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

Percentage Accurate: 67.7% → 90.8%

Time: 29.6s

Alternatives: 27

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.7% 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: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_1 -5e-290)
     (fma (- y x) (/ (- z t) (- a t)) x)
     (if (<= t_1 0.0)
       (+ y (/ (- (* z (- x y)) (* a (- x y))) t))
       (+ x (pow (/ (/ (- a t) (- z t)) (- y x)) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -5e-290) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else if (t_1 <= 0.0) {
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t);
	} else {
		tmp = x + pow((((a - t) / (z - t)) / (y - x)), -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-290)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z * Float64(x - y)) - Float64(a * Float64(x - y))) / t));
	else
		tmp = Float64(x + (Float64(Float64(Float64(a - t) / Float64(z - t)) / Float64(y - x)) ^ -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-290], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[Power[N[(N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000001e-290

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 92.9%

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

      3. fma-define 92.9%

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

   3. Simplified 92.9%

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

   if -5.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 5.0%

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

   3. Taylor expanded in t around -inf 99.9%

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

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

   1. Initial program 73.1%

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

      1. clear-num 73.0%

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

      2. inv-pow 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/r* 91.8%

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

   4. Applied egg-rr 91.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (or (<= t_1 -5e-290) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (- (* z (- x y)) (* a (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(z * Float64(x - y)) - Float64(a * Float64(x - y))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000001e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

   if -5.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 5.0%

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

   3. Taylor expanded in t around -inf 99.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-290} \lor \neg \left(x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -70:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -2.15e+151)
     (+ x (/ y (/ a z)))
     (if (<= a -4.1e+145)
       t_1
       (if (<= a -1.6e+64)
         (* x (- 1.0 (/ z a)))
         (if (<= a -70.0)
           (* t (/ y (- t a)))
           (if (<= a -5.7e-11)
             t_2
             (if (<= a -5.6e-228)
               t_1
               (if (<= a 6.8e-203)
                 (* z (/ (- x y) t))
                 (if (<= a 3e-36)
                   t_1
                   (if (<= a 7e+64) (* z (/ (- y x) a)) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.15e+151) {
		tmp = x + (y / (a / z));
	} else if (a <= -4.1e+145) {
		tmp = t_1;
	} else if (a <= -1.6e+64) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -70.0) {
		tmp = t * (y / (t - a));
	} else if (a <= -5.7e-11) {
		tmp = t_2;
	} else if (a <= -5.6e-228) {
		tmp = t_1;
	} else if (a <= 6.8e-203) {
		tmp = z * ((x - y) / t);
	} else if (a <= 3e-36) {
		tmp = t_1;
	} else if (a <= 7e+64) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y * (z / a))
    if (a <= (-2.15d+151)) then
        tmp = x + (y / (a / z))
    else if (a <= (-4.1d+145)) then
        tmp = t_1
    else if (a <= (-1.6d+64)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= (-70.0d0)) then
        tmp = t * (y / (t - a))
    else if (a <= (-5.7d-11)) then
        tmp = t_2
    else if (a <= (-5.6d-228)) then
        tmp = t_1
    else if (a <= 6.8d-203) then
        tmp = z * ((x - y) / t)
    else if (a <= 3d-36) then
        tmp = t_1
    else if (a <= 7d+64) then
        tmp = z * ((y - x) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.15e+151) {
		tmp = x + (y / (a / z));
	} else if (a <= -4.1e+145) {
		tmp = t_1;
	} else if (a <= -1.6e+64) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -70.0) {
		tmp = t * (y / (t - a));
	} else if (a <= -5.7e-11) {
		tmp = t_2;
	} else if (a <= -5.6e-228) {
		tmp = t_1;
	} else if (a <= 6.8e-203) {
		tmp = z * ((x - y) / t);
	} else if (a <= 3e-36) {
		tmp = t_1;
	} else if (a <= 7e+64) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -2.15e+151:
		tmp = x + (y / (a / z))
	elif a <= -4.1e+145:
		tmp = t_1
	elif a <= -1.6e+64:
		tmp = x * (1.0 - (z / a))
	elif a <= -70.0:
		tmp = t * (y / (t - a))
	elif a <= -5.7e-11:
		tmp = t_2
	elif a <= -5.6e-228:
		tmp = t_1
	elif a <= 6.8e-203:
		tmp = z * ((x - y) / t)
	elif a <= 3e-36:
		tmp = t_1
	elif a <= 7e+64:
		tmp = z * ((y - x) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -2.15e+151)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= -4.1e+145)
		tmp = t_1;
	elseif (a <= -1.6e+64)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= -70.0)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	elseif (a <= -5.7e-11)
		tmp = t_2;
	elseif (a <= -5.6e-228)
		tmp = t_1;
	elseif (a <= 6.8e-203)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 3e-36)
		tmp = t_1;
	elseif (a <= 7e+64)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -2.15e+151)
		tmp = x + (y / (a / z));
	elseif (a <= -4.1e+145)
		tmp = t_1;
	elseif (a <= -1.6e+64)
		tmp = x * (1.0 - (z / a));
	elseif (a <= -70.0)
		tmp = t * (y / (t - a));
	elseif (a <= -5.7e-11)
		tmp = t_2;
	elseif (a <= -5.6e-228)
		tmp = t_1;
	elseif (a <= 6.8e-203)
		tmp = z * ((x - y) / t);
	elseif (a <= 3e-36)
		tmp = t_1;
	elseif (a <= 7e+64)
		tmp = z * ((y - x) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+151], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e+145], t$95$1, If[LessEqual[a, -1.6e+64], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -70.0], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.7e-11], t$95$2, If[LessEqual[a, -5.6e-228], t$95$1, If[LessEqual[a, 6.8e-203], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-36], t$95$1, If[LessEqual[a, 7e+64], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.14999999999999991e151

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.1%

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

   10. Applied egg-rr 73.1%

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

   if -2.14999999999999991e151 < a < -4.1000000000000001e145 or -5.6999999999999997e-11 < a < -5.6000000000000005e-228 or 6.7999999999999998e-203 < a < 3.0000000000000002e-36

   1. Initial program 72.1%

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

      1. clear-num 72.0%

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

      2. inv-pow 72.0%

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

      3. *-commutative 72.0%

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

      4. associate-/r* 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

      2. clear-num 85.3%

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

      3. div-sub 80.9%

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

   6. Applied egg-rr 80.9%

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

      1. div-sub 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in x around 0 57.5%

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

       1. *-commutative 57.5%

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

       2. associate-/l* 60.8%

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

   11. Simplified 60.8%

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

   12. Taylor expanded in a around 0 49.1%

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

       1. mul-1-neg 49.1%

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

       2. associate-/l* 60.4%

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

       3. distribute-rgt-neg-in 60.4%

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

   14. Simplified 60.4%

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

   if -4.1000000000000001e145 < a < -1.60000000000000009e64

   1. Initial program 77.9%

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

   3. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in t around 0 60.9%

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

   if -1.60000000000000009e64 < a < -70

   1. Initial program 56.8%

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

      1. clear-num 56.3%

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

      2. inv-pow 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-/r* 74.1%

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

   4. Applied egg-rr 74.1%

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

      1. unpow-1 74.1%

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

      2. clear-num 74.4%

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

      3. div-sub 74.4%

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

   6. Applied egg-rr 74.4%

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

      1. div-sub 74.4%

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

   8. Simplified 74.4%

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

   9. Taylor expanded in x around 0 56.9%

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

       1. *-commutative 56.9%

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

       2. associate-/l* 62.0%

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

   11. Simplified 62.0%

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

   12. Taylor expanded in z around 0 46.7%

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

       1. mul-1-neg 46.7%

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

       2. associate-/l* 51.8%

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

       3. distribute-lft-neg-out 51.8%

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

       4. *-commutative 51.8%

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

   14. Simplified 51.8%

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

   if -70 < a < -5.6999999999999997e-11 or 6.9999999999999997e64 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around 0 63.8%

