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

Percentage Accurate: 68.7% → 91.0%

Time: 24.3s

Alternatives: 26

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.7% 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: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-295)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 5e+253) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (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 <= -4e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+253) {
		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 = x + ((z - t) * ((y - x) / (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 <= -4e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+253) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-295:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 5e+253:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / 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 <= -4e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+253)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 5e+253)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $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, -4e-295], 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+253], 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 4.9999999999999997e253 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 47.5%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999997e253

   1. Initial program 97.7%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 4.0%

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

   3. Simplified 4.0%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+253}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot a}{t} - \left(\frac{\left(y - x\right) \cdot z}{t} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -4e-295) (not (<= t_1 0.0)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (- (/ (* (- y x) a) t) (- (/ (* (- y x) z) t) y)))))

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 <= -4e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = (((y - x) * a) / t) - ((((y - x) * z) / t) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-4d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = (((y - x) * a) / t) - ((((y - x) * z) / t) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = (((y - x) * a) / t) - ((((y - x) * z) / t) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -4e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = (((y - x) * a) / t) - ((((y - x) * z) / t) - y)
	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 <= -4e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(Float64(Float64(Float64(y - x) * a) / t) - Float64(Float64(Float64(Float64(y - x) * z) / t) - y));
	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 <= -4e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = (((y - x) * a) / t) - ((((y - x) * z) / t) - y);
	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, -4e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] / t), $MachinePrecision] - N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 77.9%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

      1. associate-/r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 4.0%

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

   3. Simplified 4.0%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. mul-1-neg 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -4 \cdot 10^{-295} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot a}{t} - \left(\frac{\left(y - x\right) \cdot z}{t} - y\right)\\ \end{array} \]

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -4e-295) (not (<= t_1 0.0)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-4d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -4e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -4e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -4e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 77.9%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

      1. associate-/r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate-*l/ 4.0%

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

   3. Simplified 4.0%

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

   4. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -4 \cdot 10^{-295} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 4: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+63} \lor \neg \left(t \leq 2.15 \cdot 10^{+73}\right) \land t \leq 2.6 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.5e+96)
     y
     (if (<= t -9e-21)
       t_1
       (if (<= t 7.2e-144)
         (+ x (* y (/ z a)))
         (if (<= t 3.1e+48)
           t_1
           (if (or (<= t 3.1e+63) (and (not (<= t 2.15e+73)) (<= t 2.6e+179)))
             (* x (/ (- z a) t))
             y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.5e+96) {
		tmp = y;
	} else if (t <= -9e-21) {
		tmp = t_1;
	} else if (t <= 7.2e-144) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.1e+48) {
		tmp = t_1;
	} else if ((t <= 3.1e+63) || (!(t <= 2.15e+73) && (t <= 2.6e+179))) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.5d+96)) then
        tmp = y
    else if (t <= (-9d-21)) then
        tmp = t_1
    else if (t <= 7.2d-144) then
        tmp = x + (y * (z / a))
    else if (t <= 3.1d+48) then
        tmp = t_1
    else if ((t <= 3.1d+63) .or. (.not. (t <= 2.15d+73)) .and. (t <= 2.6d+179)) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.5e+96) {
		tmp = y;
	} else if (t <= -9e-21) {
		tmp = t_1;
	} else if (t <= 7.2e-144) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.1e+48) {
		tmp = t_1;
	} else if ((t <= 3.1e+63) || (!(t <= 2.15e+73) && (t <= 2.6e+179))) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.5e+96:
		tmp = y
	elif t <= -9e-21:
		tmp = t_1
	elif t <= 7.2e-144:
		tmp = x + (y * (z / a))
	elif t <= 3.1e+48:
		tmp = t_1
	elif (t <= 3.1e+63) or (not (t <= 2.15e+73) and (t <= 2.6e+179)):
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.5e+96)
		tmp = y;
	elseif (t <= -9e-21)
		tmp = t_1;
	elseif (t <= 7.2e-144)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 3.1e+48)
		tmp = t_1;
	elseif ((t <= 3.1e+63) || (!(t <= 2.15e+73) && (t <= 2.6e+179)))
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.5e+96)
		tmp = y;
	elseif (t <= -9e-21)
		tmp = t_1;
	elseif (t <= 7.2e-144)
		tmp = x + (y * (z / a));
	elseif (t <= 3.1e+48)
		tmp = t_1;
	elseif ((t <= 3.1e+63) || (~((t <= 2.15e+73)) && (t <= 2.6e+179)))
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+96], y, If[LessEqual[t, -9e-21], t$95$1, If[LessEqual[t, 7.2e-144], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+48], t$95$1, If[Or[LessEqual[t, 3.1e+63], And[N[Not[LessEqual[t, 2.15e+73]], $MachinePrecision], LessEqual[t, 2.6e+179]]], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.4999999999999999e96 or 3.1000000000000001e63 < t < 2.15000000000000007e73 or 2.6000000000000002e179 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in t around inf 55.2%

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

   if -3.4999999999999999e96 < t < -8.99999999999999936e-21 or 7.2000000000000001e-144 < t < 3.10000000000000005e48

   1. Initial program 81.8%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around 0 51.7%

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

      1. associate-/l* 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in x around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

   9. Simplified 52.8%

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

   if -8.99999999999999936e-21 < t < 7.2000000000000001e-144

   1. Initial program 92.7%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 69.1%

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

   9. Simplified 69.1%

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

   if 3.10000000000000005e48 < t < 3.1000000000000001e63 or 2.15000000000000007e73 < t < 2.6000000000000002e179

   1. Initial program 58.5%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 66.3%

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

      1. associate-*r/ 66.3%

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

      2. mul-1-neg 66.3%

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

      3. associate-*r/ 66.3%

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

      4. mul-1-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in x around inf 54.3%

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

      1. div-sub 54.4%

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

   9. Simplified 54.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+63} \lor \neg \left(t \leq 2.15 \cdot 10^{+73}\right) \land t \leq 2.6 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+62} \lor \neg \left(t \leq 1.25 \cdot 10^{+73}\right) \land t \leq 6.5 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+97)
   y
   (if (<= t -2.5e-20)
     (- x (/ (* x z) a))
     (if (<= t 3.75e-143)
       (+ x (* y (/ z a)))
       (if (<= t 8.8e+49)
         (* x (- 1.0 (/ z a)))
         (if (or (<= t 3.1e+62) (and (not (<= t 1.25e+73)) (<= t 6.5e+177)))
           (* x (/ (- z a) t))
           y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+97) {
		tmp = y;
	} else if (t <= -2.5e-20) {
		tmp = x - ((x * z) / a);
	} else if (t <= 3.75e-143) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.8e+49) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 3.1e+62) || (!(t <= 1.25e+73) && (t <= 6.5e+177))) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+97)) then
        tmp = y
    else if (t <= (-2.5d-20)) then
        tmp = x - ((x * z) / a)
    else if (t <= 3.75d-143) then
        tmp = x + (y * (z / a))
    else if (t <= 8.8d+49) then
        tmp = x * (1.0d0 - (z / a))
    else if ((t <= 3.1d+62) .or. (.not. (t <= 1.25d+73)) .and. (t <= 6.5d+177)) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+97) {
		tmp = y;
	} else if (t <= -2.5e-20) {
		tmp = x - ((x * z) / a);
	} else if (t <= 3.75e-143) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.8e+49) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 3.1e+62) || (!(t <= 1.25e+73) && (t <= 6.5e+177))) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+97:
		tmp = y
	elif t <= -2.5e-20:
		tmp = x - ((x * z) / a)
	elif t <= 3.75e-143:
		tmp = x + (y * (z / a))
	elif t <= 8.8e+49:
		tmp = x * (1.0 - (z / a))
	elif (t <= 3.1e+62) or (not (t <= 1.25e+73) and (t <= 6.5e+177)):
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+97)
		tmp = y;
	elseif (t <= -2.5e-20)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= 3.75e-143)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 8.8e+49)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((t <= 3.1e+62) || (!(t <= 1.25e+73) && (t <= 6.5e+177)))
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+97)
		tmp = y;
	elseif (t <= -2.5e-20)
		tmp = x - ((x * z) / a);
	elseif (t <= 3.75e-143)
		tmp = x + (y * (z / a));
	elseif (t <= 8.8e+49)
		tmp = x * (1.0 - (z / a));
	elseif ((t <= 3.1e+62) || (~((t <= 1.25e+73)) && (t <= 6.5e+177)))
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+97], y, If[LessEqual[t, -2.5e-20], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.75e-143], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+49], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.1e+62], And[N[Not[LessEqual[t, 1.25e+73]], $MachinePrecision], LessEqual[t, 6.5e+177]]], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.90000000000000018e97 or 3.10000000000000014e62 < t < 1.24999999999999994e73 or 6.5000000000000002e177 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in t around inf 55.2%

