 7.2e-67)
		tmp = y;
	elseif (a <= 5.7e-36)
		tmp = (x * z) / t;
	elseif (a <= 1.25e+137)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+113], x, If[LessEqual[a, -6e+71], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e+21], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e-133], y, If[LessEqual[a, 5.4e-303], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-67], y, If[LessEqual[a, 5.7e-36], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.25e+137], N[(x + y), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.10000000000000005e113 or 1.25e137 < a

   1. Initial program 64.2%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 59.5%

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

   if -1.10000000000000005e113 < a < -6.00000000000000025e71

   1. Initial program 59.6%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in y around inf 44.8%

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

   6. Taylor expanded in x around 0 45.4%

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

      1. associate-*r/ 58.8%

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

   8. Simplified 58.8%

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

   if -6.00000000000000025e71 < a < -1.55e21 or 5.6999999999999999e-36 < a < 1.25e137

   1. Initial program 69.6%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 49.0%

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

      1. fma-def 49.0%

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

      2. associate-*r/ 59.3%

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

      3. fma-def 59.3%

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

      4. neg-mul-1 59.3%

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

      5. +-commutative 59.3%

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

      6. unsub-neg 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around inf 57.9%

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

   8. Taylor expanded in t around inf 47.2%

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

      1. neg-mul-1 47.2%

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

   10. Simplified 47.2%

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

   if -1.55e21 < a < -2.1000000000000001e-133 or 5.39999999999999972e-303 < a < 7.19999999999999998e-67

   1. Initial program 55.6%

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

      1. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around inf 46.2%

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

   if -2.1000000000000001e-133 < a < 5.39999999999999972e-303

   1. Initial program 55.0%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in x around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-in 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in a around 0 44.1%

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

      1. associate-/l* 44.2%

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

   9. Simplified 44.2%

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

       1. associate-/r/ 52.9%

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

   11. Applied egg-rr 52.9%

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

   if 7.19999999999999998e-67 < a < 5.6999999999999999e-36

   1. Initial program 63.6%

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

      1. associate-/l* 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in x around -inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-rgt-neg-in 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in a around 0 61.0%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-133}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-67}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ x t))))
   (if (<= a -1.1e+113)
     x
     (if (<= a -2.3e+71)
       (* y (/ z a))
       (if (<= a -7.2e+21)
         (+ x y)
         (if (<= a -7e-190)
           y
           (if (<= a 1.65e-299)
             t_1
             (if (<= a 9e-70)
               y
               (if (<= a 2.9e+24) t_1 (if (<= a 6.6e+38) y x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (x / t);
	double tmp;
	if (a <= -1.1e+113) {
		tmp = x;
	} else if (a <= -2.3e+71) {
		tmp = y * (z / a);
	} else if (a <= -7.2e+21) {
		tmp = x + y;
	} else if (a <= -7e-190) {
		tmp = y;
	} else if (a <= 1.65e-299) {
		tmp = t_1;
	} else if (a <= 9e-70) {
		tmp = y;
	} else if (a <= 2.9e+24) {
		tmp = t_1;
	} else if (a <= 6.6e+38) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (x / t)
    if (a <= (-1.1d+113)) then
        tmp = x
    else if (a <= (-2.3d+71)) then
        tmp = y * (z / a)
    else if (a <= (-7.2d+21)) then
        tmp = x + y
    else if (a <= (-7d-190)) then
        tmp = y
    else if (a <= 1.65d-299) then
        tmp = t_1
    else if (a <= 9d-70) then
        tmp = y
    else if (a <= 2.9d+24) then
        tmp = t_1
    else if (a <= 6.6d+38) 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 t_1 = z * (x / t);
	double tmp;
	if (a <= -1.1e+113) {
		tmp = x;
	} else if (a <= -2.3e+71) {
		tmp = y * (z / a);
	} else if (a <= -7.2e+21) {
		tmp = x + y;
	} else if (a <= -7e-190) {
		tmp = y;
	} else if (a <= 1.65e-299) {
		tmp = t_1;
	} else if (a <= 9e-70) {
		tmp = y;
	} else if (a <= 2.9e+24) {
		tmp = t_1;
	} else if (a <= 6.6e+38) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (x / t)
	tmp = 0
	if a <= -1.1e+113:
		tmp = x
	elif a <= -2.3e+71:
		tmp = y * (z / a)
	elif a <= -7.2e+21:
		tmp = x + y
	elif a <= -7e-190:
		tmp = y
	elif a <= 1.65e-299:
		tmp = t_1
	elif a <= 9e-70:
		tmp = y
	elif a <= 2.9e+24:
		tmp = t_1
	elif a <= 6.6e+38:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(x / t))
	tmp = 0.0
	if (a <= -1.1e+113)
		tmp = x;
	elseif (a <= -2.3e+71)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -7.2e+21)
		tmp = Float64(x + y);
	elseif (a <= -7e-190)
		tmp = y;
	elseif (a <= 1.65e-299)
		tmp = t_1;
	elseif (a <= 9e-70)
		tmp = y;
	elseif (a <= 2.9e+24)
		tmp = t_1;
	elseif (a <= 6.6e+38)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (x / t);
	tmp = 0.0;
	if (a <= -1.1e+113)
		tmp = x;
	elseif (a <= -2.3e+71)
		tmp = y * (z / a);
	elseif (a <= -7.2e+21)
		tmp = x + y;
	elseif (a <= -7e-190)
		tmp = y;
	elseif (a <= 1.65e-299)
		tmp = t_1;
	elseif (a <= 9e-70)
		tmp = y;
	elseif (a <= 2.9e+24)
		tmp = t_1;
	elseif (a <= 6.6e+38)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+113], x, If[LessEqual[a, -2.3e+71], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e+21], N[(x + y), $MachinePrecision], If[LessEqual[a, -7e-190], y, If[LessEqual[a, 1.65e-299], t$95$1, If[LessEqual[a, 9e-70], y, If[LessEqual[a, 2.9e+24], t$95$1, If[LessEqual[a, 6.6e+38], y, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.10000000000000005e113 or 6.5999999999999998e38 < a