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

      1. associate-/l* 71.9%

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

   8. Simplified 71.9%

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

   if -5.6000000000000005e-228 < a < 6.7999999999999998e-203

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 63.5%

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

   4. Taylor expanded in a around 0 63.0%

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

      1. distribute-lft-out-- 63.0%

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

      2. div-sub 65.8%

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

      3. associate-*r/ 65.8%

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

      4. neg-mul-1 65.8%

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

   6. Simplified 65.8%

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

   if 3.0000000000000002e-36 < a < 6.9999999999999997e64

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 68.7%

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

   4. Taylor expanded in a around inf 63.4%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -70:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -65:\\ \;\;\;\;\frac{y \cdot t}{t - a}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{+64}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -2.15e+151)
     (+ x (/ y (/ a z)))
     (if (<= a -4.1e+145)
       t_1
       (if (<= a -4.4e+79)
         (* x (- 1.0 (/ z a)))
         (if (<= a -65.0)
           (/ (* y t) (- t a))
           (if (<= a -1.02e-14)
             t_2
             (if (<= a -5.1e-228)
               t_1
               (if (<= a 1.22e-203)
                 (* z (/ (- x y) t))
                 (if (<= a 4.4e-36)
                   t_1
                   (if (<= a 1e+64) (* z (/ (- y x) a)) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.15e+151) {
		tmp = x + (y / (a / z));
	} else if (a <= -4.1e+145) {
		tmp = t_1;
	} else if (a <= -4.4e+79) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -65.0) {
		tmp = (y * t) / (t - a);
	} else if (a <= -1.02e-14) {
		tmp = t_2;
	} else if (a <= -5.1e-228) {
		tmp = t_1;
	} else if (a <= 1.22e-203) {
		tmp = z * ((x - y) / t);
	} else if (a <= 4.4e-36) {
		tmp = t_1;
	} else if (a <= 1e+64) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y * (z / a))
    if (a <= (-2.15d+151)) then
        tmp = x + (y / (a / z))
    else if (a <= (-4.1d+145)) then
        tmp = t_1
    else if (a <= (-4.4d+79)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= (-65.0d0)) then
        tmp = (y * t) / (t - a)
    else if (a <= (-1.02d-14)) then
        tmp = t_2
    else if (a <= (-5.1d-228)) then
        tmp = t_1
    else if (a <= 1.22d-203) then
        tmp = z * ((x - y) / t)
    else if (a <= 4.4d-36) then
        tmp = t_1
    else if (a <= 1d+64) then
        tmp = z * ((y - x) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.15e+151) {
		tmp = x + (y / (a / z));
	} else if (a <= -4.1e+145) {
		tmp = t_1;
	} else if (a <= -4.4e+79) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= -65.0) {
		tmp = (y * t) / (t - a);
	} else if (a <= -1.02e-14) {
		tmp = t_2;
	} else if (a <= -5.1e-228) {
		tmp = t_1;
	} else if (a <= 1.22e-203) {
		tmp = z * ((x - y) / t);
	} else if (a <= 4.4e-36) {
		tmp = t_1;
	} else if (a <= 1e+64) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -2.15e+151:
		tmp = x + (y / (a / z))
	elif a <= -4.1e+145:
		tmp = t_1
	elif a <= -4.4e+79:
		tmp = x * (1.0 - (z / a))
	elif a <= -65.0:
		tmp = (y * t) / (t - a)
	elif a <= -1.02e-14:
		tmp = t_2
	elif a <= -5.1e-228:
		tmp = t_1
	elif a <= 1.22e-203:
		tmp = z * ((x - y) / t)
	elif a <= 4.4e-36:
		tmp = t_1
	elif a <= 1e+64:
		tmp = z * ((y - x) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -2.15e+151)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= -4.1e+145)
		tmp = t_1;
	elseif (a <= -4.4e+79)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= -65.0)
		tmp = Float64(Float64(y * t) / Float64(t - a));
	elseif (a <= -1.02e-14)
		tmp = t_2;
	elseif (a <= -5.1e-228)
		tmp = t_1;
	elseif (a <= 1.22e-203)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 4.4e-36)
		tmp = t_1;
	elseif (a <= 1e+64)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -2.15e+151)
		tmp = x + (y / (a / z));
	elseif (a <= -4.1e+145)
		tmp = t_1;
	elseif (a <= -4.4e+79)
		tmp = x * (1.0 - (z / a));
	elseif (a <= -65.0)
		tmp = (y * t) / (t - a);
	elseif (a <= -1.02e-14)
		tmp = t_2;
	elseif (a <= -5.1e-228)
		tmp = t_1;
	elseif (a <= 1.22e-203)
		tmp = z * ((x - y) / t);
	elseif (a <= 4.4e-36)
		tmp = t_1;
	elseif (a <= 1e+64)
		tmp = z * ((y - x) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+151], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e+145], t$95$1, If[LessEqual[a, -4.4e+79], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -65.0], N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.02e-14], t$95$2, If[LessEqual[a, -5.1e-228], t$95$1, If[LessEqual[a, 1.22e-203], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-36], t$95$1, If[LessEqual[a, 1e+64], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.14999999999999991e151

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.1%

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

   10. Applied egg-rr 73.1%

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

   if -2.14999999999999991e151 < a < -4.1000000000000001e145 or -1.02e-14 < a < -5.1000000000000002e-228 or 1.21999999999999995e-203 < a < 4.3999999999999999e-36

   1. Initial program 72.1%

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

      1. clear-num 72.0%

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

      2. inv-pow 72.0%

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

      3. *-commutative 72.0%

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

      4. associate-/r* 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

      2. clear-num 85.3%

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

      3. div-sub 80.9%

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

   6. Applied egg-rr 80.9%

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

      1. div-sub 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in x around 0 57.5%

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

       1. *-commutative 57.5%

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

       2. associate-/l* 60.8%

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

   11. Simplified 60.8%

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

   12. Taylor expanded in a around 0 49.1%

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

       1. mul-1-neg 49.1%

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

       2. associate-/l* 60.4%

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

       3. distribute-rgt-neg-in 60.4%

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

   14. Simplified 60.4%

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

   if -4.1000000000000001e145 < a < -4.3999999999999998e79

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around 0 66.4%

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

   if -4.3999999999999998e79 < a < -65

   1. Initial program 59.7%

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

      1. clear-num 59.3%

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

      2. inv-pow 59.3%

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

      3. *-commutative 59.3%

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

      4. associate-/r* 80.3%

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

   4. Applied egg-rr 80.3%

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

      1. unpow-1 80.3%

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

      2. clear-num 80.8%

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

      3. div-sub 80.8%

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

   6. Applied egg-rr 80.8%

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

      1. div-sub 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in x around 0 59.3%

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

       1. *-commutative 59.3%

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

       2. associate-/l* 47.2%

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

   11. Simplified 47.2%

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

   12. Taylor expanded in z around 0 51.8%

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

       1. mul-1-neg 51.8%

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

       2. distribute-neg-frac 51.8%

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

       3. *-commutative 51.8%

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

       4. distribute-rgt-neg-out 51.8%

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

   14. Simplified 51.8%

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

   if -65 < a < -1.02e-14 or 1.00000000000000002e64 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around 0 63.8%

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

      1. associate-/l* 71.9%

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

   8. Simplified 71.9%

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

   if -5.1000000000000002e-228 < a < 1.21999999999999995e-203

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 63.5%

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

   4. Taylor expanded in a around 0 63.0%

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

      1. distribute-lft-out-- 63.0%

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

      2. div-sub 65.8%

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

      3. associate-*r/ 65.8%

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

      4. neg-mul-1 65.8%

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

   6. Simplified 65.8%

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

   if 4.3999999999999999e-36 < a < 1.00000000000000002e64

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 68.7%

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

   4. Taylor expanded in a around inf 63.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -65:\\ \;\;\;\;\frac{y \cdot t}{t - a}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 10^{+64}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (or (<= t_1 -5e-290) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (- (* z (- x y)) (* a (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((x - y) * (t - z)) / (a - t))
    if ((t_1 <= (-5d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (((z * (x - y)) - (a * (x - y))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-290) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z * Float64(x - y)) - Float64(a * Float64(x - y))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-290) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((z * (x - y)) - (a * (x - y))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000001e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.4%

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

      1. clear-num 73.3%

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

      2. inv-pow 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-/r* 92.3%

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

   4. Applied egg-rr 92.3%

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

      1. unpow-1 92.3%

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

      2. clear-num 92.3%

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

      3. div-sub 88.6%

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

   6. Applied egg-rr 88.6%

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

      1. div-sub 92.3%

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

   8. Simplified 92.3%

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

   if -5.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 5.0%

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

   3. Taylor expanded in t around -inf 99.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-290} \lor \neg \left(x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right) - a \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-69} \lor \neg \left(t \leq 6.8 \cdot 10^{-34}\right) \land t \leq 3 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -1.3e+103)
     t_1
     (if (<= t -2.4e+49)
       (* x (/ (- z a) t))
       (if (<= t -3.7e-21)
         t_1
         (if (<= t 1.15e-203)
           t_2
           (if (<= t 7e-176)
             (* x (- 1.0 (/ z a)))
             (if (or (<= t 8.8e-69) (and (not (<= t 6.8e-34)) (<= t 3e+16)))
               t_2
               t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.3e+103) {
		tmp = t_1;
	} else if (t <= -2.4e+49) {
		tmp = x * ((z - a) / t);
	} else if (t <= -3.7e-21) {
		tmp = t_1;
	} else if (t <= 1.15e-203) {
		tmp = t_2;
	} else if (t <= 7e-176) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 8.8e-69) || (!(t <= 6.8e-34) && (t <= 3e+16))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y * (z / a))
    if (t <= (-1.3d+103)) then
        tmp = t_1
    else if (t <= (-2.4d+49)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-3.7d-21)) then
        tmp = t_1
    else if (t <= 1.15d-203) then
        tmp = t_2
    else if (t <= 7d-176) then
        tmp = x * (1.0d0 - (z / a))
    else if ((t <= 8.8d-69) .or. (.not. (t <= 6.8d-34)) .and. (t <= 3d+16)) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.3e+103) {
		tmp = t_1;
	} else if (t <= -2.4e+49) {
		tmp = x * ((z - a) / t);
	} else if (t <= -3.7e-21) {
		tmp = t_1;
	} else if (t <= 1.15e-203) {
		tmp = t_2;
	} else if (t <= 7e-176) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 8.8e-69) || (!(t <= 6.8e-34) && (t <= 3e+16))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -1.3e+103:
		tmp = t_1
	elif t <= -2.4e+49:
		tmp = x * ((z - a) / t)
	elif t <= -3.7e-21:
		tmp = t_1
	elif t <= 1.15e-203:
		tmp = t_2
	elif t <= 7e-176:
		tmp = x * (1.0 - (z / a))
	elif (t <= 8.8e-69) or (not (t <= 6.8e-34) and (t <= 3e+16)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.3e+103)
		tmp = t_1;
	elseif (t <= -2.4e+49)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -3.7e-21)
		tmp = t_1;
	elseif (t <= 1.15e-203)
		tmp = t_2;
	elseif (t <= 7e-176)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((t <= 8.8e-69) || (!(t <= 6.8e-34) && (t <= 3e+16)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.3e+103)
		tmp = t_1;
	elseif (t <= -2.4e+49)
		tmp = x * ((z - a) / t);
	elseif (t <= -3.7e-21)
		tmp = t_1;
	elseif (t <= 1.15e-203)
		tmp = t_2;
	elseif (t <= 7e-176)
		tmp = x * (1.0 - (z / a));
	elseif ((t <= 8.8e-69) || (~((t <= 6.8e-34)) && (t <= 3e+16)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+103], t$95$1, If[LessEqual[t, -2.4e+49], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e-21], t$95$1, If[LessEqual[t, 1.15e-203], t$95$2, If[LessEqual[t, 7e-176], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.8e-69], And[N[Not[LessEqual[t, 6.8e-34]], $MachinePrecision], LessEqual[t, 3e+16]]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3000000000000001e103 or -2.4e49 < t < -3.7000000000000002e-21 or 8.8000000000000001e-69 < t < 6.8000000000000001e-34 or 3e16 < t