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

   if -1.90000000000000018e97 < t < -2.4999999999999999e-20

   1. Initial program 86.0%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

      3. associate-/l* 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in t around 0 50.9%

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

   if -2.4999999999999999e-20 < t < 3.7500000000000002e-143

   1. Initial program 92.7%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 69.1%

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

   9. Simplified 69.1%

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

   if 3.7500000000000002e-143 < t < 8.8000000000000003e49

   1. Initial program 79.1%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in t around 0 51.8%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   9. Simplified 53.9%

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

   if 8.8000000000000003e49 < t < 3.10000000000000014e62 or 1.24999999999999994e73 < t < 6.5000000000000002e177

   1. Initial program 58.5%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 66.3%

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

      1. associate-*r/ 66.3%

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

      2. mul-1-neg 66.3%

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

      3. associate-*r/ 66.3%

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

      4. mul-1-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in x around inf 54.3%

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

      1. div-sub 54.4%

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

   9. Simplified 54.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+97}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+62} \lor \neg \left(t \leq 1.25 \cdot 10^{+73}\right) \land t \leq 6.5 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+95)
   y
   (if (<= t -5.9e-21)
     (- x (/ (* x z) a))
     (if (<= t 1.76e-143)
       (+ x (* y (/ z a)))
       (if (<= t 7.5e+49)
         (* x (- 1.0 (/ z a)))
         (if (<= t 6.5e+63)
           (/ x (/ t (- z a)))
           (if (<= t 1.45e+73)
             y
             (if (<= t 2.85e+178) (* x (/ (- z a) t)) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+95) {
		tmp = y;
	} else if (t <= -5.9e-21) {
		tmp = x - ((x * z) / a);
	} else if (t <= 1.76e-143) {
		tmp = x + (y * (z / a));
	} else if (t <= 7.5e+49) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.5e+63) {
		tmp = x / (t / (z - a));
	} else if (t <= 1.45e+73) {
		tmp = y;
	} else if (t <= 2.85e+178) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+95)) then
        tmp = y
    else if (t <= (-5.9d-21)) then
        tmp = x - ((x * z) / a)
    else if (t <= 1.76d-143) then
        tmp = x + (y * (z / a))
    else if (t <= 7.5d+49) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6.5d+63) then
        tmp = x / (t / (z - a))
    else if (t <= 1.45d+73) then
        tmp = y
    else if (t <= 2.85d+178) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+95) {
		tmp = y;
	} else if (t <= -5.9e-21) {
		tmp = x - ((x * z) / a);
	} else if (t <= 1.76e-143) {
		tmp = x + (y * (z / a));
	} else if (t <= 7.5e+49) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.5e+63) {
		tmp = x / (t / (z - a));
	} else if (t <= 1.45e+73) {
		tmp = y;
	} else if (t <= 2.85e+178) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+95:
		tmp = y
	elif t <= -5.9e-21:
		tmp = x - ((x * z) / a)
	elif t <= 1.76e-143:
		tmp = x + (y * (z / a))
	elif t <= 7.5e+49:
		tmp = x * (1.0 - (z / a))
	elif t <= 6.5e+63:
		tmp = x / (t / (z - a))
	elif t <= 1.45e+73:
		tmp = y
	elif t <= 2.85e+178:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+95)
		tmp = y;
	elseif (t <= -5.9e-21)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= 1.76e-143)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 7.5e+49)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.5e+63)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (t <= 1.45e+73)
		tmp = y;
	elseif (t <= 2.85e+178)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+95)
		tmp = y;
	elseif (t <= -5.9e-21)
		tmp = x - ((x * z) / a);
	elseif (t <= 1.76e-143)
		tmp = x + (y * (z / a));
	elseif (t <= 7.5e+49)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6.5e+63)
		tmp = x / (t / (z - a));
	elseif (t <= 1.45e+73)
		tmp = y;
	elseif (t <= 2.85e+178)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+95], y, If[LessEqual[t, -5.9e-21], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.76e-143], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+49], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+63], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+73], y, If[LessEqual[t, 2.85e+178], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.9e95 or 6.49999999999999992e63 < t < 1.4500000000000001e73 or 2.85000000000000017e178 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in t around inf 55.2%

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

   if -1.9e95 < t < -5.9000000000000003e-21

   1. Initial program 86.0%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

      3. associate-/l* 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in t around 0 50.9%

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

   if -5.9000000000000003e-21 < t < 1.76000000000000005e-143

   1. Initial program 92.7%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 69.1%

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

   9. Simplified 69.1%

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

   if 1.76000000000000005e-143 < t < 7.4999999999999995e49

   1. Initial program 79.1%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in t around 0 51.8%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   9. Simplified 53.9%

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

   if 7.4999999999999995e49 < t < 6.49999999999999992e63

   1. Initial program 67.4%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 99.0%

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

      1. div-sub 99.5%

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

   9. Simplified 99.5%

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

       1. clear-num 100.0%

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

       2. un-div-inv 100.0%

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

   11. Applied egg-rr 100.0%

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

   if 1.4500000000000001e73 < t < 2.85000000000000017e178

   1. Initial program 57.1%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around inf 61.2%

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

      1. associate-*r/ 61.2%

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

      2. mul-1-neg 61.2%

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

      3. associate-*r/ 61.2%

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

      4. mul-1-neg 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in x around inf 47.6%

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

      1. div-sub 47.6%

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

   9. Simplified 47.6%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.48 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -8e+58)
     (+ x (* y (/ z a)))
     (if (<= a -1.48e-64)
       (* z (/ (- y x) (- a t)))
       (if (<= a 3e-249)
         t_1
         (if (<= a 2.1e-215)
           (/ (* x (- z)) (- a t))
           (if (<= a 3.5e-7) t_1 (* x (- 1.0 (/ z a))))))))))