   1. Initial program 68.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around inf 57.7%

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

   if -1.10000000000000005e113 < a < -2.3000000000000002e71

   1. Initial program 59.6%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in y around inf 44.8%

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

   6. Taylor expanded in x around 0 45.4%

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

      1. associate-*r/ 58.8%

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

   8. Simplified 58.8%

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

   if -2.3000000000000002e71 < a < -7.2e21

   1. Initial program 61.8%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in z around 0 50.9%

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

      1. fma-def 50.9%

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

      2. associate-*r/ 51.0%

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

      3. fma-def 51.0%

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

      4. neg-mul-1 51.0%

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

      5. +-commutative 51.0%

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

      6. unsub-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in y around inf 46.5%

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

   8. Taylor expanded in t around inf 45.2%

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

      1. neg-mul-1 45.2%

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

   10. Simplified 45.2%

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

   if -7.2e21 < a < -6.9999999999999999e-190 or 1.6500000000000001e-299 < a < 9.00000000000000044e-70 or 2.89999999999999979e24 < a < 6.5999999999999998e38

   1. Initial program 54.9%

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

      1. associate-/l* 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in t around inf 45.5%

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

   if -6.9999999999999999e-190 < a < 1.6500000000000001e-299 or 9.00000000000000044e-70 < a < 2.89999999999999979e24

   1. Initial program 56.7%

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

      1. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in x around -inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-rgt-neg-in 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in a around 0 47.1%

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

      1. associate-/l* 46.3%

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

   9. Simplified 46.3%

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

   10. Taylor expanded in z around 0 47.1%

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

       1. associate-*r/ 46.3%

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

   12. Simplified 46.3%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -7.3 \cdot 10^{+202}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -7.3e+202)
     y
     (if (<= t -1.6e+140)
       (+ x y)
       (if (<= t -1.45e+38)
         (* z (/ x t))
         (if (<= t -4.3e-249)
           t_1
           (if (<= t 9.5e-128)
             (* x (- 1.0 (/ z a)))
             (if (<= t 1.6e+80) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -7.3e+202) {
		tmp = y;
	} else if (t <= -1.6e+140) {
		tmp = x + y;
	} else if (t <= -1.45e+38) {
		tmp = z * (x / t);
	} else if (t <= -4.3e-249) {
		tmp = t_1;
	} else if (t <= 9.5e-128) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.6e+80) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-7.3d+202)) then
        tmp = y
    else if (t <= (-1.6d+140)) then
        tmp = x + y
    else if (t <= (-1.45d+38)) then
        tmp = z * (x / t)
    else if (t <= (-4.3d-249)) then
        tmp = t_1
    else if (t <= 9.5d-128) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.6d+80) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -7.3e+202) {
		tmp = y;
	} else if (t <= -1.6e+140) {
		tmp = x + y;
	} else if (t <= -1.45e+38) {
		tmp = z * (x / t);
	} else if (t <= -4.3e-249) {
		tmp = t_1;
	} else if (t <= 9.5e-128) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.6e+80) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -7.3e+202:
		tmp = y
	elif t <= -1.6e+140:
		tmp = x + y
	elif t <= -1.45e+38:
		tmp = z * (x / t)
	elif t <= -4.3e-249:
		tmp = t_1
	elif t <= 9.5e-128:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.6e+80:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -7.3e+202)
		tmp = y;
	elseif (t <= -1.6e+140)
		tmp = Float64(x + y);
	elseif (t <= -1.45e+38)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -4.3e-249)
		tmp = t_1;
	elseif (t <= 9.5e-128)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.6e+80)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -7.3e+202)
		tmp = y;
	elseif (t <= -1.6e+140)
		tmp = x + y;
	elseif (t <= -1.45e+38)
		tmp = z * (x / t);
	elseif (t <= -4.3e-249)
		tmp = t_1;
	elseif (t <= 9.5e-128)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.6e+80)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.3e+202], y, If[LessEqual[t, -1.6e+140], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.45e+38], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.3e-249], t$95$1, If[LessEqual[t, 9.5e-128], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+80], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.30000000000000037e202

   1. Initial program 22.2%

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

      1. associate-/l* 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -7.30000000000000037e202 < t < -1.60000000000000005e140 or 1.59999999999999995e80 < t

   1. Initial program 37.4%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around 0 28.3%

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

      1. fma-def 28.3%

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

      2. associate-*r/ 53.9%

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

      3. fma-def 53.9%

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

      4. neg-mul-1 53.9%

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

      5. +-commutative 53.9%

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

      6. unsub-neg 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around inf 53.1%

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

   8. Taylor expanded in t around inf 47.5%

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

      1. neg-mul-1 47.5%

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

   10. Simplified 47.5%

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

   if -1.60000000000000005e140 < t < -1.45000000000000003e38

   1. Initial program 44.7%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in a around 0 36.9%

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

      1. associate-/l* 37.1%

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

   9. Simplified 37.1%

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

   10. Taylor expanded in z around 0 36.9%

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

       1. associate-*r/ 37.2%

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

   12. Simplified 37.2%

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

   if -1.45000000000000003e38 < t < -4.3000000000000002e-249 or 9.50000000000000006e-128 < t < 1.59999999999999995e80