   1. Initial program 52.9%

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

      1. clear-num 52.8%

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

      2. inv-pow 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-/r* 80.8%

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

   4. Applied egg-rr 80.8%

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

      1. unpow-1 80.8%

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

      2. clear-num 80.9%

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

      3. div-sub 80.1%

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

   6. Applied egg-rr 80.1%

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

      1. div-sub 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in x around 0 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-/l* 55.3%

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

   11. Simplified 55.3%

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

   12. Taylor expanded in a around 0 43.1%

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

       1. mul-1-neg 43.1%

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

       2. associate-/l* 60.5%

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

       3. distribute-rgt-neg-in 60.5%

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

   14. Simplified 60.5%

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

   if -1.3000000000000001e103 < t < -2.4e49

   1. Initial program 55.5%

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

   3. Taylor expanded in x around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. unsub-neg 32.7%

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

   5. Simplified 32.7%

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

   6. Taylor expanded in t around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. sub-neg 62.3%

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

      3. mul-1-neg 62.3%

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

   8. Simplified 62.3%

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

   if -3.7000000000000002e-21 < t < 1.14999999999999996e-203 or 7e-176 < t < 8.8000000000000001e-69 or 6.8000000000000001e-34 < t < 3e16

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0 58.7%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

   if 1.14999999999999996e-203 < t < 7e-176

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 70.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-69} \lor \neg \left(t \leq 6.8 \cdot 10^{-34}\right) \land t \leq 3 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (or (<= t_1 -5e-290) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((x - y) * (t - z)) / (a - t))
    if ((t_1 <= (-5d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-290) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-290) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-290) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000001e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.4%

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

      1. clear-num 73.3%

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

      2. inv-pow 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-/r* 92.3%

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

   4. Applied egg-rr 92.3%

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

      1. unpow-1 92.3%

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

      2. clear-num 92.3%

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

      3. div-sub 88.6%

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

   6. Applied egg-rr 88.6%

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

      1. div-sub 92.3%

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

   8. Simplified 92.3%

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

   if -5.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 5.0%

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

   3. Taylor expanded in t around inf 99.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. 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. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. associate-*r/ 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

      10. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. *-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-290} \lor \neg \left(x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -1.06e+101)
     y
     (if (<= t -4.4e+49)
       (/ (* x z) t)
       (if (<= t -2.65e-11)
         (+ x y)
         (if (<= t 1.8e-202)
           t_1
           (if (<= t 3.15e-176)
             (* x (- 1.0 (/ z a)))
             (if (<= t 4.7e+30) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.06e+101) {
		tmp = y;
	} else if (t <= -4.4e+49) {
		tmp = (x * z) / t;
	} else if (t <= -2.65e-11) {
		tmp = x + y;
	} else if (t <= 1.8e-202) {
		tmp = t_1;
	} else if (t <= 3.15e-176) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4.7e+30) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-1.06d+101)) then
        tmp = y
    else if (t <= (-4.4d+49)) then
        tmp = (x * z) / t
    else if (t <= (-2.65d-11)) then
        tmp = x + y
    else if (t <= 1.8d-202) then
        tmp = t_1
    else if (t <= 3.15d-176) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 4.7d+30) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.06e+101) {
		tmp = y;
	} else if (t <= -4.4e+49) {
		tmp = (x * z) / t;
	} else if (t <= -2.65e-11) {
		tmp = x + y;
	} else if (t <= 1.8e-202) {
		tmp = t_1;
	} else if (t <= 3.15e-176) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4.7e+30) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -1.06e+101:
		tmp = y
	elif t <= -4.4e+49:
		tmp = (x * z) / t
	elif t <= -2.65e-11:
		tmp = x + y
	elif t <= 1.8e-202:
		tmp = t_1
	elif t <= 3.15e-176:
		tmp = x * (1.0 - (z / a))
	elif t <= 4.7e+30:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.06e+101)
		tmp = y;
	elseif (t <= -4.4e+49)
		tmp = Float64(Float64(x * z) / t);
	elseif (t <= -2.65e-11)
		tmp = Float64(x + y);
	elseif (t <= 1.8e-202)
		tmp = t_1;
	elseif (t <= 3.15e-176)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 4.7e+30)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.06e+101)
		tmp = y;
	elseif (t <= -4.4e+49)
		tmp = (x * z) / t;
	elseif (t <= -2.65e-11)
		tmp = x + y;
	elseif (t <= 1.8e-202)
		tmp = t_1;
	elseif (t <= 3.15e-176)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 4.7e+30)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+101], y, If[LessEqual[t, -4.4e+49], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -2.65e-11], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.8e-202], t$95$1, If[LessEqual[t, 3.15e-176], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+30], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.06e101

   1. Initial program 42.9%

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

   3. Taylor expanded in t around inf 68.0%

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

   if -1.06e101 < t < -4.4000000000000001e49

   1. Initial program 51.9%

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

   3. Taylor expanded in x around inf 35.2%

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

      1. mul-1-neg 35.2%

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

      2. unsub-neg 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in a around 0 51.1%

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

   if -4.4000000000000001e49 < t < -2.6499999999999999e-11 or 4.6999999999999999e30 < t

   1. Initial program 55.0%

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

   3. Taylor expanded in y around inf 49.8%

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

      1. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{x + y} \]
   7. Step-by-step derivation

      1. +-commutative 45.5%

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

   8. Simplified 45.5%

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

   if -2.6499999999999999e-11 < t < 1.8000000000000001e-202 or 3.15000000000000006e-176 < t < 4.6999999999999999e30

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around 0 55.1%

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

      1. associate-/l* 62.1%

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

   8. Simplified 62.1%

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

   if 1.8000000000000001e-202 < t < 3.15000000000000006e-176

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 70.9%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+30}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+102}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -1.65e+102)
     y
     (if (<= t -2.2e+49)
       (* x (/ (- z a) t))
       (if (<= t -1.35e-12)
         (+ x y)
         (if (<= t 9.5e-204)
           t_1
           (if (<= t 7.8e-176)
             (* x (- 1.0 (/ z a)))
             (if (<= t 1.45e+36) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.65e+102) {
		tmp = y;
	} else if (t <= -2.2e+49) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.35e-12) {
		tmp = x + y;
	} else if (t <= 9.5e-204) {
		tmp = t_1;
	} else if (t <= 7.8e-176) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.45e+36) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-1.65d+102)) then
        tmp = y
    else if (t <= (-2.2d+49)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.35d-12)) then
        tmp = x + y
    else if (t <= 9.5d-204) then
        tmp = t_1
    else if (t <= 7.8d-176) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.45d+36) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.65e+102) {
		tmp = y;
	} else if (t <= -2.2e+49) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.35e-12) {
		tmp = x + y;
	} else if (t <= 9.5e-204) {
		tmp = t_1;
	} else if (t <= 7.8e-176) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.45e+36) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -1.65e+102:
		tmp = y
	elif t <= -2.2e+49:
		tmp = x * ((z - a) / t)
	elif t <= -1.35e-12:
		tmp = x + y
	elif t <= 9.5e-204:
		tmp = t_1
	elif t <= 7.8e-176:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.45e+36:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.65e+102)
		tmp = y;
	elseif (t <= -2.2e+49)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.35e-12)
		tmp = Float64(x + y);
	elseif (t <= 9.5e-204)
		tmp = t_1;
	elseif (t <= 7.8e-176)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.45e+36)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.65e+102)
		tmp = y;
	elseif (t <= -2.2e+49)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.35e-12)
		tmp = x + y;
	elseif (t <= 9.5e-204)
		tmp = t_1;
	elseif (t <= 7.8e-176)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.45e+36)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+102], y, If[LessEqual[t, -2.2e+49], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-12], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.5e-204], t$95$1, If[LessEqual[t, 7.8e-176], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+36], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.64999999999999999e102

   1. Initial program 42.9%

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

   3. Taylor expanded in t around inf 68.0%

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

   if -1.64999999999999999e102 < t < -2.2000000000000001e49

   1. Initial program 55.5%

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

   3. Taylor expanded in x around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. unsub-neg 32.7%

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

   5. Simplified 32.7%

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

   6. Taylor expanded in t around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. sub-neg 62.3%

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

      3. mul-1-neg 62.3%

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

   8. Simplified 62.3%

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

   if -2.2000000000000001e49 < t < -1.3499999999999999e-12 or 1.45e36 < t

   1. Initial program 54.5%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in t around inf 46.0%

      \[\leadsto \color{blue}{x + y} \]
   7. Step-by-step derivation

      1. +-commutative 46.0%

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

   8. Simplified 46.0%

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

   if -1.3499999999999999e-12 < t < 9.50000000000000063e-204 or 7.7999999999999994e-176 < t < 1.45e36