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 <= -8e+58) {
		tmp = x + (y * (z / a));
	} else if (a <= -1.48e-64) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 3e-249) {
		tmp = t_1;
	} else if (a <= 2.1e-215) {
		tmp = (x * -z) / (a - t);
	} else if (a <= 3.5e-7) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-8d+58)) then
        tmp = x + (y * (z / a))
    else if (a <= (-1.48d-64)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 3d-249) then
        tmp = t_1
    else if (a <= 2.1d-215) then
        tmp = (x * -z) / (a - t)
    else if (a <= 3.5d-7) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -8e+58) {
		tmp = x + (y * (z / a));
	} else if (a <= -1.48e-64) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 3e-249) {
		tmp = t_1;
	} else if (a <= 2.1e-215) {
		tmp = (x * -z) / (a - t);
	} else if (a <= 3.5e-7) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -8e+58:
		tmp = x + (y * (z / a))
	elif a <= -1.48e-64:
		tmp = z * ((y - x) / (a - t))
	elif a <= 3e-249:
		tmp = t_1
	elif a <= 2.1e-215:
		tmp = (x * -z) / (a - t)
	elif a <= 3.5e-7:
		tmp = t_1
	else:
		tmp = x * (1.0 - (z / a))
	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 <= -8e+58)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -1.48e-64)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 3e-249)
		tmp = t_1;
	elseif (a <= 2.1e-215)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(a - t));
	elseif (a <= 3.5e-7)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	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 <= -8e+58)
		tmp = x + (y * (z / a));
	elseif (a <= -1.48e-64)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 3e-249)
		tmp = t_1;
	elseif (a <= 2.1e-215)
		tmp = (x * -z) / (a - t);
	elseif (a <= 3.5e-7)
		tmp = t_1;
	else
		tmp = x * (1.0 - (z / a));
	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, -8e+58], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.48e-64], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-249], t$95$1, If[LessEqual[a, 2.1e-215], N[(N[(x * (-z)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-7], t$95$1, N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.99999999999999955e58

   1. Initial program 68.9%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around 0 59.6%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 61.9%

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

      1. associate-*r/ 68.6%

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

   9. Simplified 68.6%

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

   if -7.99999999999999955e58 < a < -1.48e-64

   1. Initial program 79.4%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. div-sub 63.0%

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

   6. Simplified 63.0%

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

   if -1.48e-64 < a < 3.00000000000000004e-249 or 2.1e-215 < a < 3.49999999999999984e-7

   1. Initial program 69.1%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in y around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if 3.00000000000000004e-249 < a < 2.1e-215

   1. Initial program 87.4%

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

      1. associate-*l/ 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in y around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in z around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   9. Simplified 88.7%

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

   if 3.49999999999999984e-7 < a

   1. Initial program 76.7%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around 0 64.3%

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

      1. associate-/l* 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

   9. Simplified 63.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.48 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 8: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{-t}{z - t}}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ (- t) (- z t)))))
   (if (<= t -1.75e+27)
     t_1
     (if (<= t 1.75e-28)
       (+ x (* y (/ z a)))
       (if (<= t 3.6e+34)
         t_1
         (if (<= t 1.1e+47)
           (* x (- 1.0 (/ z a)))
           (if (<= t 2.25e+139) (* x (/ (- z a) t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (-t / (z - t));
	double tmp;
	if (t <= -1.75e+27) {
		tmp = t_1;
	} else if (t <= 1.75e-28) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.6e+34) {
		tmp = t_1;
	} else if (t <= 1.1e+47) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.25e+139) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (-t / (z - t))
    if (t <= (-1.75d+27)) then
        tmp = t_1
    else if (t <= 1.75d-28) then
        tmp = x + (y * (z / a))
    else if (t <= 3.6d+34) then
        tmp = t_1
    else if (t <= 1.1d+47) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2.25d+139) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (-t / (z - t));
	double tmp;
	if (t <= -1.75e+27) {
		tmp = t_1;
	} else if (t <= 1.75e-28) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.6e+34) {
		tmp = t_1;
	} else if (t <= 1.1e+47) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.25e+139) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (-t / (z - t))
	tmp = 0
	if t <= -1.75e+27:
		tmp = t_1
	elif t <= 1.75e-28:
		tmp = x + (y * (z / a))
	elif t <= 3.6e+34:
		tmp = t_1
	elif t <= 1.1e+47:
		tmp = x * (1.0 - (z / a))
	elif t <= 2.25e+139:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(Float64(-t) / Float64(z - t)))
	tmp = 0.0
	if (t <= -1.75e+27)
		tmp = t_1;
	elseif (t <= 1.75e-28)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 3.6e+34)
		tmp = t_1;
	elseif (t <= 1.1e+47)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2.25e+139)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (-t / (z - t));
	tmp = 0.0;
	if (t <= -1.75e+27)
		tmp = t_1;
	elseif (t <= 1.75e-28)
		tmp = x + (y * (z / a));
	elseif (t <= 3.6e+34)
		tmp = t_1;
	elseif (t <= 1.1e+47)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2.25e+139)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[((-t) / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+27], t$95$1, If[LessEqual[t, 1.75e-28], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+34], t$95$1, If[LessEqual[t, 1.1e+47], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+139], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7500000000000001e27 or 1.75e-28 < t < 3.6e34 or 2.25e139 < t

   1. Initial program 53.1%

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

      1. associate-*l/ 66.2%

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

      2. div-inv 66.2%

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

      3. associate-*l* 72.3%

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

   3. Applied egg-rr 72.3%

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

   4. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in a around 0 58.2%

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

      1. neg-mul-1 58.2%

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

      2. distribute-neg-frac 58.2%

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

   9. Simplified 58.2%

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

   if -1.7500000000000001e27 < t < 1.75e-28

   1. Initial program 93.1%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. associate-/l* 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around inf 62.8%

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

      1. associate-*r/ 64.2%

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

   9. Simplified 64.2%

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

   if 3.6e34 < t < 1.1e47

   1. Initial program 35.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 35.1%

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

      1. associate-/l* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   9. Simplified 100.0%

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

   if 1.1e47 < t < 2.25e139

   1. Initial program 52.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. mul-1-neg 69.3%

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

      3. associate-*r/ 69.3%

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

      4. mul-1-neg 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. div-sub 52.5%

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

   9. Simplified 52.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \end{array} \]

Alternative 9: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -5.2e+28)
     t_1
     (if (<= t 2.6e-38)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 7.4e+33)
         t_1
         (if (<= t 1.15e+47)
           (* x (- 1.0 (/ z a)))
           (if (<= t 8e+138) (* x (/ (- z a) t)) (/ y (/ (- t) (- z 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 (t <= -5.2e+28) {
		tmp = t_1;
	} else if (t <= 2.6e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7.4e+33) {
		tmp = t_1;
	} else if (t <= 1.15e+47) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8e+138) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y / (-t / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-5.2d+28)) then
        tmp = t_1
    else if (t <= 2.6d-38) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 7.4d+33) then
        tmp = t_1
    else if (t <= 1.15d+47) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 8d+138) then
        tmp = x * ((z - a) / t)
    else
        tmp = y / (-t / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5.2e+28) {
		tmp = t_1;
	} else if (t <= 2.6e-38) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7.4e+33) {
		tmp = t_1;
	} else if (t <= 1.15e+47) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8e+138) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y / (-t / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -5.2e+28:
		tmp = t_1
	elif t <= 2.6e-38:
		tmp = x + (z / (a / (y - x)))
	elif t <= 7.4e+33:
		tmp = t_1
	elif t <= 1.15e+47:
		tmp = x * (1.0 - (z / a))
	elif t <= 8e+138:
		tmp = x * ((z - a) / t)
	else:
		tmp = y / (-t / (z - 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 (t <= -5.2e+28)
		tmp = t_1;
	elseif (t <= 2.6e-38)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 7.4e+33)
		tmp = t_1;
	elseif (t <= 1.15e+47)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 8e+138)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = Float64(y / Float64(Float64(-t) / Float64(z - 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 (t <= -5.2e+28)
		tmp = t_1;
	elseif (t <= 2.6e-38)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 7.4e+33)
		tmp = t_1;
	elseif (t <= 1.15e+47)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 8e+138)
		tmp = x * ((z - a) / t);
	else
		tmp = y / (-t / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+28], t$95$1, If[LessEqual[t, 2.6e-38], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e+33], t$95$1, If[LessEqual[t, 1.15e+47], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+138], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y / N[((-t) / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.2000000000000004e28 or 2.60000000000000011e-38 < t < 7.3999999999999997e33