   1. Initial program 79.8%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around 0 64.2%

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

   5. Taylor expanded in y around inf 56.6%

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

      1. associate-/l* 59.6%

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

      2. associate-/r/ 59.6%

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

   7. Simplified 59.6%

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

   if -4.3000000000000002e-249 < t < 9.50000000000000006e-128

   1. Initial program 85.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 86.5%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   7. Simplified 67.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.3 \cdot 10^{+202}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-249}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+80}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (+ x (/ z (/ a (- y x)))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -2e+19)
     t_2
     (if (<= a -1.35e-134)
       t_1
       (if (<= a 3.5e-300)
         t_3
         (if (<= a 4.9e-73) t_1 (if (<= a 1.85e+31) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -2e+19) {
		tmp = t_2;
	} else if (a <= -1.35e-134) {
		tmp = t_1;
	} else if (a <= 3.5e-300) {
		tmp = t_3;
	} else if (a <= 4.9e-73) {
		tmp = t_1;
	} else if (a <= 1.85e+31) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (z / (a / (y - x)))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-2d+19)) then
        tmp = t_2
    else if (a <= (-1.35d-134)) then
        tmp = t_1
    else if (a <= 3.5d-300) then
        tmp = t_3
    else if (a <= 4.9d-73) then
        tmp = t_1
    else if (a <= 1.85d+31) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -2e+19) {
		tmp = t_2;
	} else if (a <= -1.35e-134) {
		tmp = t_1;
	} else if (a <= 3.5e-300) {
		tmp = t_3;
	} else if (a <= 4.9e-73) {
		tmp = t_1;
	} else if (a <= 1.85e+31) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (z / (a / (y - x)))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -2e+19:
		tmp = t_2
	elif a <= -1.35e-134:
		tmp = t_1
	elif a <= 3.5e-300:
		tmp = t_3
	elif a <= 4.9e-73:
		tmp = t_1
	elif a <= 1.85e+31:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -2e+19)
		tmp = t_2;
	elseif (a <= -1.35e-134)
		tmp = t_1;
	elseif (a <= 3.5e-300)
		tmp = t_3;
	elseif (a <= 4.9e-73)
		tmp = t_1;
	elseif (a <= 1.85e+31)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (z / (a / (y - x)));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -2e+19)
		tmp = t_2;
	elseif (a <= -1.35e-134)
		tmp = t_1;
	elseif (a <= 3.5e-300)
		tmp = t_3;
	elseif (a <= 4.9e-73)
		tmp = t_1;
	elseif (a <= 1.85e+31)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+19], t$95$2, If[LessEqual[a, -1.35e-134], t$95$1, If[LessEqual[a, 3.5e-300], t$95$3, If[LessEqual[a, 4.9e-73], t$95$1, If[LessEqual[a, 1.85e+31], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e19 or 1.8499999999999999e31 < a

   1. Initial program 67.5%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/l* 73.2%

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

   6. Simplified 73.2%

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

   if -2e19 < a < -1.3499999999999999e-134 or 3.5000000000000002e-300 < a < 4.90000000000000028e-73

   1. Initial program 55.1%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 50.6%

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

      1. associate-*r/ 70.8%

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

   6. Simplified 70.8%

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

   if -1.3499999999999999e-134 < a < 3.5000000000000002e-300 or 4.90000000000000028e-73 < a < 1.8499999999999999e31

   1. Initial program 55.4%

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

      1. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 66.9%

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

      1. div-sub 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 14: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (+ x (/ (- y x) (/ a z))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -6.2e+19)
     t_2
     (if (<= a -1.6e-128)
       t_1
       (if (<= a 1.95e-296)
         t_3
         (if (<= a 1.6e-68) t_1 (if (<= a 1.75e+31) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -6.2e+19) {
		tmp = t_2;
	} else if (a <= -1.6e-128) {
		tmp = t_1;
	} else if (a <= 1.95e-296) {
		tmp = t_3;
	} else if (a <= 1.6e-68) {
		tmp = t_1;
	} else if (a <= 1.75e+31) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((y - x) / (a / z))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-6.2d+19)) then
        tmp = t_2
    else if (a <= (-1.6d-128)) then
        tmp = t_1
    else if (a <= 1.95d-296) then
        tmp = t_3
    else if (a <= 1.6d-68) then
        tmp = t_1
    else if (a <= 1.75d+31) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -6.2e+19) {
		tmp = t_2;
	} else if (a <= -1.6e-128) {
		tmp = t_1;
	} else if (a <= 1.95e-296) {
		tmp = t_3;
	} else if (a <= 1.6e-68) {
		tmp = t_1;
	} else if (a <= 1.75e+31) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((y - x) / (a / z))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -6.2e+19:
		tmp = t_2
	elif a <= -1.6e-128:
		tmp = t_1
	elif a <= 1.95e-296:
		tmp = t_3
	elif a <= 1.6e-68:
		tmp = t_1
	elif a <= 1.75e+31:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -6.2e+19)
		tmp = t_2;
	elseif (a <= -1.6e-128)
		tmp = t_1;
	elseif (a <= 1.95e-296)
		tmp = t_3;
	elseif (a <= 1.6e-68)
		tmp = t_1;
	elseif (a <= 1.75e+31)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((y - x) / (a / z));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -6.2e+19)
		tmp = t_2;
	elseif (a <= -1.6e-128)
		tmp = t_1;
	elseif (a <= 1.95e-296)
		tmp = t_3;
	elseif (a <= 1.6e-68)
		tmp = t_1;
	elseif (a <= 1.75e+31)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+19], t$95$2, If[LessEqual[a, -1.6e-128], t$95$1, If[LessEqual[a, 1.95e-296], t$95$3, If[LessEqual[a, 1.6e-68], t$95$1, If[LessEqual[a, 1.75e+31], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2e19 or 1.75e31 < a