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around 0 55.1%

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

      1. associate-/l* 62.1%

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

   8. Simplified 62.1%

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

   if 9.50000000000000063e-204 < t < 7.7999999999999994e-176

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 70.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+102}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-204}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{-12}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= t -9.6e-12)
     (+ y (* (/ z t) (- x y)))
     (if (<= t -4.4e-198)
       t_1
       (if (<= t 4.6e-262)
         (+ x (* (- x y) (/ (- t z) a)))
         (if (<= t 1.2e-62)
           t_1
           (if (<= t 1.25e+159)
             (+ x (* (- z t) (/ y (- a t))))
             (+ y (* x (/ (- z a) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -9.6e-12) {
		tmp = y + ((z / t) * (x - y));
	} else if (t <= -4.4e-198) {
		tmp = t_1;
	} else if (t <= 4.6e-262) {
		tmp = x + ((x - y) * ((t - z) / a));
	} else if (t <= 1.2e-62) {
		tmp = t_1;
	} else if (t <= 1.25e+159) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / (a - t)))
    if (t <= (-9.6d-12)) then
        tmp = y + ((z / t) * (x - y))
    else if (t <= (-4.4d-198)) then
        tmp = t_1
    else if (t <= 4.6d-262) then
        tmp = x + ((x - y) * ((t - z) / a))
    else if (t <= 1.2d-62) then
        tmp = t_1
    else if (t <= 1.25d+159) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -9.6e-12) {
		tmp = y + ((z / t) * (x - y));
	} else if (t <= -4.4e-198) {
		tmp = t_1;
	} else if (t <= 4.6e-262) {
		tmp = x + ((x - y) * ((t - z) / a));
	} else if (t <= 1.2e-62) {
		tmp = t_1;
	} else if (t <= 1.25e+159) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if t <= -9.6e-12:
		tmp = y + ((z / t) * (x - y))
	elif t <= -4.4e-198:
		tmp = t_1
	elif t <= 4.6e-262:
		tmp = x + ((x - y) * ((t - z) / a))
	elif t <= 1.2e-62:
		tmp = t_1
	elif t <= 1.25e+159:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (t <= -9.6e-12)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	elseif (t <= -4.4e-198)
		tmp = t_1;
	elseif (t <= 4.6e-262)
		tmp = Float64(x + Float64(Float64(x - y) * Float64(Float64(t - z) / a)));
	elseif (t <= 1.2e-62)
		tmp = t_1;
	elseif (t <= 1.25e+159)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (t <= -9.6e-12)
		tmp = y + ((z / t) * (x - y));
	elseif (t <= -4.4e-198)
		tmp = t_1;
	elseif (t <= 4.6e-262)
		tmp = x + ((x - y) * ((t - z) / a));
	elseif (t <= 1.2e-62)
		tmp = t_1;
	elseif (t <= 1.25e+159)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e-12], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-198], t$95$1, If[LessEqual[t, 4.6e-262], N[(x + N[(N[(x - y), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-62], t$95$1, If[LessEqual[t, 1.25e+159], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.59999999999999948e-12

   1. Initial program 54.4%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. associate-*r/ 72.1%

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

      3. associate-*r/ 72.1%

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

      4. div-sub 72.1%

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

      5. distribute-lft-out-- 72.1%

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

      6. associate-*r/ 72.1%

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

      7. mul-1-neg 72.1%

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

      8. unsub-neg 72.1%

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

      9. distribute-rgt-out-- 72.2%

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

      10. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in z around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   if -9.59999999999999948e-12 < t < -4.4000000000000001e-198 or 4.6000000000000002e-262 < t < 1.19999999999999992e-62

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   if -4.4000000000000001e-198 < t < 4.6000000000000002e-262

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf 85.3%

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

      1. associate-/l* 96.6%

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

   5. Simplified 96.6%

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

   if 1.19999999999999992e-62 < t < 1.25000000000000001e159

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   if 1.25000000000000001e159 < t

   1. Initial program 33.2%

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

   3. Taylor expanded in t around inf 53.6%

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

      1. associate--l+ 53.6%

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

      2. associate-*r/ 53.6%

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

      3. associate-*r/ 53.6%

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

      4. div-sub 53.6%

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

      5. distribute-lft-out-- 53.6%

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

      6. associate-*r/ 53.6%

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

      7. mul-1-neg 53.6%

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

      8. unsub-neg 53.6%

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

      9. distribute-rgt-out-- 53.6%

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

      10. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. associate-/l* 74.8%

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

      3. distribute-lft-neg-out 74.8%

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

      4. *-commutative 74.8%

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

   8. Simplified 74.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-12}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ t_2 := y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+155}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t)))))
        (t_2 (+ y (* (/ (- z a) t) (- x y)))))
   (if (<= t -2.35e-11)
     t_2
     (if (<= t -3.4e-199)
       t_1
       (if (<= t 4.8e-262)
         (+ x (* (- x y) (/ (- t z) a)))
         (if (<= t 1.86e-62)
           t_1
           (if (<= t 3.8e+155) (+ x (* (- z t) (/ y (- a t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = y + (((z - a) / t) * (x - y));
	double tmp;
	if (t <= -2.35e-11) {
		tmp = t_2;
	} else if (t <= -3.4e-199) {
		tmp = t_1;
	} else if (t <= 4.8e-262) {
		tmp = x + ((x - y) * ((t - z) / a));
	} else if (t <= 1.86e-62) {
		tmp = t_1;
	} else if (t <= 3.8e+155) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / (a - t)))
    t_2 = y + (((z - a) / t) * (x - y))
    if (t <= (-2.35d-11)) then
        tmp = t_2
    else if (t <= (-3.4d-199)) then
        tmp = t_1
    else if (t <= 4.8d-262) then
        tmp = x + ((x - y) * ((t - z) / a))
    else if (t <= 1.86d-62) then
        tmp = t_1
    else if (t <= 3.8d+155) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = y + (((z - a) / t) * (x - y));
	double tmp;
	if (t <= -2.35e-11) {
		tmp = t_2;
	} else if (t <= -3.4e-199) {
		tmp = t_1;
	} else if (t <= 4.8e-262) {
		tmp = x + ((x - y) * ((t - z) / a));
	} else if (t <= 1.86e-62) {
		tmp = t_1;
	} else if (t <= 3.8e+155) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	t_2 = y + (((z - a) / t) * (x - y))
	tmp = 0
	if t <= -2.35e-11:
		tmp = t_2
	elif t <= -3.4e-199:
		tmp = t_1
	elif t <= 4.8e-262:
		tmp = x + ((x - y) * ((t - z) / a))
	elif t <= 1.86e-62:
		tmp = t_1
	elif t <= 3.8e+155:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(Float64(z - a) / t) * Float64(x - y)))
	tmp = 0.0
	if (t <= -2.35e-11)
		tmp = t_2;
	elseif (t <= -3.4e-199)
		tmp = t_1;
	elseif (t <= 4.8e-262)
		tmp = Float64(x + Float64(Float64(x - y) * Float64(Float64(t - z) / a)));
	elseif (t <= 1.86e-62)
		tmp = t_1;
	elseif (t <= 3.8e+155)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	t_2 = y + (((z - a) / t) * (x - y));
	tmp = 0.0;
	if (t <= -2.35e-11)
		tmp = t_2;
	elseif (t <= -3.4e-199)
		tmp = t_1;
	elseif (t <= 4.8e-262)
		tmp = x + ((x - y) * ((t - z) / a));
	elseif (t <= 1.86e-62)
		tmp = t_1;
	elseif (t <= 3.8e+155)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e-11], t$95$2, If[LessEqual[t, -3.4e-199], t$95$1, If[LessEqual[t, 4.8e-262], N[(x + N[(N[(x - y), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.86e-62], t$95$1, If[LessEqual[t, 3.8e+155], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.34999999999999996e-11 or 3.8000000000000001e155 < t

   1. Initial program 46.5%

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

   3. Taylor expanded in t around inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. associate-*r/ 65.2%

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

      3. associate-*r/ 65.2%

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

      4. div-sub 65.2%

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

      5. distribute-lft-out-- 65.2%

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

      6. associate-*r/ 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. distribute-rgt-out-- 65.3%

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

      10. associate-/l* 82.6%

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

   5. Simplified 82.6%

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

   if -2.34999999999999996e-11 < t < -3.40000000000000006e-199 or 4.8000000000000001e-262 < t < 1.86000000000000001e-62

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   if -3.40000000000000006e-199 < t < 4.8000000000000001e-262