   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/ 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.6%

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

   6. Simplified 63.6%

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

   if -5.2000000000000004e28 < t < 2.60000000000000011e-38

   1. Initial program 93.1%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around 0 78.7%

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

      1. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

   if 7.3999999999999997e33 < t < 1.1499999999999999e47

   1. Initial program 35.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 35.1%

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

      1. associate-/l* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   9. Simplified 100.0%

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

   if 1.1499999999999999e47 < t < 8.0000000000000003e138

   1. Initial program 52.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. mul-1-neg 69.3%

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

      3. associate-*r/ 69.3%

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

      4. mul-1-neg 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. div-sub 52.5%

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

   9. Simplified 52.5%

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

   if 8.0000000000000003e138 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 57.0%

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

      2. div-inv 56.9%

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

      3. associate-*l* 63.3%

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

   3. Applied egg-rr 63.3%

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

   4. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in a around 0 72.4%

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

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \end{array} \]

Alternative 10: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a z)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.15e+23)
     t_2
     (if (<= t 3.6e-35)
       t_1
       (if (<= t 2.45e+30)
         t_2
         (if (<= t 5.8e+45)
           t_1
           (if (<= t 9.2e+138)
             (* x (/ (- z a) t))
             (/ y (/ (- t) (- z t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.15e+23) {
		tmp = t_2;
	} else if (t <= 3.6e-35) {
		tmp = t_1;
	} else if (t <= 2.45e+30) {
		tmp = t_2;
	} else if (t <= 5.8e+45) {
		tmp = t_1;
	} else if (t <= 9.2e+138) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y / (-t / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) / (a / z))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-1.15d+23)) then
        tmp = t_2
    else if (t <= 3.6d-35) then
        tmp = t_1
    else if (t <= 2.45d+30) then
        tmp = t_2
    else if (t <= 5.8d+45) then
        tmp = t_1
    else if (t <= 9.2d+138) then
        tmp = x * ((z - a) / t)
    else
        tmp = y / (-t / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.15e+23) {
		tmp = t_2;
	} else if (t <= 3.6e-35) {
		tmp = t_1;
	} else if (t <= 2.45e+30) {
		tmp = t_2;
	} else if (t <= 5.8e+45) {
		tmp = t_1;
	} else if (t <= 9.2e+138) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y / (-t / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / z))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.15e+23:
		tmp = t_2
	elif t <= 3.6e-35:
		tmp = t_1
	elif t <= 2.45e+30:
		tmp = t_2
	elif t <= 5.8e+45:
		tmp = t_1
	elif t <= 9.2e+138:
		tmp = x * ((z - a) / t)
	else:
		tmp = y / (-t / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.15e+23)
		tmp = t_2;
	elseif (t <= 3.6e-35)
		tmp = t_1;
	elseif (t <= 2.45e+30)
		tmp = t_2;
	elseif (t <= 5.8e+45)
		tmp = t_1;
	elseif (t <= 9.2e+138)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = Float64(y / Float64(Float64(-t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / z));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.15e+23)
		tmp = t_2;
	elseif (t <= 3.6e-35)
		tmp = t_1;
	elseif (t <= 2.45e+30)
		tmp = t_2;
	elseif (t <= 5.8e+45)
		tmp = t_1;
	elseif (t <= 9.2e+138)
		tmp = x * ((z - a) / t);
	else
		tmp = y / (-t / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+23], t$95$2, If[LessEqual[t, 3.6e-35], t$95$1, If[LessEqual[t, 2.45e+30], t$95$2, If[LessEqual[t, 5.8e+45], t$95$1, If[LessEqual[t, 9.2e+138], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y / N[((-t) / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e23 or 3.60000000000000019e-35 < t < 2.44999999999999992e30

   1. Initial program 60.4%

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

      1. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. div-sub 63.9%

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

   6. Simplified 63.9%

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

   if -1.15e23 < t < 3.60000000000000019e-35 or 2.44999999999999992e30 < t < 5.7999999999999994e45

   1. Initial program 91.8%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in t around 0 83.4%

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

   if 5.7999999999999994e45 < t < 9.2000000000000003e138

   1. Initial program 52.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. mul-1-neg 69.3%

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

      3. associate-*r/ 69.3%

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

      4. mul-1-neg 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. div-sub 52.5%

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

   9. Simplified 52.5%

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

   if 9.2000000000000003e138 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 57.0%

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

      2. div-inv 56.9%

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

      3. associate-*l* 63.3%

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

   3. Applied egg-rr 63.3%

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

   4. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in a around 0 72.4%

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

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z - t}}\\ \end{array} \]

Alternative 11: 36.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-245}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+104)
   x
   (if (<= a -6.2e-25)
     (/ (- x) (/ a z))
     (if (<= a -3.9e-85)
       y
       (if (<= a -2.5e-145)
         (/ y (/ a z))
         (if (<= a 1.25e-245)
           y
           (if (<= a 5.2e-156) (* x (/ z t)) (if (<= a 1.6e-6) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+104) {
		tmp = x;
	} else if (a <= -6.2e-25) {
		tmp = -x / (a / z);
	} else if (a <= -3.9e-85) {
		tmp = y;
	} else if (a <= -2.5e-145) {
		tmp = y / (a / z);
	} else if (a <= 1.25e-245) {
		tmp = y;
	} else if (a <= 5.2e-156) {
		tmp = x * (z / t);
	} else if (a <= 1.6e-6) {
		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 <= (-1.5d+104)) then
        tmp = x
    else if (a <= (-6.2d-25)) then
        tmp = -x / (a / z)
    else if (a <= (-3.9d-85)) then
        tmp = y
    else if (a <= (-2.5d-145)) then
        tmp = y / (a / z)
    else if (a <= 1.25d-245) then
        tmp = y
    else if (a <= 5.2d-156) then
        tmp = x * (z / t)
    else if (a <= 1.6d-6) 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 <= -1.5e+104) {
		tmp = x;
	} else if (a <= -6.2e-25) {
		tmp = -x / (a / z);
	} else if (a <= -3.9e-85) {
		tmp = y;
	} else if (a <= -2.5e-145) {
		tmp = y / (a / z);
	} else if (a <= 1.25e-245) {
		tmp = y;
	} else if (a <= 5.2e-156) {
		tmp = x * (z / t);
	} else if (a <= 1.6e-6) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+104:
		tmp = x
	elif a <= -6.2e-25:
		tmp = -x / (a / z)
	elif a <= -3.9e-85:
		tmp = y
	elif a <= -2.5e-145:
		tmp = y / (a / z)
	elif a <= 1.25e-245:
		tmp = y
	elif a <= 5.2e-156:
		tmp = x * (z / t)
	elif a <= 1.6e-6:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+104)
		tmp = x;
	elseif (a <= -6.2e-25)
		tmp = Float64(Float64(-x) / Float64(a / z));
	elseif (a <= -3.9e-85)
		tmp = y;
	elseif (a <= -2.5e-145)
		tmp = Float64(y / Float64(a / z));
	elseif (a <= 1.25e-245)
		tmp = y;
	elseif (a <= 5.2e-156)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.6e-6)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+104)
		tmp = x;
	elseif (a <= -6.2e-25)
		tmp = -x / (a / z);
	elseif (a <= -3.9e-85)
		tmp = y;
	elseif (a <= -2.5e-145)
		tmp = y / (a / z);
	elseif (a <= 1.25e-245)
		tmp = y;
	elseif (a <= 5.2e-156)
		tmp = x * (z / t);
	elseif (a <= 1.6e-6)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+104], x, If[LessEqual[a, -6.2e-25], N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e-85], y, If[LessEqual[a, -2.5e-145], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-245], y, If[LessEqual[a, 5.2e-156], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-6], y, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.49999999999999984e104 or 1.5999999999999999e-6 < a