   1. Initial program 67.5%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around 0 73.9%

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

   if -6.2e19 < a < -1.5999999999999999e-128 or 1.95000000000000005e-296 < a < 1.5999999999999999e-68

   1. Initial program 55.1%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 50.6%

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

      1. associate-*r/ 70.8%

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

   6. Simplified 70.8%

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

   if -1.5999999999999999e-128 < a < 1.95000000000000005e-296 or 1.5999999999999999e-68 < a < 1.75e31

   1. Initial program 55.4%

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

      1. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 66.9%

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

      1. div-sub 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 15: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= a -3.5e+18)
     (+ x (/ (- y x) (/ a z)))
     (if (<= a -4e-125)
       t_1
       (if (<= a 8e-297)
         t_2
         (if (<= a 1.25e-67)
           t_1
           (if (<= a 5.8e+37) t_2 (- x (* t (/ y (- a t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -3.5e+18) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -4e-125) {
		tmp = t_1;
	} else if (a <= 8e-297) {
		tmp = t_2;
	} else if (a <= 1.25e-67) {
		tmp = t_1;
	} else if (a <= 5.8e+37) {
		tmp = t_2;
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (a <= (-3.5d+18)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= (-4d-125)) then
        tmp = t_1
    else if (a <= 8d-297) then
        tmp = t_2
    else if (a <= 1.25d-67) then
        tmp = t_1
    else if (a <= 5.8d+37) then
        tmp = t_2
    else
        tmp = x - (t * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -3.5e+18) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -4e-125) {
		tmp = t_1;
	} else if (a <= 8e-297) {
		tmp = t_2;
	} else if (a <= 1.25e-67) {
		tmp = t_1;
	} else if (a <= 5.8e+37) {
		tmp = t_2;
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -3.5e+18:
		tmp = x + ((y - x) / (a / z))
	elif a <= -4e-125:
		tmp = t_1
	elif a <= 8e-297:
		tmp = t_2
	elif a <= 1.25e-67:
		tmp = t_1
	elif a <= 5.8e+37:
		tmp = t_2
	else:
		tmp = x - (t * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.5e+18)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= -4e-125)
		tmp = t_1;
	elseif (a <= 8e-297)
		tmp = t_2;
	elseif (a <= 1.25e-67)
		tmp = t_1;
	elseif (a <= 5.8e+37)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -3.5e+18)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= -4e-125)
		tmp = t_1;
	elseif (a <= 8e-297)
		tmp = t_2;
	elseif (a <= 1.25e-67)
		tmp = t_1;
	elseif (a <= 5.8e+37)
		tmp = t_2;
	else
		tmp = x - (t * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+18], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-125], t$95$1, If[LessEqual[a, 8e-297], t$95$2, If[LessEqual[a, 1.25e-67], t$95$1, If[LessEqual[a, 5.8e+37], t$95$2, N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5e18

   1. Initial program 63.0%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 72.7%

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

   if -3.5e18 < a < -4.00000000000000005e-125 or 8.00000000000000032e-297 < a < 1.25e-67

   1. Initial program 55.1%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 50.6%

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

      1. associate-*r/ 70.8%

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

   6. Simplified 70.8%

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

   if -4.00000000000000005e-125 < a < 8.00000000000000032e-297 or 1.25e-67 < a < 5.79999999999999957e37

   1. Initial program 56.1%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in z around inf 67.4%

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

      1. div-sub 69.2%

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

   6. Simplified 69.2%

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

   if 5.79999999999999957e37 < a

   1. Initial program 72.4%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 62.3%

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

      1. fma-def 62.3%

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

      2. associate-*r/ 75.7%

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

      3. fma-def 75.7%

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

      4. neg-mul-1 75.7%

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

      5. +-commutative 75.7%

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

      6. unsub-neg 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in y around inf 75.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-125}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-297}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 16: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -6.4e+19)
     (+ x (/ (- y x) (/ a z)))
     (if (<= a -9e-127)
       t_1
       (if (<= a 3.8e-296)
         (/ (* (- y x) z) (- a t))
         (if (<= a 6e-68)
           t_1
           (if (<= a 2.8e+33)
             (* z (/ (- y x) (- a t)))
             (- x (* t (/ y (- a t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6.4e+19) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -9e-127) {
		tmp = t_1;
	} else if (a <= 3.8e-296) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 6e-68) {
		tmp = t_1;
	} else if (a <= 2.8e+33) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-6.4d+19)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= (-9d-127)) then
        tmp = t_1
    else if (a <= 3.8d-296) then
        tmp = ((y - x) * z) / (a - t)
    else if (a <= 6d-68) then
        tmp = t_1
    else if (a <= 2.8d+33) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x - (t * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6.4e+19) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -9e-127) {
		tmp = t_1;
	} else if (a <= 3.8e-296) {
		tmp = ((y - x) * z) / (a - t);
	} else if (a <= 6e-68) {
		tmp = t_1;
	} else if (a <= 2.8e+33) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -6.4e+19:
		tmp = x + ((y - x) / (a / z))
	elif a <= -9e-127:
		tmp = t_1
	elif a <= 3.8e-296:
		tmp = ((y - x) * z) / (a - t)
	elif a <= 6e-68:
		tmp = t_1
	elif a <= 2.8e+33:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x - (t * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -6.4e+19)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= -9e-127)
		tmp = t_1;
	elseif (a <= 3.8e-296)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (a <= 6e-68)
		tmp = t_1;
	elseif (a <= 2.8e+33)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -6.4e+19)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= -9e-127)
		tmp = t_1;
	elseif (a <= 3.8e-296)
		tmp = ((y - x) * z) / (a - t);
	elseif (a <= 6e-68)
		tmp = t_1;
	elseif (a <= 2.8e+33)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x - (t * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.4e+19], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e-127], t$95$1, If[LessEqual[a, 3.8e-296], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-68], t$95$1, If[LessEqual[a, 2.8e+33], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.4e19