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf 85.3%

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

      1. associate-/l* 96.6%

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

   5. Simplified 96.6%

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

   if 1.86000000000000001e-62 < t < 3.8000000000000001e155

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+155}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ t_2 := x \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+121}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+233}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))) (t_2 (* x (/ z t))))
   (if (<= z -5.2e+230)
     t_2
     (if (<= z -3.3e+41)
       t_1
       (if (<= z -1.52e-235)
         (+ x y)
         (if (<= z 2.06e-72)
           y
           (if (<= z 3.6e+121) (+ x y) (if (<= z 1.5e+233) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double t_2 = x * (z / t);
	double tmp;
	if (z <= -5.2e+230) {
		tmp = t_2;
	} else if (z <= -3.3e+41) {
		tmp = t_1;
	} else if (z <= -1.52e-235) {
		tmp = x + y;
	} else if (z <= 2.06e-72) {
		tmp = y;
	} else if (z <= 3.6e+121) {
		tmp = x + y;
	} else if (z <= 1.5e+233) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (y / a)
    t_2 = x * (z / t)
    if (z <= (-5.2d+230)) then
        tmp = t_2
    else if (z <= (-3.3d+41)) then
        tmp = t_1
    else if (z <= (-1.52d-235)) then
        tmp = x + y
    else if (z <= 2.06d-72) then
        tmp = y
    else if (z <= 3.6d+121) then
        tmp = x + y
    else if (z <= 1.5d+233) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double t_2 = x * (z / t);
	double tmp;
	if (z <= -5.2e+230) {
		tmp = t_2;
	} else if (z <= -3.3e+41) {
		tmp = t_1;
	} else if (z <= -1.52e-235) {
		tmp = x + y;
	} else if (z <= 2.06e-72) {
		tmp = y;
	} else if (z <= 3.6e+121) {
		tmp = x + y;
	} else if (z <= 1.5e+233) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	t_2 = x * (z / t)
	tmp = 0
	if z <= -5.2e+230:
		tmp = t_2
	elif z <= -3.3e+41:
		tmp = t_1
	elif z <= -1.52e-235:
		tmp = x + y
	elif z <= 2.06e-72:
		tmp = y
	elif z <= 3.6e+121:
		tmp = x + y
	elif z <= 1.5e+233:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	t_2 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (z <= -5.2e+230)
		tmp = t_2;
	elseif (z <= -3.3e+41)
		tmp = t_1;
	elseif (z <= -1.52e-235)
		tmp = Float64(x + y);
	elseif (z <= 2.06e-72)
		tmp = y;
	elseif (z <= 3.6e+121)
		tmp = Float64(x + y);
	elseif (z <= 1.5e+233)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	t_2 = x * (z / t);
	tmp = 0.0;
	if (z <= -5.2e+230)
		tmp = t_2;
	elseif (z <= -3.3e+41)
		tmp = t_1;
	elseif (z <= -1.52e-235)
		tmp = x + y;
	elseif (z <= 2.06e-72)
		tmp = y;
	elseif (z <= 3.6e+121)
		tmp = x + y;
	elseif (z <= 1.5e+233)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+230], t$95$2, If[LessEqual[z, -3.3e+41], t$95$1, If[LessEqual[z, -1.52e-235], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.06e-72], y, If[LessEqual[z, 3.6e+121], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.5e+233], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999997e230 or 1.50000000000000007e233 < z

   1. Initial program 61.7%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in a around 0 54.3%

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

   if -5.1999999999999997e230 < z < -3.3e41 or 3.59999999999999981e121 < z < 1.50000000000000007e233

   1. Initial program 74.5%

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

      1. clear-num 74.5%

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

      2. inv-pow 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-/r* 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. unpow-1 96.9%

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

      2. clear-num 96.9%

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

      3. div-sub 92.4%

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

   6. Applied egg-rr 92.4%

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

      1. div-sub 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in x around 0 43.6%

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

       1. *-commutative 43.6%

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

       2. associate-/l* 53.6%

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

   11. Simplified 53.6%

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

   12. Taylor expanded in t around 0 32.2%

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

       1. *-commutative 32.2%

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

       2. associate-*r/ 41.9%

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

   14. Simplified 41.9%

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

   if -3.3e41 < z < -1.52e-235 or 2.06e-72 < z < 3.59999999999999981e121

   1. Initial program 76.7%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in t around inf 49.2%

      \[\leadsto \color{blue}{x + y} \]
   7. Step-by-step derivation

      1. +-commutative 49.2%

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

   8. Simplified 49.2%

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

   if -1.52e-235 < z < 2.06e-72

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf 46.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-235}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+121}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-46}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -2.1e+158)
     (- x (* y (/ (- t z) a)))
     (if (<= a -3.9e+145)
       t_1
       (if (<= a -9.2e+73)
         t_2
         (if (<= a -3.45e-37)
           t_1
           (if (<= a 2.55e-46) (+ y (* z (/ (- x y) t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -2.1e+158) {
		tmp = x - (y * ((t - z) / a));
	} else if (a <= -3.9e+145) {
		tmp = t_1;
	} else if (a <= -9.2e+73) {
		tmp = t_2;
	} else if (a <= -3.45e-37) {
		tmp = t_1;
	} else if (a <= 2.55e-46) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((y - x) / (a / z))
    if (a <= (-2.1d+158)) then
        tmp = x - (y * ((t - z) / a))
    else if (a <= (-3.9d+145)) then
        tmp = t_1
    else if (a <= (-9.2d+73)) then
        tmp = t_2
    else if (a <= (-3.45d-37)) then
        tmp = t_1
    else if (a <= 2.55d-46) then
        tmp = y + (z * ((x - y) / t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -2.1e+158) {
		tmp = x - (y * ((t - z) / a));
	} else if (a <= -3.9e+145) {
		tmp = t_1;
	} else if (a <= -9.2e+73) {
		tmp = t_2;
	} else if (a <= -3.45e-37) {
		tmp = t_1;
	} else if (a <= 2.55e-46) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -2.1e+158:
		tmp = x - (y * ((t - z) / a))
	elif a <= -3.9e+145:
		tmp = t_1
	elif a <= -9.2e+73:
		tmp = t_2
	elif a <= -3.45e-37:
		tmp = t_1
	elif a <= 2.55e-46:
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.1e+158)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (a <= -3.9e+145)
		tmp = t_1;
	elseif (a <= -9.2e+73)
		tmp = t_2;
	elseif (a <= -3.45e-37)
		tmp = t_1;
	elseif (a <= 2.55e-46)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -2.1e+158)
		tmp = x - (y * ((t - z) / a));
	elseif (a <= -3.9e+145)
		tmp = t_1;
	elseif (a <= -9.2e+73)
		tmp = t_2;
	elseif (a <= -3.45e-37)
		tmp = t_1;
	elseif (a <= 2.55e-46)
		tmp = y + (z * ((x - y) / t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+158], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e+145], t$95$1, If[LessEqual[a, -9.2e+73], t$95$2, If[LessEqual[a, -3.45e-37], t$95$1, If[LessEqual[a, 2.55e-46], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.0999999999999999e158

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around inf 73.3%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -2.0999999999999999e158 < a < -3.8999999999999998e145 or -9.199999999999999e73 < a < -3.4499999999999999e-37

   1. Initial program 67.7%

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

      1. clear-num 67.6%

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

      2. inv-pow 67.6%

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

      3. *-commutative 67.6%

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

      4. associate-/r* 84.0%

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

   4. Applied egg-rr 84.0%

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

   5. Taylor expanded in x around 0 58.0%

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

      1. associate-*r/ 77.4%

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

   7. Simplified 77.4%

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

   if -3.8999999999999998e145 < a < -9.199999999999999e73 or 2.5499999999999999e-46 < a

   1. Initial program 70.5%

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

      1. clear-num 70.4%

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

      2. inv-pow 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-/r* 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. unpow-1 96.9%

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

      2. clear-num 96.8%

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

      3. div-sub 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. div-sub 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in t around 0 73.2%

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

   if -3.4499999999999999e-37 < a < 2.5499999999999999e-46

   1. Initial program 70.1%

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

   3. Taylor expanded in t around inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. associate-*r/ 78.1%

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

      3. associate-*r/ 78.1%

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

      4. div-sub 79.8%

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

      5. distribute-lft-out-- 79.8%

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

      6. associate-*r/ 79.8%

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

      7. mul-1-neg 79.8%

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

      8. unsub-neg 79.8%

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

      9. distribute-rgt-out-- 79.8%

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

      10. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 77.0%

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

      1. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-46}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-46}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -2.1e+158)
     (- x (* y (/ (- t z) a)))
     (if (<= a -3.6e+145)
       t_1
       (if (<= a -2.25e+77)
         t_2
         (if (<= a -7.6e-56)
           t_1
           (if (<= a 1.7e-46) (+ y (* (/ z t) (- x y))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -2.1e+158) {
		tmp = x - (y * ((t - z) / a));
	} else if (a <= -3.6e+145) {
		tmp = t_1;
	} else if (a <= -2.25e+77) {
		tmp = t_2;
	} else if (a <= -7.6e-56) {
		tmp = t_1;
	} else if (a <= 1.7e-46) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((y - x) / (a / z))
    if (a <= (-2.1d+158)) then
        tmp = x - (y * ((t - z) / a))
    else if (a <= (-3.6d+145)) then
        tmp = t_1
    else if (a <= (-2.25d+77)) then
        tmp = t_2
    else if (a <= (-7.6d-56)) then
        tmp = t_1
    else if (a <= 1.7d-46) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -2.1e+158) {
		tmp = x - (y * ((t - z) / a));
	} else if (a <= -3.6e+145) {
		tmp = t_1;
	} else if (a <= -2.25e+77) {
		tmp = t_2;
	} else if (a <= -7.6e-56) {
		tmp = t_1;
	} else if (a <= 1.7e-46) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -2.1e+158:
		tmp = x - (y * ((t - z) / a))
	elif a <= -3.6e+145:
		tmp = t_1
	elif a <= -2.25e+77:
		tmp = t_2
	elif a <= -7.6e-56:
		tmp = t_1
	elif a <= 1.7e-46:
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.1e+158)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (a <= -3.6e+145)
		tmp = t_1;
	elseif (a <= -2.25e+77)
		tmp = t_2;
	elseif (a <= -7.6e-56)
		tmp = t_1;
	elseif (a <= 1.7e-46)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -2.1e+158)
		tmp = x - (y * ((t - z) / a));
	elseif (a <= -3.6e+145)
		tmp = t_1;
	elseif (a <= -2.25e+77)
		tmp = t_2;
	elseif (a <= -7.6e-56)
		tmp = t_1;
	elseif (a <= 1.7e-46)
		tmp = y + ((z / t) * (x - y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+158], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e+145], t$95$1, If[LessEqual[a, -2.25e+77], t$95$2, If[LessEqual[a, -7.6e-56], t$95$1, If[LessEqual[a, 1.7e-46], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.0999999999999999e158