   1. Initial program 73.2%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 54.8%

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

   if -1.49999999999999984e104 < a < -6.19999999999999989e-25

   1. Initial program 77.7%

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

      1. associate-*l/ 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in y around 0 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

      3. associate-/l* 49.8%

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

   6. Simplified 49.8%

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

   7. Taylor expanded in t around 0 45.6%

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

   8. Taylor expanded in z around inf 35.7%

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

      1. mul-1-neg 35.7%

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

      2. associate-/l* 32.9%

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

      3. distribute-neg-frac 32.9%

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

   10. Simplified 32.9%

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

   if -6.19999999999999989e-25 < a < -3.89999999999999988e-85 or -2.4999999999999999e-145 < a < 1.2499999999999999e-245 or 5.2000000000000002e-156 < a < 1.5999999999999999e-6

   1. Initial program 66.9%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around inf 43.6%

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

   if -3.89999999999999988e-85 < a < -2.4999999999999999e-145

   1. Initial program 84.1%

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

      1. associate-*l/ 75.6%

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

      2. div-inv 76.0%

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

      3. associate-*l* 83.4%

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

   3. Applied egg-rr 83.4%

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

   4. Taylor expanded in x around 0 68.2%

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

      1. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around 0 52.2%

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

      1. associate-/l* 52.2%

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

   9. Simplified 52.2%

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

   if 1.2499999999999999e-245 < a < 5.2000000000000002e-156

   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/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in x around inf 49.3%

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

      1. div-sub 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in z around inf 49.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-245}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 48.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -8.2e+94)
     y
     (if (<= t 3.6e-235)
       t_1
       (if (<= t 9.8e-216)
         (/ y (/ a z))
         (if (<= t 1.5e+43) t_1 (if (<= t 7e+177) (* x (/ (- z a) t)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.2e+94) {
		tmp = y;
	} else if (t <= 3.6e-235) {
		tmp = t_1;
	} else if (t <= 9.8e-216) {
		tmp = y / (a / z);
	} else if (t <= 1.5e+43) {
		tmp = t_1;
	} else if (t <= 7e+177) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-8.2d+94)) then
        tmp = y
    else if (t <= 3.6d-235) then
        tmp = t_1
    else if (t <= 9.8d-216) then
        tmp = y / (a / z)
    else if (t <= 1.5d+43) then
        tmp = t_1
    else if (t <= 7d+177) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.2e+94) {
		tmp = y;
	} else if (t <= 3.6e-235) {
		tmp = t_1;
	} else if (t <= 9.8e-216) {
		tmp = y / (a / z);
	} else if (t <= 1.5e+43) {
		tmp = t_1;
	} else if (t <= 7e+177) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -8.2e+94:
		tmp = y
	elif t <= 3.6e-235:
		tmp = t_1
	elif t <= 9.8e-216:
		tmp = y / (a / z)
	elif t <= 1.5e+43:
		tmp = t_1
	elif t <= 7e+177:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -8.2e+94)
		tmp = y;
	elseif (t <= 3.6e-235)
		tmp = t_1;
	elseif (t <= 9.8e-216)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.5e+43)
		tmp = t_1;
	elseif (t <= 7e+177)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -8.2e+94)
		tmp = y;
	elseif (t <= 3.6e-235)
		tmp = t_1;
	elseif (t <= 9.8e-216)
		tmp = y / (a / z);
	elseif (t <= 1.5e+43)
		tmp = t_1;
	elseif (t <= 7e+177)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+94], y, If[LessEqual[t, 3.6e-235], t$95$1, If[LessEqual[t, 9.8e-216], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+43], t$95$1, If[LessEqual[t, 7e+177], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.20000000000000061e94 or 6.99999999999999983e177 < t

   1. Initial program 38.6%

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

      1. associate-*l/ 56.0%

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

   3. Simplified 56.0%

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

   4. Taylor expanded in t around inf 53.9%

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

   if -8.20000000000000061e94 < t < 3.59999999999999999e-235 or 9.8000000000000003e-216 < t < 1.50000000000000008e43

   1. Initial program 87.8%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in x around inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. unsub-neg 55.3%

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

   9. Simplified 55.3%

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

   if 3.59999999999999999e-235 < t < 9.8000000000000003e-216

   1. Initial program 99.6%

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

      1. associate-*l/ 59.4%

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

      2. div-inv 59.4%

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

      3. associate-*l* 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in x around 0 99.6%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around 0 86.2%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

   if 1.50000000000000008e43 < t < 6.99999999999999983e177

   1. Initial program 56.0%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. associate-*r/ 69.0%

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

      4. mul-1-neg 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in x around inf 48.9%

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

      1. div-sub 49.0%

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

   9. Simplified 49.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -4.2e+99)
     (+ x (* y (/ z a)))
     (if (<= a 8.5e-243)
       t_1
       (if (<= a 8.5e-216)
         (/ (* x (- z)) (- a t))
         (if (<= a 3.2e-6) t_1 (* x (- 1.0 (/ z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -4.2e+99) {
		tmp = x + (y * (z / a));
	} else if (a <= 8.5e-243) {
		tmp = t_1;
	} else if (a <= 8.5e-216) {
		tmp = (x * -z) / (a - t);
	} else if (a <= 3.2e-6) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-4.2d+99)) then
        tmp = x + (y * (z / a))
    else if (a <= 8.5d-243) then
        tmp = t_1
    else if (a <= 8.5d-216) then
        tmp = (x * -z) / (a - t)
    else if (a <= 3.2d-6) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -4.2e+99) {
		tmp = x + (y * (z / a));
	} else if (a <= 8.5e-243) {
		tmp = t_1;
	} else if (a <= 8.5e-216) {
		tmp = (x * -z) / (a - t);
	} else if (a <= 3.2e-6) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -4.2e+99:
		tmp = x + (y * (z / a))
	elif a <= 8.5e-243:
		tmp = t_1
	elif a <= 8.5e-216:
		tmp = (x * -z) / (a - t)
	elif a <= 3.2e-6:
		tmp = t_1
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -4.2e+99)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 8.5e-243)
		tmp = t_1;
	elseif (a <= 8.5e-216)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(a - t));
	elseif (a <= 3.2e-6)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -4.2e+99)
		tmp = x + (y * (z / a));
	elseif (a <= 8.5e-243)
		tmp = t_1;
	elseif (a <= 8.5e-216)
		tmp = (x * -z) / (a - t);
	elseif (a <= 3.2e-6)
		tmp = t_1;
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+99], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-243], t$95$1, If[LessEqual[a, 8.5e-216], N[(N[(x * (-z)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-6], t$95$1, N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2000000000000002e99