   1. Initial program 63.0%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 72.7%

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

   if -6.4e19 < a < -8.9999999999999998e-127 or 3.8000000000000002e-296 < a < 6e-68

   1. Initial program 55.1%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 50.6%

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

      1. associate-*r/ 70.8%

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

   6. Simplified 70.8%

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

   if -8.9999999999999998e-127 < a < 3.8000000000000002e-296

   1. Initial program 54.7%

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

      1. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. div-sub 71.3%

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

      2. associate-*r/ 74.1%

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

   6. Simplified 74.1%

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

   if 6e-68 < a < 2.8000000000000001e33

   1. Initial program 58.2%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in z around inf 66.1%

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

      1. div-sub 66.1%

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

   6. Simplified 66.1%

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

   if 2.8000000000000001e33 < a

   1. Initial program 72.4%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 62.3%

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

      1. fma-def 62.3%

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

      2. associate-*r/ 75.7%

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

      3. fma-def 75.7%

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

      4. neg-mul-1 75.7%

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

      5. +-commutative 75.7%

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

      6. unsub-neg 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in y around inf 75.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 17: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 2.06 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -6.5e+148)
     (+ x (* z (/ y a)))
     (if (<= a -3.9e+59)
       t_1
       (if (<= a -4.4e+18)
         (* x (- 1.0 (/ z a)))
         (if (<= a 2.06e+43) t_1 (- x (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6.5e+148) {
		tmp = x + (z * (y / a));
	} else if (a <= -3.9e+59) {
		tmp = t_1;
	} else if (a <= -4.4e+18) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 2.06e+43) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-6.5d+148)) then
        tmp = x + (z * (y / a))
    else if (a <= (-3.9d+59)) then
        tmp = t_1
    else if (a <= (-4.4d+18)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= 2.06d+43) then
        tmp = t_1
    else
        tmp = x - (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6.5e+148) {
		tmp = x + (z * (y / a));
	} else if (a <= -3.9e+59) {
		tmp = t_1;
	} else if (a <= -4.4e+18) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 2.06e+43) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -6.5e+148:
		tmp = x + (z * (y / a))
	elif a <= -3.9e+59:
		tmp = t_1
	elif a <= -4.4e+18:
		tmp = x * (1.0 - (z / a))
	elif a <= 2.06e+43:
		tmp = t_1
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -6.5e+148)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (a <= -3.9e+59)
		tmp = t_1;
	elseif (a <= -4.4e+18)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= 2.06e+43)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -6.5e+148)
		tmp = x + (z * (y / a));
	elseif (a <= -3.9e+59)
		tmp = t_1;
	elseif (a <= -4.4e+18)
		tmp = x * (1.0 - (z / a));
	elseif (a <= 2.06e+43)
		tmp = t_1;
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+148], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e+59], t$95$1, If[LessEqual[a, -4.4e+18], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.06e+43], t$95$1, N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.49999999999999947e148

   1. Initial program 62.7%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 82.5%

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

   5. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 75.7%

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

      2. associate-/r/ 75.7%

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

   7. Simplified 75.7%

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

   if -6.49999999999999947e148 < a < -3.90000000000000021e59 or -4.4e18 < a < 2.0600000000000001e43

   1. Initial program 55.5%

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

      1. associate-/l* 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in x around 0 43.5%

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

      1. associate-*r/ 60.7%

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

   6. Simplified 60.7%

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

   if -3.90000000000000021e59 < a < -4.4e18

   1. Initial program 76.5%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around 0 76.4%

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

   5. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   7. Simplified 76.4%

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

   if 2.0600000000000001e43 < a

   1. Initial program 73.6%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. fma-def 63.3%

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

      2. associate-*r/ 75.3%

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

      3. fma-def 75.3%

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

      4. neg-mul-1 75.3%

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

      5. +-commutative 75.3%

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

      6. unsub-neg 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around inf 75.0%