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around inf 73.3%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -2.0999999999999999e158 < a < -3.59999999999999974e145 or -2.25000000000000012e77 < a < -7.6000000000000004e-56

   1. Initial program 67.7%

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

      1. clear-num 67.6%

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

      2. inv-pow 67.6%

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

      3. *-commutative 67.6%

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

      4. associate-/r* 84.0%

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

   4. Applied egg-rr 84.0%

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

   5. Taylor expanded in x around 0 58.0%

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

      1. associate-*r/ 77.4%

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

   7. Simplified 77.4%

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

   if -3.59999999999999974e145 < a < -2.25000000000000012e77 or 1.69999999999999998e-46 < a

   1. Initial program 70.5%

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

      1. clear-num 70.4%

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

      2. inv-pow 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-/r* 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. unpow-1 96.9%

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

      2. clear-num 96.8%

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

      3. div-sub 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. div-sub 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in t around 0 73.2%

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

   if -7.6000000000000004e-56 < a < 1.69999999999999998e-46

   1. Initial program 70.1%

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

   3. Taylor expanded in t around inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. associate-*r/ 78.1%

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

      3. associate-*r/ 78.1%

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

      4. div-sub 79.8%

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

      5. distribute-lft-out-- 79.8%

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

      6. associate-*r/ 79.8%

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

      7. mul-1-neg 79.8%

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

      8. unsub-neg 79.8%

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

      9. distribute-rgt-out-- 79.8%

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

      10. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-46}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-221}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -3.4e-47)
     t_1
     (if (<= x -7.5e-214)
       y
       (if (<= x 1.18e-287)
         (* z (/ y (- a t)))
         (if (<= x 2.6e-221)
           y
           (if (<= x 2.4e-17) (* y (/ (- z t) a)) 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 <= -3.4e-47) {
		tmp = t_1;
	} else if (x <= -7.5e-214) {
		tmp = y;
	} else if (x <= 1.18e-287) {
		tmp = z * (y / (a - t));
	} else if (x <= 2.6e-221) {
		tmp = y;
	} else if (x <= 2.4e-17) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-3.4d-47)) then
        tmp = t_1
    else if (x <= (-7.5d-214)) then
        tmp = y
    else if (x <= 1.18d-287) then
        tmp = z * (y / (a - t))
    else if (x <= 2.6d-221) then
        tmp = y
    else if (x <= 2.4d-17) then
        tmp = y * ((z - t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -3.4e-47) {
		tmp = t_1;
	} else if (x <= -7.5e-214) {
		tmp = y;
	} else if (x <= 1.18e-287) {
		tmp = z * (y / (a - t));
	} else if (x <= 2.6e-221) {
		tmp = y;
	} else if (x <= 2.4e-17) {
		tmp = y * ((z - t) / a);
	} 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 <= -3.4e-47:
		tmp = t_1
	elif x <= -7.5e-214:
		tmp = y
	elif x <= 1.18e-287:
		tmp = z * (y / (a - t))
	elif x <= 2.6e-221:
		tmp = y
	elif x <= 2.4e-17:
		tmp = y * ((z - t) / a)
	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 <= -3.4e-47)
		tmp = t_1;
	elseif (x <= -7.5e-214)
		tmp = y;
	elseif (x <= 1.18e-287)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (x <= 2.6e-221)
		tmp = y;
	elseif (x <= 2.4e-17)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	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 <= -3.4e-47)
		tmp = t_1;
	elseif (x <= -7.5e-214)
		tmp = y;
	elseif (x <= 1.18e-287)
		tmp = z * (y / (a - t));
	elseif (x <= 2.6e-221)
		tmp = y;
	elseif (x <= 2.4e-17)
		tmp = y * ((z - t) / a);
	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, -3.4e-47], t$95$1, If[LessEqual[x, -7.5e-214], y, If[LessEqual[x, 1.18e-287], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-221], y, If[LessEqual[x, 2.4e-17], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4000000000000002e-47 or 2.39999999999999986e-17 < x

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 54.9%

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

   if -3.4000000000000002e-47 < x < -7.49999999999999966e-214 or 1.18000000000000003e-287 < x < 2.6000000000000002e-221

   1. Initial program 68.5%

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

   3. Taylor expanded in t around inf 53.2%

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

   if -7.49999999999999966e-214 < x < 1.18000000000000003e-287

   1. Initial program 82.5%

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

   3. Taylor expanded in z around inf 53.3%

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

   4. Taylor expanded in y around inf 47.5%

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

   if 2.6000000000000002e-221 < x < 2.39999999999999986e-17

   1. Initial program 82.1%

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

      1. clear-num 82.0%

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

      2. inv-pow 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-/r* 92.9%

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

   4. Applied egg-rr 92.9%

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

      1. unpow-1 92.9%

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

      2. clear-num 93.0%

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

      3. div-sub 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. div-sub 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in x around 0 66.1%

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

       1. *-commutative 66.1%

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

       2. associate-/l* 70.8%

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

   11. Simplified 70.8%

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

   12. Taylor expanded in a around inf 45.7%

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

       1. associate-/l* 48.0%

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

   14. Simplified 48.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-221}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+273}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= x -1.8e-25)
     t_1
     (if (<= x 1.26e-82)
       (* y (/ (- z t) (- a t)))
       (if (<= x 2.4e+245)
         t_1
         (if (<= x 6e+273)
           (+ y (* x (/ (- z a) t)))
           (* x (+ (/ (- t z) (- a t)) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (x <= -1.8e-25) {
		tmp = t_1;
	} else if (x <= 1.26e-82) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 2.4e+245) {
		tmp = t_1;
	} else if (x <= 6e+273) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / (a - t)))
    if (x <= (-1.8d-25)) then
        tmp = t_1
    else if (x <= 1.26d-82) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 2.4d+245) then
        tmp = t_1
    else if (x <= 6d+273) then
        tmp = y + (x * ((z - a) / t))
    else
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (x <= -1.8e-25) {
		tmp = t_1;
	} else if (x <= 1.26e-82) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 2.4e+245) {
		tmp = t_1;
	} else if (x <= 6e+273) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if x <= -1.8e-25:
		tmp = t_1
	elif x <= 1.26e-82:
		tmp = y * ((z - t) / (a - t))
	elif x <= 2.4e+245:
		tmp = t_1
	elif x <= 6e+273:
		tmp = y + (x * ((z - a) / t))
	else:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (x <= -1.8e-25)
		tmp = t_1;
	elseif (x <= 1.26e-82)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 2.4e+245)
		tmp = t_1;
	elseif (x <= 6e+273)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	else
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (x <= -1.8e-25)
		tmp = t_1;
	elseif (x <= 1.26e-82)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 2.4e+245)
		tmp = t_1;
	elseif (x <= 6e+273)
		tmp = y + (x * ((z - a) / t));
	else
		tmp = x * (((t - z) / (a - t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-25], t$95$1, If[LessEqual[x, 1.26e-82], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+245], t$95$1, If[LessEqual[x, 6e+273], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8e-25 or 1.25999999999999993e-82 < x < 2.3999999999999998e245

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   if -1.8e-25 < x < 1.25999999999999993e-82

   1. Initial program 72.3%

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

      1. clear-num 72.2%

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

      2. inv-pow 72.2%

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

      3. *-commutative 72.2%

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

      4. associate-/r* 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in x around 0 67.2%

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

      1. associate-*r/ 86.7%

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

   7. Simplified 86.7%

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

   if 2.3999999999999998e245 < x < 5.9999999999999999e273

   1. Initial program 46.7%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. associate--l+ 56.9%

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

      2. associate-*r/ 56.9%

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

      3. associate-*r/ 56.9%

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

      4. div-sub 68.0%

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

      5. distribute-lft-out-- 68.0%

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

      6. associate-*r/ 68.0%

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

      7. mul-1-neg 68.0%

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

      8. unsub-neg 68.0%

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

      9. distribute-rgt-out-- 68.0%

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

      10. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   if 5.9999999999999999e273 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+245}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+273}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;x \leq -1.26 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+273}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= x -1.26e-25)
     t_1
     (if (<= x 1.9e-80)
       (* y (/ (- z t) (- a t)))
       (if (<= x 5.2e+245)
         t_1
         (if (<= x 1.85e+273)
           (+ y (* x (/ (- z a) t)))
           (+ x (* (- x y) (/ (- t z) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (x <= -1.26e-25) {
		tmp = t_1;
	} else if (x <= 1.9e-80) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 5.2e+245) {
		tmp = t_1;
	} else if (x <= 1.85e+273) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = x + ((x - y) * ((t - 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 = x + (z * ((y - x) / (a - t)))
    if (x <= (-1.26d-25)) then
        tmp = t_1
    else if (x <= 1.9d-80) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 5.2d+245) then
        tmp = t_1
    else if (x <= 1.85d+273) then
        tmp = y + (x * ((z - a) / t))
    else
        tmp = x + ((x - y) * ((t - 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 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (x <= -1.26e-25) {
		tmp = t_1;
	} else if (x <= 1.9e-80) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 5.2e+245) {
		tmp = t_1;
	} else if (x <= 1.85e+273) {
		tmp = y + (x * ((z - a) / t));
	} else {
		tmp = x + ((x - y) * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if x <= -1.26e-25:
		tmp = t_1
	elif x <= 1.9e-80:
		tmp = y * ((z - t) / (a - t))
	elif x <= 5.2e+245:
		tmp = t_1
	elif x <= 1.85e+273:
		tmp = y + (x * ((z - a) / t))
	else:
		tmp = x + ((x - y) * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (x <= -1.26e-25)
		tmp = t_1;
	elseif (x <= 1.9e-80)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 5.2e+245)
		tmp = t_1;
	elseif (x <= 1.85e+273)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	else
		tmp = Float64(x + Float64(Float64(x - y) * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (x <= -1.26e-25)
		tmp = t_1;
	elseif (x <= 1.9e-80)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 5.2e+245)
		tmp = t_1;
	elseif (x <= 1.85e+273)
		tmp = y + (x * ((z - a) / t));
	else
		tmp = x + ((x - y) * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.26e-25], t$95$1, If[LessEqual[x, 1.9e-80], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+245], t$95$1, If[LessEqual[x, 1.85e+273], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - y), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.26e-25 or 1.89999999999999983e-80 < x < 5.20000000000000008e245