   1. Initial program 69.8%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 73.1%

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

   9. Simplified 73.1%

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

   if -4.2000000000000002e99 < a < 8.5000000000000002e-243 or 8.50000000000000003e-216 < a < 3.1999999999999999e-6

   1. Initial program 71.1%

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

      1. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in y around inf 64.5%

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

      1. div-sub 64.5%

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

   6. Simplified 64.5%

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

   if 8.5000000000000002e-243 < a < 8.50000000000000003e-216

   1. Initial program 87.4%

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

      1. associate-*l/ 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in y around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in z around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   9. Simplified 88.7%

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

   if 3.1999999999999999e-6 < a

   1. Initial program 76.7%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around 0 64.3%

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

      1. associate-/l* 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

   9. Simplified 63.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 14: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+77} \lor \neg \left(t \leq 3.35 \cdot 10^{+177}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e+77) (not (<= t 3.35e+177)))
   (+ y (/ (- x y) (/ t z)))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e+77) || !(t <= 3.35e+177)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.1d+77)) .or. (.not. (t <= 3.35d+177))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e+77) || !(t <= 3.35e+177)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.1e+77) or not (t <= 3.35e+177):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.1e+77) || !(t <= 3.35e+177))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.1e+77) || ~((t <= 3.35e+177)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.1e+77], N[Not[LessEqual[t, 3.35e+177]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1000000000000001e77 or 3.3500000000000002e177 < t

   1. Initial program 40.1%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in t around inf 69.4%

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

      1. associate-*r/ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. associate-*r/ 69.4%

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

      4. mul-1-neg 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in a around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. *-commutative 69.5%

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

      3. unsub-neg 69.5%

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

      4. associate-/l* 76.8%

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

   9. Simplified 76.8%

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

   if -4.1000000000000001e77 < t < 3.3500000000000002e177

   1. Initial program 84.3%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+77} \lor \neg \left(t \leq 3.35 \cdot 10^{+177}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 15: 48.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -4.8e+95)
     y
     (if (<= t 5e-235)
       t_1
       (if (<= t 1.55e-214) (/ y (/ a z)) (if (<= t 7e+139) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -4.8e+95) {
		tmp = y;
	} else if (t <= 5e-235) {
		tmp = t_1;
	} else if (t <= 1.55e-214) {
		tmp = y / (a / z);
	} else if (t <= 7e+139) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-4.8d+95)) then
        tmp = y
    else if (t <= 5d-235) then
        tmp = t_1
    else if (t <= 1.55d-214) then
        tmp = y / (a / z)
    else if (t <= 7d+139) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -4.8e+95) {
		tmp = y;
	} else if (t <= 5e-235) {
		tmp = t_1;
	} else if (t <= 1.55e-214) {
		tmp = y / (a / z);
	} else if (t <= 7e+139) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -4.8e+95:
		tmp = y
	elif t <= 5e-235:
		tmp = t_1
	elif t <= 1.55e-214:
		tmp = y / (a / z)
	elif t <= 7e+139:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -4.8e+95)
		tmp = y;
	elseif (t <= 5e-235)
		tmp = t_1;
	elseif (t <= 1.55e-214)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 7e+139)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -4.8e+95)
		tmp = y;
	elseif (t <= 5e-235)
		tmp = t_1;
	elseif (t <= 1.55e-214)
		tmp = y / (a / z);
	elseif (t <= 7e+139)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+95], y, If[LessEqual[t, 5e-235], t$95$1, If[LessEqual[t, 1.55e-214], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+139], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000001e95 or 6.99999999999999957e139 < t

   1. Initial program 41.1%

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

      1. associate-*l/ 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -4.8000000000000001e95 < t < 4.9999999999999998e-235 or 1.55000000000000002e-214 < t < 6.99999999999999957e139

   1. Initial program 83.6%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in t around 0 61.6%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   9. Simplified 51.9%

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

   if 4.9999999999999998e-235 < t < 1.55000000000000002e-214

   1. Initial program 99.6%

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

      1. associate-*l/ 59.4%

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

      2. div-inv 59.4%

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

      3. associate-*l* 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in x around 0 99.6%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around 0 86.2%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+33} \lor \neg \left(t \leq 3.6 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+33) (not (<= t 3.6e-29)))
   (+ y (/ (- x y) (/ t z)))
   (+ x (* (- z t) (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+33) || !(t <= 3.6e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((z - t) * ((y - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d+33)) .or. (.not. (t <= 3.6d-29))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x + ((z - t) * ((y - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+33) || !(t <= 3.6e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((z - t) * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+33) or not (t <= 3.6e-29):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + ((z - t) * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+33) || !(t <= 3.6e-29))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+33) || ~((t <= 3.6e-29)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + ((z - t) * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+33], N[Not[LessEqual[t, 3.6e-29]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.9999999999999996e33 or 3.59999999999999974e-29 < t

   1. Initial program 51.6%

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

      1. associate-*l/ 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. mul-1-neg 66.0%

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

      3. associate-*r/ 66.0%

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

      4. mul-1-neg 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in a around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. unsub-neg 63.5%

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

      4. associate-/l* 69.5%

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

   9. Simplified 69.5%

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

   if -7.9999999999999996e33 < t < 3.59999999999999974e-29

   1. Initial program 93.2%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 84.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+33} \lor \neg \left(t \leq 3.6 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \end{array} \]

Alternative 17: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+34} \lor \neg \left(t \leq 6.2 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e+34) (not (<= t 6.2e-29)))
   (+ y (/ (- x y) (/ t z)))
   (- x (/ (- x y) (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e+34) || !(t <= 6.2e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((x - y) / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.75d+34)) .or. (.not. (t <= 6.2d-29))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x - ((x - y) / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e+34) || !(t <= 6.2e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - ((x - y) / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.75e+34) or not (t <= 6.2e-29):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x - ((x - y) / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.75e+34) || !(t <= 6.2e-29))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.75e+34) || ~((t <= 6.2e-29)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x - ((x - y) / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.75e+34], N[Not[LessEqual[t, 6.2e-29]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.74999999999999999e34 or 6.20000000000000052e-29 < t

   1. Initial program 51.6%

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

      1. associate-*l/ 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. mul-1-neg 66.0%

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

      3. associate-*r/ 66.0%

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

      4. mul-1-neg 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in a around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. unsub-neg 63.5%

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

      4. associate-/l* 69.5%

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

   9. Simplified 69.5%

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

   if -1.74999999999999999e34 < t < 6.20000000000000052e-29

   1. Initial program 93.2%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 82.1%

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

      1. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+34} \lor \neg \left(t \leq 6.2 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 18: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e+34)
   (+ y (/ (- x y) (/ t z)))
   (if (<= t 2.2e-28)
     (- x (/ (- x y) (/ a (- z t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+34) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 2.2e-28) {
		tmp = x - ((x - y) / (a / (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) :: tmp
    if (t <= (-1.6d+34)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 2.2d-28) then
        tmp = x - ((x - y) / (a / (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 tmp;
	if (t <= -1.6e+34) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 2.2e-28) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e+34:
		tmp = y + ((x - y) / (t / z))
	elif t <= 2.2e-28:
		tmp = x - ((x - y) / (a / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e+34)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 2.2e-28)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / 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)
	tmp = 0.0;
	if (t <= -1.6e+34)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 2.2e-28)
		tmp = x - ((x - y) / (a / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e+34], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-28], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / 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 3 regimes