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

   8. Taylor expanded in t around 0 63.3%

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

      1. associate-/l* 66.5%

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

   10. Simplified 66.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 2.06 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 18: 37.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= a -1.12e+113)
     x
     (if (<= a -2.15e+71)
       t_1
       (if (<= a -1.16e+21)
         (+ x y)
         (if (<= a -5.1e-192)
           y
           (if (<= a -1.2e-264) t_1 (if (<= a 1.7e+42) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (a <= -1.12e+113) {
		tmp = x;
	} else if (a <= -2.15e+71) {
		tmp = t_1;
	} else if (a <= -1.16e+21) {
		tmp = x + y;
	} else if (a <= -5.1e-192) {
		tmp = y;
	} else if (a <= -1.2e-264) {
		tmp = t_1;
	} else if (a <= 1.7e+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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (a <= (-1.12d+113)) then
        tmp = x
    else if (a <= (-2.15d+71)) then
        tmp = t_1
    else if (a <= (-1.16d+21)) then
        tmp = x + y
    else if (a <= (-5.1d-192)) then
        tmp = y
    else if (a <= (-1.2d-264)) then
        tmp = t_1
    else if (a <= 1.7d+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 t_1 = y * (z / a);
	double tmp;
	if (a <= -1.12e+113) {
		tmp = x;
	} else if (a <= -2.15e+71) {
		tmp = t_1;
	} else if (a <= -1.16e+21) {
		tmp = x + y;
	} else if (a <= -5.1e-192) {
		tmp = y;
	} else if (a <= -1.2e-264) {
		tmp = t_1;
	} else if (a <= 1.7e+42) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if a <= -1.12e+113:
		tmp = x
	elif a <= -2.15e+71:
		tmp = t_1
	elif a <= -1.16e+21:
		tmp = x + y
	elif a <= -5.1e-192:
		tmp = y
	elif a <= -1.2e-264:
		tmp = t_1
	elif a <= 1.7e+42:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (a <= -1.12e+113)
		tmp = x;
	elseif (a <= -2.15e+71)
		tmp = t_1;
	elseif (a <= -1.16e+21)
		tmp = Float64(x + y);
	elseif (a <= -5.1e-192)
		tmp = y;
	elseif (a <= -1.2e-264)
		tmp = t_1;
	elseif (a <= 1.7e+42)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (a <= -1.12e+113)
		tmp = x;
	elseif (a <= -2.15e+71)
		tmp = t_1;
	elseif (a <= -1.16e+21)
		tmp = x + y;
	elseif (a <= -5.1e-192)
		tmp = y;
	elseif (a <= -1.2e-264)
		tmp = t_1;
	elseif (a <= 1.7e+42)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e+113], x, If[LessEqual[a, -2.15e+71], t$95$1, If[LessEqual[a, -1.16e+21], N[(x + y), $MachinePrecision], If[LessEqual[a, -5.1e-192], y, If[LessEqual[a, -1.2e-264], t$95$1, If[LessEqual[a, 1.7e+42], y, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1200000000000001e113 or 1.69999999999999988e42 < a

   1. Initial program 68.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around inf 57.7%

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

   if -1.1200000000000001e113 < a < -2.14999999999999992e71 or -5.1000000000000002e-192 < a < -1.1999999999999999e-264

   1. Initial program 54.4%

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

      1. associate-/l* 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in t around 0 47.4%

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

   5. Taylor expanded in y around inf 39.3%

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

   6. Taylor expanded in x around 0 39.7%

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

      1. associate-*r/ 44.3%

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

   8. Simplified 44.3%

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

   if -2.14999999999999992e71 < a < -1.16e21

   1. Initial program 61.8%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in z around 0 50.9%

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

      1. fma-def 50.9%

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

      2. associate-*r/ 51.0%

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

      3. fma-def 51.0%

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

      4. neg-mul-1 51.0%

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

      5. +-commutative 51.0%

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

      6. unsub-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in y around inf 46.5%

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

   8. Taylor expanded in t around inf 45.2%

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

      1. neg-mul-1 45.2%

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

   10. Simplified 45.2%

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

   if -1.16e21 < a < -5.1000000000000002e-192 or -1.1999999999999999e-264 < a < 1.69999999999999988e42

   1. Initial program 55.9%

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

      1. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in t around inf 38.8%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 46.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+210}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+210)
   y
   (if (<= t -5.5e+140)
     (+ x y)
     (if (<= t -2.15e+38)
       (* z (/ x t))
       (if (<= t 3.4e+77) (* x (- 1.0 (/ z a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+210) {
		tmp = y;
	} else if (t <= -5.5e+140) {
		tmp = x + y;
	} else if (t <= -2.15e+38) {
		tmp = z * (x / t);
	} else if (t <= 3.4e+77) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d+210)) then
        tmp = y
    else if (t <= (-5.5d+140)) then
        tmp = x + y
    else if (t <= (-2.15d+38)) then
        tmp = z * (x / t)
    else if (t <= 3.4d+77) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+210) {
		tmp = y;
	} else if (t <= -5.5e+140) {
		tmp = x + y;
	} else if (t <= -2.15e+38) {
		tmp = z * (x / t);
	} else if (t <= 3.4e+77) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+210:
		tmp = y
	elif t <= -5.5e+140:
		tmp = x + y
	elif t <= -2.15e+38:
		tmp = z * (x / t)
	elif t <= 3.4e+77:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+210)
		tmp = y;
	elseif (t <= -5.5e+140)
		tmp = Float64(x + y);
	elseif (t <= -2.15e+38)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= 3.4e+77)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+210)
		tmp = y;
	elseif (t <= -5.5e+140)
		tmp = x + y;
	elseif (t <= -2.15e+38)
		tmp = z * (x / t);
	elseif (t <= 3.4e+77)
		tmp = x * (1.0 - (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+210], y, If[LessEqual[t, -5.5e+140], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.15e+38], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+77], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2499999999999999e210

   1. Initial program 22.2%

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

      1. associate-/l* 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -1.2499999999999999e210 < t < -5.5e140 or 3.39999999999999997e77 < t

   1. Initial program 37.4%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in z around 0 28.3%

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

      1. fma-def 28.3%

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

      2. associate-*r/ 53.9%

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

      3. fma-def 53.9%

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

      4. neg-mul-1 53.9%

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

      5. +-commutative 53.9%

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

      6. unsub-neg 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around inf 53.1%