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   if -1.26e-25 < x < 1.89999999999999983e-80

   1. Initial program 72.3%

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

      1. clear-num 72.2%

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

      2. inv-pow 72.2%

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

      3. *-commutative 72.2%

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

      4. associate-/r* 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in x around 0 67.2%

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

      1. associate-*r/ 86.7%

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

   7. Simplified 86.7%

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

   if 5.20000000000000008e245 < x < 1.8499999999999999e273

   1. Initial program 46.7%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. associate--l+ 56.9%

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

      2. associate-*r/ 56.9%

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

      3. associate-*r/ 56.9%

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

      4. div-sub 68.0%

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

      5. distribute-lft-out-- 68.0%

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

      6. associate-*r/ 68.0%

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

      7. mul-1-neg 68.0%

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

      8. unsub-neg 68.0%

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

      9. distribute-rgt-out-- 68.0%

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

      10. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   if 1.8499999999999999e273 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 72.6%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+245}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+273}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+228}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;x \leq -0.0085 \lor \neg \left(x \leq 2 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.6e+228)
   (* z (/ x (- t a)))
   (if (<= x -1.02e+101)
     (+ x (/ (* y z) a))
     (if (or (<= x -0.0085) (not (<= x 2e+93)))
       (* x (- 1.0 (/ z a)))
       (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.6e+228) {
		tmp = z * (x / (t - a));
	} else if (x <= -1.02e+101) {
		tmp = x + ((y * z) / a);
	} else if ((x <= -0.0085) || !(x <= 2e+93)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.6d+228)) then
        tmp = z * (x / (t - a))
    else if (x <= (-1.02d+101)) then
        tmp = x + ((y * z) / a)
    else if ((x <= (-0.0085d0)) .or. (.not. (x <= 2d+93))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.6e+228) {
		tmp = z * (x / (t - a));
	} else if (x <= -1.02e+101) {
		tmp = x + ((y * z) / a);
	} else if ((x <= -0.0085) || !(x <= 2e+93)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.6e+228:
		tmp = z * (x / (t - a))
	elif x <= -1.02e+101:
		tmp = x + ((y * z) / a)
	elif (x <= -0.0085) or not (x <= 2e+93):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.6e+228)
		tmp = Float64(z * Float64(x / Float64(t - a)));
	elseif (x <= -1.02e+101)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif ((x <= -0.0085) || !(x <= 2e+93))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.6e+228)
		tmp = z * (x / (t - a));
	elseif (x <= -1.02e+101)
		tmp = x + ((y * z) / a);
	elseif ((x <= -0.0085) || ~((x <= 2e+93)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.6e+228], N[(z * N[(x / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.02e+101], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -0.0085], N[Not[LessEqual[x, 2e+93]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.60000000000000007e228

   1. Initial program 57.7%

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

   3. Taylor expanded in z around inf 58.4%

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

   4. Taylor expanded in y around 0 58.4%

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

      1. neg-mul-1 58.4%

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

      2. distribute-neg-frac2 58.4%

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

   6. Simplified 58.4%

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

   if -2.60000000000000007e228 < x < -1.02000000000000002e101

   1. Initial program 72.8%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in t around 0 61.6%

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

   if -1.02000000000000002e101 < x < -0.0085000000000000006 or 2.00000000000000009e93 < x

   1. Initial program 62.8%

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

   3. Taylor expanded in x around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0 65.7%

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

   if -0.0085000000000000006 < x < 2.00000000000000009e93

   1. Initial program 74.1%

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

      1. clear-num 74.0%

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

      2. inv-pow 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-/r* 92.0%

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

   4. Applied egg-rr 92.0%

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

   5. Taylor expanded in x around 0 60.6%

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

      1. associate-*r/ 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+228}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;x \leq -0.0085 \lor \neg \left(x \leq 2 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- z a) t) (- x y)))))
   (if (<= t -4.1e+49)
     t_1
     (if (<= t 1.75e-124)
       (+ x (/ (* (- x y) (- t z)) (- a t)))
       (if (<= t 3.8e+159) (+ x (* (- z t) (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((z - a) / t) * (x - y));
	double tmp;
	if (t <= -4.1e+49) {
		tmp = t_1;
	} else if (t <= 1.75e-124) {
		tmp = x + (((x - y) * (t - z)) / (a - t));
	} else if (t <= 3.8e+159) {
		tmp = x + ((z - t) * (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 = y + (((z - a) / t) * (x - y))
    if (t <= (-4.1d+49)) then
        tmp = t_1
    else if (t <= 1.75d-124) then
        tmp = x + (((x - y) * (t - z)) / (a - t))
    else if (t <= 3.8d+159) then
        tmp = x + ((z - t) * (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 = y + (((z - a) / t) * (x - y));
	double tmp;
	if (t <= -4.1e+49) {
		tmp = t_1;
	} else if (t <= 1.75e-124) {
		tmp = x + (((x - y) * (t - z)) / (a - t));
	} else if (t <= 3.8e+159) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((z - a) / t) * (x - y))
	tmp = 0
	if t <= -4.1e+49:
		tmp = t_1
	elif t <= 1.75e-124:
		tmp = x + (((x - y) * (t - z)) / (a - t))
	elif t <= 3.8e+159:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(z - a) / t) * Float64(x - y)))
	tmp = 0.0
	if (t <= -4.1e+49)
		tmp = t_1;
	elseif (t <= 1.75e-124)
		tmp = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)));
	elseif (t <= 3.8e+159)
		tmp = Float64(x + Float64(Float64(z - t) * 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 = y + (((z - a) / t) * (x - y));
	tmp = 0.0;
	if (t <= -4.1e+49)
		tmp = t_1;
	elseif (t <= 1.75e-124)
		tmp = x + (((x - y) * (t - z)) / (a - t));
	elseif (t <= 3.8e+159)
		tmp = x + ((z - t) * (y / (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[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+49], t$95$1, If[LessEqual[t, 1.75e-124], N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+159], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1e49 or 3.79999999999999965e159 < t

   1. Initial program 40.1%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. associate-*r/ 62.6%

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

      3. associate-*r/ 62.6%

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

      4. div-sub 62.6%

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

      5. distribute-lft-out-- 62.6%

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

      6. associate-*r/ 62.6%

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

      7. mul-1-neg 62.6%

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

      8. unsub-neg 62.6%

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

      9. distribute-rgt-out-- 62.7%

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

      10. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if -4.1e49 < t < 1.7499999999999999e-124

   1. Initial program 87.7%

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

   if 1.7499999999999999e-124 < t < 3.79999999999999965e159

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-236}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= z -1.4e+185)
     t_1
     (if (<= z -7.6e-236)
       (+ x y)
       (if (<= z 8.6e-79) y (if (<= z 2.4e+158) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (z <= -1.4e+185) {
		tmp = t_1;
	} else if (z <= -7.6e-236) {
		tmp = x + y;
	} else if (z <= 8.6e-79) {
		tmp = y;
	} else if (z <= 2.4e+158) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (z <= (-1.4d+185)) then
        tmp = t_1
    else if (z <= (-7.6d-236)) then
        tmp = x + y
    else if (z <= 8.6d-79) then
        tmp = y
    else if (z <= 2.4d+158) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (z <= -1.4e+185) {
		tmp = t_1;
	} else if (z <= -7.6e-236) {
		tmp = x + y;
	} else if (z <= 8.6e-79) {
		tmp = y;
	} else if (z <= 2.4e+158) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if z <= -1.4e+185:
		tmp = t_1
	elif z <= -7.6e-236:
		tmp = x + y
	elif z <= 8.6e-79:
		tmp = y
	elif z <= 2.4e+158:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (z <= -1.4e+185)
		tmp = t_1;
	elseif (z <= -7.6e-236)
		tmp = Float64(x + y);
	elseif (z <= 8.6e-79)
		tmp = y;
	elseif (z <= 2.4e+158)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (z <= -1.4e+185)
		tmp = t_1;
	elseif (z <= -7.6e-236)
		tmp = x + y;
	elseif (z <= 8.6e-79)
		tmp = y;
	elseif (z <= 2.4e+158)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+185], t$95$1, If[LessEqual[z, -7.6e-236], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.6e-79], y, If[LessEqual[z, 2.4e+158], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.39999999999999991e185 or 2.40000000000000008e158 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in x around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in a around 0 39.0%

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

   if -1.39999999999999991e185 < z < -7.5999999999999998e-236 or 8.59999999999999963e-79 < z < 2.40000000000000008e158