2. if t < -1.5999999999999999e34

   1. Initial program 54.8%

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

      1. associate-*l/ 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in t around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. mul-1-neg 64.8%

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

      3. associate-*r/ 64.8%

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

      4. mul-1-neg 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in a around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. *-commutative 63.0%

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

      3. unsub-neg 63.0%

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

      4. associate-/l* 71.5%

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

   9. Simplified 71.5%

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

   if -1.5999999999999999e34 < t < 2.19999999999999996e-28

   1. Initial program 93.2%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 82.1%

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

      1. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

   if 2.19999999999999996e-28 < t

   1. Initial program 49.0%

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

      1. associate-*l/ 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. distribute-lft-out-- 67.0%

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

      3. div-sub 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. distribute-rgt-out-- 68.5%

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

   6. Simplified 68.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 19: 36.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-250}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.15e+102)
   x
   (if (<= a -2.85e-145)
     (* z (/ y a))
     (if (<= a 6.8e-250)
       y
       (if (<= a 5.1e-155) (* x (/ z t)) (if (<= a 4e-7) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e+102) {
		tmp = x;
	} else if (a <= -2.85e-145) {
		tmp = z * (y / a);
	} else if (a <= 6.8e-250) {
		tmp = y;
	} else if (a <= 5.1e-155) {
		tmp = x * (z / t);
	} else if (a <= 4e-7) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.15d+102)) then
        tmp = x
    else if (a <= (-2.85d-145)) then
        tmp = z * (y / a)
    else if (a <= 6.8d-250) then
        tmp = y
    else if (a <= 5.1d-155) then
        tmp = x * (z / t)
    else if (a <= 4d-7) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e+102) {
		tmp = x;
	} else if (a <= -2.85e-145) {
		tmp = z * (y / a);
	} else if (a <= 6.8e-250) {
		tmp = y;
	} else if (a <= 5.1e-155) {
		tmp = x * (z / t);
	} else if (a <= 4e-7) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.15e+102:
		tmp = x
	elif a <= -2.85e-145:
		tmp = z * (y / a)
	elif a <= 6.8e-250:
		tmp = y
	elif a <= 5.1e-155:
		tmp = x * (z / t)
	elif a <= 4e-7:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.15e+102)
		tmp = x;
	elseif (a <= -2.85e-145)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 6.8e-250)
		tmp = y;
	elseif (a <= 5.1e-155)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 4e-7)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.15e+102)
		tmp = x;
	elseif (a <= -2.85e-145)
		tmp = z * (y / a);
	elseif (a <= 6.8e-250)
		tmp = y;
	elseif (a <= 5.1e-155)
		tmp = x * (z / t);
	elseif (a <= 4e-7)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.15e+102], x, If[LessEqual[a, -2.85e-145], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-250], y, If[LessEqual[a, 5.1e-155], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-7], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.15e102 or 3.9999999999999998e-7 < a

   1. Initial program 73.2%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 54.8%

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

   if -2.15e102 < a < -2.85000000000000016e-145

   1. Initial program 79.3%

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

      1. associate-*l/ 74.2%

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

      2. div-inv 74.3%

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

      3. associate-*l* 80.8%

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

   3. Applied egg-rr 80.8%

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

   4. Taylor expanded in x around 0 53.4%

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

      1. associate-/l* 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in t around 0 28.2%

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

      1. associate-/l* 29.8%

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

      2. associate-/r/ 28.1%

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

   9. Simplified 28.1%

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

   if -2.85000000000000016e-145 < a < 6.79999999999999987e-250 or 5.0999999999999996e-155 < a < 3.9999999999999998e-7

   1. Initial program 64.4%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in t around inf 44.3%

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

   if 6.79999999999999987e-250 < a < 5.0999999999999996e-155

   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/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in x around inf 49.3%

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

      1. div-sub 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in z around inf 49.3%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-250}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 36.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-247}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+102)
   x
   (if (<= a -5.5e-146)
     (/ y (/ a z))
     (if (<= a 3.1e-247)
       y
       (if (<= a 2e-155) (* x (/ z t)) (if (<= a 2.2e-6) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+102) {
		tmp = x;
	} else if (a <= -5.5e-146) {
		tmp = y / (a / z);
	} else if (a <= 3.1e-247) {
		tmp = y;
	} else if (a <= 2e-155) {
		tmp = x * (z / t);
	} else if (a <= 2.2e-6) {
		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+102)) then
        tmp = x
    else if (a <= (-5.5d-146)) then
        tmp = y / (a / z)
    else if (a <= 3.1d-247) then
        tmp = y
    else if (a <= 2d-155) then
        tmp = x * (z / t)
    else if (a <= 2.2d-6) 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+102) {
		tmp = x;
	} else if (a <= -5.5e-146) {
		tmp = y / (a / z);
	} else if (a <= 3.1e-247) {
		tmp = y;
	} else if (a <= 2e-155) {
		tmp = x * (z / t);
	} else if (a <= 2.2e-6) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+102:
		tmp = x
	elif a <= -5.5e-146:
		tmp = y / (a / z)
	elif a <= 3.1e-247:
		tmp = y
	elif a <= 2e-155:
		tmp = x * (z / t)
	elif a <= 2.2e-6:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+102)
		tmp = x;
	elseif (a <= -5.5e-146)
		tmp = Float64(y / Float64(a / z));
	elseif (a <= 3.1e-247)
		tmp = y;
	elseif (a <= 2e-155)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 2.2e-6)
		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+102)
		tmp = x;
	elseif (a <= -5.5e-146)
		tmp = y / (a / z);
	elseif (a <= 3.1e-247)
		tmp = y;
	elseif (a <= 2e-155)
		tmp = x * (z / t);
	elseif (a <= 2.2e-6)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+102], x, If[LessEqual[a, -5.5e-146], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-247], y, If[LessEqual[a, 2e-155], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-6], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1499999999999999e102 or 2.2000000000000001e-6 < a

   1. Initial program 73.2%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 54.8%

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

   if -1.1499999999999999e102 < a < -5.49999999999999998e-146

   1. Initial program 79.3%

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

      1. associate-*l/ 74.2%

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

      2. div-inv 74.3%

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

      3. associate-*l* 80.8%

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

   3. Applied egg-rr 80.8%

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

   4. Taylor expanded in x around 0 53.4%

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

      1. associate-/l* 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in t around 0 28.2%

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

      1. associate-/l* 29.8%

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

   9. Simplified 29.8%

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

   if -5.49999999999999998e-146 < a < 3.10000000000000015e-247 or 2.00000000000000003e-155 < a < 2.2000000000000001e-6

   1. Initial program 64.4%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in t around inf 44.3%

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

   if 3.10000000000000015e-247 < a < 2.00000000000000003e-155

   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/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in x around inf 49.3%