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

   8. Taylor expanded in t around inf 47.5%

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

      1. neg-mul-1 47.5%

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

   10. Simplified 47.5%

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

   if -5.5e140 < t < -2.1499999999999998e38

   1. Initial program 44.7%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in a around 0 36.9%

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

      1. associate-/l* 37.1%

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

   9. Simplified 37.1%

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

   10. Taylor expanded in z around 0 36.9%

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

       1. associate-*r/ 37.2%

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

   12. Simplified 37.2%

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

   if -2.1499999999999998e38 < t < 3.39999999999999997e77

   1. Initial program 81.9%

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

      1. associate-/l* 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 71.9%

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

   5. Taylor expanded in x around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+210}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 20: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= a -2.4e+16)
     (* x (- 1.0 (/ z a)))
     (if (<= a -9.6e-253)
       t_1
       (if (<= a 3.6e-303)
         (* x (/ z t))
         (if (<= a 1e+43) t_1 (- x (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -2.4e+16) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -9.6e-253) {
		tmp = t_1;
	} else if (a <= 3.6e-303) {
		tmp = x * (z / t);
	} else if (a <= 1e+43) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (a <= (-2.4d+16)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= (-9.6d-253)) then
        tmp = t_1
    else if (a <= 3.6d-303) then
        tmp = x * (z / t)
    else if (a <= 1d+43) then
        tmp = t_1
    else
        tmp = x - (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -2.4e+16) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -9.6e-253) {
		tmp = t_1;
	} else if (a <= 3.6e-303) {
		tmp = x * (z / t);
	} else if (a <= 1e+43) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if a <= -2.4e+16:
		tmp = x * (1.0 - (z / a))
	elif a <= -9.6e-253:
		tmp = t_1
	elif a <= 3.6e-303:
		tmp = x * (z / t)
	elif a <= 1e+43:
		tmp = t_1
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (a <= -2.4e+16)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= -9.6e-253)
		tmp = t_1;
	elseif (a <= 3.6e-303)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1e+43)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (a <= -2.4e+16)
		tmp = x * (1.0 - (z / a));
	elseif (a <= -9.6e-253)
		tmp = t_1;
	elseif (a <= 3.6e-303)
		tmp = x * (z / t);
	elseif (a <= 1e+43)
		tmp = t_1;
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+16], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.6e-253], t$95$1, If[LessEqual[a, 3.6e-303], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+43], t$95$1, N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4e16

   1. Initial program 62.3%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 71.7%

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

   5. Taylor expanded in x around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   7. Simplified 60.9%

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

   if -2.4e16 < a < -9.60000000000000037e-253 or 3.5999999999999998e-303 < a < 1.00000000000000001e43

   1. Initial program 56.3%

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

      1. associate-/l* 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around 0 45.6%

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

      1. associate-*r/ 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in a around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. neg-mul-1 53.3%

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

   9. Simplified 53.3%

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

   if -9.60000000000000037e-253 < a < 3.5999999999999998e-303

   1. Initial program 48.3%

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

      1. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-rgt-neg-in 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in a around 0 62.4%

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

      1. associate-/l* 62.5%

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

   9. Simplified 62.5%

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

       1. associate-/r/ 69.7%

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

   11. Applied egg-rr 69.7%

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

   if 1.00000000000000001e43 < a

   1. Initial program 73.6%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. fma-def 63.3%

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

      2. associate-*r/ 75.3%

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

      3. fma-def 75.3%

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

      4. neg-mul-1 75.3%

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

      5. +-commutative 75.3%

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

      6. unsub-neg 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around inf 75.0%

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

   8. Taylor expanded in t around 0 63.3%

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

      1. associate-/l* 66.5%

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

   10. Simplified 66.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 10^{+43}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 21: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;a \leq -28000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= a -28000000000000.0)
     (* x (- 1.0 (/ z a)))
     (if (<= a -4.8e-186)
       t_1
       (if (<= a 2.1e-303)
         (* x (/ (- z a) t))
         (if (<= a 1e+40) t_1 (- x (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -28000000000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -4.8e-186) {
		tmp = t_1;
	} else if (a <= 2.1e-303) {
		tmp = x * ((z - a) / t);
	} else if (a <= 1e+40) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (a <= (-28000000000000.0d0)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= (-4.8d-186)) then
        tmp = t_1
    else if (a <= 2.1d-303) then
        tmp = x * ((z - a) / t)
    else if (a <= 1d+40) then
        tmp = t_1
    else
        tmp = x - (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -28000000000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -4.8e-186) {
		tmp = t_1;
	} else if (a <= 2.1e-303) {
		tmp = x * ((z - a) / t);
	} else if (a <= 1e+40) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if a <= -28000000000000.0:
		tmp = x * (1.0 - (z / a))
	elif a <= -4.8e-186:
		tmp = t_1
	elif a <= 2.1e-303:
		tmp = x * ((z - a) / t)
	elif a <= 1e+40:
		tmp = t_1
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (a <= -28000000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= -4.8e-186)
		tmp = t_1;
	elseif (a <= 2.1e-303)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 1e+40)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (a <= -28000000000000.0)
		tmp = x * (1.0 - (z / a));
	elseif (a <= -4.8e-186)
		tmp = t_1;
	elseif (a <= 2.1e-303)
		tmp = x * ((z - a) / t);
	elseif (a <= 1e+40)
		tmp = t_1;
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -28000000000000.0], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-186], t$95$1, If[LessEqual[a, 2.1e-303], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+40], t$95$1, N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.8e13

   1. Initial program 62.3%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 71.7%

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

   5. Taylor expanded in x around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   7. Simplified 60.9%

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

   if -2.8e13 < a < -4.80000000000000006e-186 or 2.1e-303 < a < 1.00000000000000003e40

   1. Initial program 55.7%

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

      1. associate-/l* 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in x around 0 45.9%

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

      1. associate-*r/ 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in a around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

   9. Simplified 53.4%

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

   if -4.80000000000000006e-186 < a < 2.1e-303

   1. Initial program 54.3%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around -inf 58.3%

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

      1. mul-1-neg 58.3%

         \[\leadsto \color{blue}{-\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      2. distribute-rgt-neg-in 58.3%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