   1. Initial program 76.3%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{x + y} \]
   7. Step-by-step derivation

      1. +-commutative 42.9%

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

   8. Simplified 42.9%

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

   if -7.5999999999999998e-236 < z < 8.59999999999999963e-79

   1. Initial program 58.3%

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

   3. Taylor expanded in t around inf 46.5%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-236}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.9e+231)
   (* z (/ x (- t a)))
   (if (<= x -3.4e-25)
     (- x (* y (/ (- t z) a)))
     (if (<= x 9e+92) (* y (/ (- z t) (- a t))) (* x (- 1.0 (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.9e+231) {
		tmp = z * (x / (t - a));
	} else if (x <= -3.4e-25) {
		tmp = x - (y * ((t - z) / a));
	} else if (x <= 9e+92) {
		tmp = y * ((z - t) / (a - t));
	} 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) :: tmp
    if (x <= (-1.9d+231)) then
        tmp = z * (x / (t - a))
    else if (x <= (-3.4d-25)) then
        tmp = x - (y * ((t - z) / a))
    else if (x <= 9d+92) then
        tmp = y * ((z - t) / (a - t))
    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 tmp;
	if (x <= -1.9e+231) {
		tmp = z * (x / (t - a));
	} else if (x <= -3.4e-25) {
		tmp = x - (y * ((t - z) / a));
	} else if (x <= 9e+92) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.9e+231:
		tmp = z * (x / (t - a))
	elif x <= -3.4e-25:
		tmp = x - (y * ((t - z) / a))
	elif x <= 9e+92:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.9e+231)
		tmp = Float64(z * Float64(x / Float64(t - a)));
	elseif (x <= -3.4e-25)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (x <= 9e+92)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.9e+231)
		tmp = z * (x / (t - a));
	elseif (x <= -3.4e-25)
		tmp = x - (y * ((t - z) / a));
	elseif (x <= 9e+92)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.9e+231], N[(z * N[(x / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-25], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+92], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.9e231

   1. Initial program 57.7%

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

   3. Taylor expanded in z around inf 58.4%

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

   4. Taylor expanded in y around 0 58.4%

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

      1. neg-mul-1 58.4%

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

      2. distribute-neg-frac2 58.4%

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

   6. Simplified 58.4%

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

   if -1.9e231 < x < -3.40000000000000002e-25

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 56.7%

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

      1. associate-/l* 59.3%

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

   8. Simplified 59.3%

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

   if -3.40000000000000002e-25 < x < 8.9999999999999998e92

   1. Initial program 73.1%

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

      1. clear-num 72.9%

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

      2. inv-pow 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in x around 0 61.7%

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

      1. associate-*r/ 78.4%

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

   7. Simplified 78.4%

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

   if 8.9999999999999998e92 < x

   1. Initial program 60.4%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 65.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 40.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-222}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -5.7e-49)
     t_1
     (if (<= x 6.5e-222) y (if (<= x 1.82e-7) (* y (/ (- z t) a)) 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 <= -5.7e-49) {
		tmp = t_1;
	} else if (x <= 6.5e-222) {
		tmp = y;
	} else if (x <= 1.82e-7) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-5.7d-49)) then
        tmp = t_1
    else if (x <= 6.5d-222) then
        tmp = y
    else if (x <= 1.82d-7) then
        tmp = y * ((z - t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -5.7e-49) {
		tmp = t_1;
	} else if (x <= 6.5e-222) {
		tmp = y;
	} else if (x <= 1.82e-7) {
		tmp = y * ((z - t) / a);
	} 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 <= -5.7e-49:
		tmp = t_1
	elif x <= 6.5e-222:
		tmp = y
	elif x <= 1.82e-7:
		tmp = y * ((z - t) / a)
	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 <= -5.7e-49)
		tmp = t_1;
	elseif (x <= 6.5e-222)
		tmp = y;
	elseif (x <= 1.82e-7)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	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 <= -5.7e-49)
		tmp = t_1;
	elseif (x <= 6.5e-222)
		tmp = y;
	elseif (x <= 1.82e-7)
		tmp = y * ((z - t) / a);
	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, -5.7e-49], t$95$1, If[LessEqual[x, 6.5e-222], y, If[LessEqual[x, 1.82e-7], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7000000000000003e-49 or 1.81999999999999989e-7 < x

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 54.9%

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

   if -5.7000000000000003e-49 < x < 6.5000000000000005e-222

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 45.9%

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

   if 6.5000000000000005e-222 < x < 1.81999999999999989e-7

   1. Initial program 82.1%

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

      1. clear-num 82.0%

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

      2. inv-pow 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-/r* 92.9%

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

   4. Applied egg-rr 92.9%

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

      1. unpow-1 92.9%

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

      2. clear-num 93.0%

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

      3. div-sub 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. div-sub 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in x around 0 66.1%

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

       1. *-commutative 66.1%

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

       2. associate-/l* 70.8%

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

   11. Simplified 70.8%

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

   12. Taylor expanded in a around inf 45.7%

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

       1. associate-/l* 48.0%

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

   14. Simplified 48.0%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-222}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.5e-26)
   (+ x (* z (/ (- y x) a)))
   (if (<= x 1.3e+93) (* y (/ (- z t) (- a t))) (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.5e-26) {
		tmp = x + (z * ((y - x) / a));
	} else if (x <= 1.3e+93) {
		tmp = y * ((z - t) / (a - t));
	} 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) :: tmp
    if (x <= (-9.5d-26)) then
        tmp = x + (z * ((y - x) / a))
    else if (x <= 1.3d+93) then
        tmp = y * ((z - t) / (a - t))
    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 tmp;
	if (x <= -9.5e-26) {
		tmp = x + (z * ((y - x) / a));
	} else if (x <= 1.3e+93) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.5e-26:
		tmp = x + (z * ((y - x) / a))
	elif x <= 1.3e+93:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9.5e-26)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (x <= 1.3e+93)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9.5e-26)
		tmp = x + (z * ((y - x) / a));
	elseif (x <= 1.3e+93)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9.5e-26], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+93], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4999999999999995e-26

   1. Initial program 70.2%

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

   3. Taylor expanded in t around 0 56.7%

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

      1. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

   if -9.4999999999999995e-26 < x < 1.3e93

   1. Initial program 73.1%

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

      1. clear-num 72.9%

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

      2. inv-pow 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in x around 0 61.7%

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

      1. associate-*r/ 78.4%

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

   7. Simplified 78.4%

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

   if 1.3e93 < x

   1. Initial program 60.4%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 65.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6e-25)
   (+ x (/ (- y x) (/ a z)))
   (if (<= x 2.8e+93) (* y (/ (- z t) (- a t))) (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6e-25) {
		tmp = x + ((y - x) / (a / z));
	} else if (x <= 2.8e+93) {
		tmp = y * ((z - t) / (a - t));
	} 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) :: tmp
    if (x <= (-6d-25)) then
        tmp = x + ((y - x) / (a / z))
    else if (x <= 2.8d+93) then
        tmp = y * ((z - t) / (a - t))
    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 tmp;
	if (x <= -6e-25) {
		tmp = x + ((y - x) / (a / z));
	} else if (x <= 2.8e+93) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6e-25:
		tmp = x + ((y - x) / (a / z))
	elif x <= 2.8e+93:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6e-25)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (x <= 2.8e+93)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6e-25)
		tmp = x + ((y - x) / (a / z));
	elseif (x <= 2.8e+93)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6e-25], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+93], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.9999999999999995e-25

   1. Initial program 70.2%

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

      1. clear-num 70.2%

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

      2. inv-pow 70.2%

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

      3. *-commutative 70.2%

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

      4. associate-/r* 82.8%

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

   4. Applied egg-rr 82.8%

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

      1. unpow-1 82.8%

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

      2. clear-num 82.7%

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

      3. div-sub 73.7%

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

   6. Applied egg-rr 73.7%

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

      1. div-sub 82.7%

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

   8. Simplified 82.7%

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

   9. Taylor expanded in t around 0 60.9%

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

   if -5.9999999999999995e-25 < x < 2.79999999999999989e93

   1. Initial program 73.1%

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

      1. clear-num 72.9%

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

      2. inv-pow 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in x around 0 61.7%

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

      1. associate-*r/ 78.4%

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

   7. Simplified 78.4%

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

   if 2.79999999999999989e93 < x

   1. Initial program 60.4%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 65.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 41.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-50} \lor \neg \left(x \leq 3.85 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.4e-50) (not (<= x 3.85e-84))) (* x (- 1.0 (/ z a))) y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.4e-50) || !(x <= 3.85e-84)) {
		tmp = x * (1.0 - (z / a));
	} 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 ((x <= (-6.4d-50)) .or. (.not. (x <= 3.85d-84))) then
        tmp = x * (1.0d0 - (z / a))
    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 ((x <= -6.4e-50) || !(x <= 3.85e-84)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.4e-50) or not (x <= 3.85e-84):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.4e-50) || !(x <= 3.85e-84))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.4e-50) || ~((x <= 3.85e-84)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.4e-50], N[Not[LessEqual[x, 3.85e-84]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -6.4e-50 or 3.85e-84 < x

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 53.0%

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

   if -6.4e-50 < x < 3.85e-84

   1. Initial program 72.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.5%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-50} \lor \neg \left(x \leq 3.85 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+81) x (if (<= a 4.4e+68) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+81) {
		tmp = x;
	} else if (a <= 4.4e+68) {
		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 <= (-9d+81)) then
        tmp = x
    else if (a <= 4.4d+68) 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 <= -9e+81) {
		tmp = x;
	} else if (a <= 4.4e+68) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+81:
		tmp = x
	elif a <= 4.4e+68:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+81)
		tmp = x;
	elseif (a <= 4.4e+68)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+81)
		tmp = x;
	elseif (a <= 4.4e+68)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+81], x, If[LessEqual[a, 4.4e+68], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.00000000000000034e81 or 4.39999999999999974e68 < a

   1. Initial program 68.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.1%

      \[\leadsto \color{blue}{x} \]

   if -9.00000000000000034e81 < a < 4.39999999999999974e68

   1. Initial program 71.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 25.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 69.9%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 23.6%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 23.6%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024039 
(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))))