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

      1. div-sub 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in z around inf 49.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-247}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -0.076:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-137}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -0.076)
     t_1
     (if (<= x -2.2e-137) y (if (<= x 8.8e-100) (* z (/ y (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -0.076) {
		tmp = t_1;
	} else if (x <= -2.2e-137) {
		tmp = y;
	} else if (x <= 8.8e-100) {
		tmp = z * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-0.076d0)) then
        tmp = t_1
    else if (x <= (-2.2d-137)) then
        tmp = y
    else if (x <= 8.8d-100) then
        tmp = z * (y / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -0.076) {
		tmp = t_1;
	} else if (x <= -2.2e-137) {
		tmp = y;
	} else if (x <= 8.8e-100) {
		tmp = z * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -0.076:
		tmp = t_1
	elif x <= -2.2e-137:
		tmp = y
	elif x <= 8.8e-100:
		tmp = z * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -0.076)
		tmp = t_1;
	elseif (x <= -2.2e-137)
		tmp = y;
	elseif (x <= 8.8e-100)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -0.076)
		tmp = t_1;
	elseif (x <= -2.2e-137)
		tmp = y;
	elseif (x <= 8.8e-100)
		tmp = z * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.076], t$95$1, If[LessEqual[x, -2.2e-137], y, If[LessEqual[x, 8.8e-100], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0759999999999999981 or 8.79999999999999957e-100 < x

   1. Initial program 63.4%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in t around 0 54.6%

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

      1. associate-/l* 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

   9. Simplified 56.4%

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

   if -0.0759999999999999981 < x < -2.2000000000000001e-137

   1. Initial program 68.4%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in t around inf 48.1%

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

   if -2.2000000000000001e-137 < x < 8.79999999999999957e-100

   1. Initial program 90.1%

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

      1. associate-*l/ 83.4%

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

      2. div-inv 83.3%

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

      3. associate-*l* 93.0%

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

   3. Applied egg-rr 93.0%

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

   4. Taylor expanded in x around 0 74.4%

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

      1. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in z around inf 42.2%

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

      1. associate-*l/ 42.4%

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

      2. *-commutative 42.4%

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

   9. Simplified 42.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.076:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-137}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 22: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 5.2 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+27) (not (<= t 5.2e-29)))
   (+ y (/ (- x y) (/ t z)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+27) || !(t <= 5.2e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d+27)) .or. (.not. (t <= 5.2d-29))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+27) || !(t <= 5.2e-29)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+27) or not (t <= 5.2e-29):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+27) || !(t <= 5.2e-29))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+27) || ~((t <= 5.2e-29)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+27], N[Not[LessEqual[t, 5.2e-29]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000001e27 or 5.2000000000000004e-29 < t

   1. Initial program 52.6%

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

      1. associate-*l/ 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in t around inf 64.5%

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

      1. associate-*r/ 64.5%

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

      2. mul-1-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. mul-1-neg 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in a around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. *-commutative 62.1%

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

      3. unsub-neg 62.1%

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

      4. associate-/l* 68.0%

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

   9. Simplified 68.0%

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

   if -4.0000000000000001e27 < t < 5.2000000000000004e-29

   1. Initial program 93.1%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

      1. associate-/r/ 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in t around 0 82.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 5.2 \cdot 10^{-29}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 23: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.95e+24)
   (- x (/ x (/ (- a t) z)))
   (if (<= x 1.05e-83) (* y (/ (- z t) (- a t))) (+ x (/ (- y x) (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.95e+24) {
		tmp = x - (x / ((a - t) / z));
	} else if (x <= 1.05e-83) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.95d+24)) then
        tmp = x - (x / ((a - t) / z))
    else if (x <= 1.05d-83) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.95e+24) {
		tmp = x - (x / ((a - t) / z));
	} else if (x <= 1.05e-83) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.95e+24:
		tmp = x - (x / ((a - t) / z))
	elif x <= 1.05e-83:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.95e+24)
		tmp = Float64(x - Float64(x / Float64(Float64(a - t) / z)));
	elseif (x <= 1.05e-83)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.95e+24)
		tmp = x - (x / ((a - t) / z));
	elseif (x <= 1.05e-83)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.95e+24], N[(x - N[(x / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-83], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9499999999999999e24

   1. Initial program 56.6%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in y around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

      3. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in z around inf 65.7%

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

   if -1.9499999999999999e24 < x < 1.0499999999999999e-83

   1. Initial program 83.8%

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

      1. associate-*l/ 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in y around inf 76.1%

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

      1. div-sub 76.1%

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

   6. Simplified 76.1%

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

   if 1.0499999999999999e-83 < x

   1. Initial program 67.6%

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

      1. associate-*l/ 81.5%

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

   3. Simplified 81.5%

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

      1. associate-/r/ 82.9%

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

   5. Applied egg-rr 82.9%

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

   6. Taylor expanded in t around 0 65.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 24: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-254}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+99)
   x
   (if (<= a 2.65e-254)
     y
     (if (<= a 7.5e-155) (* x (/ z t)) (if (<= a 4.4e-7) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+99) {
		tmp = x;
	} else if (a <= 2.65e-254) {
		tmp = y;
	} else if (a <= 7.5e-155) {
		tmp = x * (z / t);
	} else if (a <= 4.4e-7) {
		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 <= (-1.3d+99)) then
        tmp = x
    else if (a <= 2.65d-254) then
        tmp = y
    else if (a <= 7.5d-155) then
        tmp = x * (z / t)
    else if (a <= 4.4d-7) 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 <= -1.3e+99) {
		tmp = x;
	} else if (a <= 2.65e-254) {
		tmp = y;
	} else if (a <= 7.5e-155) {
		tmp = x * (z / t);
	} else if (a <= 4.4e-7) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+99:
		tmp = x
	elif a <= 2.65e-254:
		tmp = y
	elif a <= 7.5e-155:
		tmp = x * (z / t)
	elif a <= 4.4e-7:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+99)
		tmp = x;
	elseif (a <= 2.65e-254)
		tmp = y;
	elseif (a <= 7.5e-155)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 4.4e-7)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+99)
		tmp = x;
	elseif (a <= 2.65e-254)
		tmp = y;
	elseif (a <= 7.5e-155)
		tmp = x * (z / t);
	elseif (a <= 4.4e-7)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+99], x, If[LessEqual[a, 2.65e-254], y, If[LessEqual[a, 7.5e-155], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-7], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e99 or 4.4000000000000002e-7 < a

   1. Initial program 73.7%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 53.9%

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

   if -1.3e99 < a < 2.65000000000000018e-254 or 7.5000000000000006e-155 < a < 4.4000000000000002e-7

   1. Initial program 70.9%

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

      1. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around inf 34.1%

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

   if 2.65000000000000018e-254 < a < 7.5000000000000006e-155

   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/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in x around inf 49.3%

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

      1. div-sub 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in z around inf 49.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-254}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+100) x (if (<= a 2.5e-6) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+100) {
		tmp = x;
	} else if (a <= 2.5e-6) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+100)) then
        tmp = x
    else if (a <= 2.5d-6) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+100) {
		tmp = x;
	} else if (a <= 2.5e-6) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+100:
		tmp = x
	elif a <= 2.5e-6:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+100)
		tmp = x;
	elseif (a <= 2.5e-6)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+100)
		tmp = x;
	elseif (a <= 2.5e-6)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+100], x, If[LessEqual[a, 2.5e-6], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000002e100 or 2.5000000000000002e-6 < a

   1. Initial program 73.7%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 53.9%

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

   if -1.00000000000000002e100 < a < 2.5000000000000002e-6

   1. Initial program 72.0%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in t around inf 31.1%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 25.0% 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 72.7%

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

   1. associate-*l/ 80.4%

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

3. Simplified 80.4%

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

4. Taylor expanded in a around inf 27.1%

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

5. Final simplification 27.1%

   \[\leadsto x \]

Developer target: 87.0% 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 2023315 
(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))))