   7. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{\frac{-1 \cdot z + a}{t}} \cdot \left(-x\right) \]
   8. Step-by-step derivation

      1. +-commutative 67.6%

         \[\leadsto \frac{\color{blue}{a + -1 \cdot z}}{t} \cdot \left(-x\right) \]

      2. mul-1-neg 67.6%

         \[\leadsto \frac{a + \color{blue}{\left(-z\right)}}{t} \cdot \left(-x\right) \]

      3. unsub-neg 67.6%

         \[\leadsto \frac{\color{blue}{a - z}}{t} \cdot \left(-x\right) \]

   9. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{a - z}{t}} \cdot \left(-x\right) \]

   if 1.00000000000000003e40 < a

   1. Initial program 73.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - x\right)}{a - t} + x} \]
   5. Step-by-step derivation

      1. fma-def 63.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t \cdot \left(y - x\right)}{a - t}, x\right)} \]

      2. associate-*r/ 75.3%

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{t \cdot \frac{y - x}{a - t}}, x\right) \]

      3. fma-def 75.3%

         \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \frac{y - x}{a - t}\right) + x} \]

      4. neg-mul-1 75.3%

         \[\leadsto \color{blue}{\left(-t \cdot \frac{y - x}{a - t}\right)} + x \]

      5. +-commutative 75.3%

         \[\leadsto \color{blue}{x + \left(-t \cdot \frac{y - x}{a - t}\right)} \]

      6. unsub-neg 75.3%

         \[\leadsto \color{blue}{x - t \cdot \frac{y - x}{a - t}} \]

   6. Simplified 75.3%

      \[\leadsto \color{blue}{x - t \cdot \frac{y - x}{a - t}} \]

   7. Taylor expanded in y around inf 75.0%

      \[\leadsto x - t \cdot \color{blue}{\frac{y}{a - t}} \]

   8. Taylor expanded in t around 0 63.3%

      \[\leadsto x - \color{blue}{\frac{y \cdot t}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 66.5%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{t}}} \]

   10. Simplified 66.5%

       \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -28000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 10^{+40}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 22: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -45000000000000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-22}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -45000000000000.0)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a 3.6e-22)
     (+ y (/ (* (- y x) (- a z)) t))
     (+ x (* t (/ (- x y) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -45000000000000.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3.6e-22) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + (t * ((x - y) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-45000000000000.0d0)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 3.6d-22) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = x + (t * ((x - y) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -45000000000000.0) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 3.6e-22) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + (t * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -45000000000000.0:
		tmp = x + ((y - x) / (a / z))
	elif a <= 3.6e-22:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = x + (t * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -45000000000000.0)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 3.6e-22)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -45000000000000.0)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 3.6e-22)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = x + (t * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -45000000000000.0], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-22], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5e13

   1. Initial program 62.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 91.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around 0 71.7%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a}{z}}} \]

   if -4.5e13 < a < 3.5999999999999998e-22

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 68.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around -inf 78.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

      2. unsub-neg 78.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      3. div-sub 77.6%

         \[\leadsto y - \color{blue}{\left(\frac{\left(y - x\right) \cdot z}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      4. *-commutative 77.6%

         \[\leadsto y - \left(\frac{\color{blue}{z \cdot \left(y - x\right)}}{t} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      5. div-sub 78.4%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. distribute-rgt-out-- 78.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

   6. Simplified 78.4%

      \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   if 3.5999999999999998e-22 < a

   1. Initial program 70.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 93.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around 0 57.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - x\right)}{a - t} + x} \]
   5. Step-by-step derivation

      1. fma-def 57.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t \cdot \left(y - x\right)}{a - t}, x\right)} \]

      2. associate-*r/ 70.5%

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{t \cdot \frac{y - x}{a - t}}, x\right) \]

      3. fma-def 70.5%

         \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \frac{y - x}{a - t}\right) + x} \]

      4. neg-mul-1 70.5%

         \[\leadsto \color{blue}{\left(-t \cdot \frac{y - x}{a - t}\right)} + x \]

      5. +-commutative 70.5%

         \[\leadsto \color{blue}{x + \left(-t \cdot \frac{y - x}{a - t}\right)} \]

      6. unsub-neg 70.5%

         \[\leadsto \color{blue}{x - t \cdot \frac{y - x}{a - t}} \]

   6. Simplified 70.5%

      \[\leadsto \color{blue}{x - t \cdot \frac{y - x}{a - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -45000000000000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-22}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{x - y}{a - t}\\ \end{array} \]

Alternative 23: 38.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+40}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+113) x (if (<= a 1.15e+40) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+113) {
		tmp = x;
	} else if (a <= 1.15e+40) {
		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 <= (-1.15d+113)) then
        tmp = x
    else if (a <= 1.15d+40) 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 <= -1.15e+113) {
		tmp = x;
	} else if (a <= 1.15e+40) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+113:
		tmp = x
	elif a <= 1.15e+40:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+113)
		tmp = x;
	elseif (a <= 1.15e+40)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+113)
		tmp = x;
	elseif (a <= 1.15e+40)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+113], x, If[LessEqual[a, 1.15e+40], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14999999999999998e113 or 1.14999999999999997e40 < a

   1. Initial program 68.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 57.7%

      \[\leadsto \color{blue}{x} \]

   if -1.14999999999999998e113 < a < 1.14999999999999997e40

   1. Initial program 56.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 71.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+40}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 25.2% 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 61.4%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 81.6%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Simplified 81.6%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

4. Taylor expanded in a around inf 28.7%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 28.7%

   \[\leadsto x \]

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 2023242 
(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))))