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

Percentage Accurate: 67.6% → 88.6%

Time: 30.4s

Alternatives: 24

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-181} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{z - y}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-181) (not (<= t_1 0.0)))
     (+ x (* (/ (- z y) (- a z)) (- x t)))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0)) {
		tmp = x + (((z - y) / (a - z)) * (x - t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-5d-181)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + (((z - y) / (a - z)) * (x - t))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    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) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0)) {
		tmp = x + (((z - y) / (a - z)) * (x - t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-181) or not (t_1 <= 0.0):
		tmp = x + (((z - y) / (a - z)) * (x - t))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(Float64(z - y) / Float64(a - z)) * Float64(x - t)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -5e-181) || ~((t_1 <= 0.0)))
		tmp = x + (((z - y) / (a - z)) * (x - t));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-181], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000001e-181 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 74.5%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   if -5.0000000000000001e-181 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.3%

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

      1. associate-*l/ 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-181} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{z - y}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 45.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -5e+50)
     t
     (if (<= z -7.5e-117)
       t_1
       (if (<= z -3.1e-220)
         (* y (/ (- t x) a))
         (if (<= z -6.5e-235)
           t_1
           (if (<= z 8.6e-267)
             (+ x (/ (* y t) a))
             (if (<= z 4.4e-28)
               t_1
               (if (<= z 2.05e+125)
                 t
                 (if (<= z 8.2e+190) (* t (/ (- y z) a)) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+50) {
		tmp = t;
	} else if (z <= -7.5e-117) {
		tmp = t_1;
	} else if (z <= -3.1e-220) {
		tmp = y * ((t - x) / a);
	} else if (z <= -6.5e-235) {
		tmp = t_1;
	} else if (z <= 8.6e-267) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.4e-28) {
		tmp = t_1;
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 8.2e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = 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 * (1.0d0 - (y / a))
    if (z <= (-5d+50)) then
        tmp = t
    else if (z <= (-7.5d-117)) then
        tmp = t_1
    else if (z <= (-3.1d-220)) then
        tmp = y * ((t - x) / a)
    else if (z <= (-6.5d-235)) then
        tmp = t_1
    else if (z <= 8.6d-267) then
        tmp = x + ((y * t) / a)
    else if (z <= 4.4d-28) then
        tmp = t_1
    else if (z <= 2.05d+125) then
        tmp = t
    else if (z <= 8.2d+190) then
        tmp = t * ((y - z) / a)
    else
        tmp = 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 * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+50) {
		tmp = t;
	} else if (z <= -7.5e-117) {
		tmp = t_1;
	} else if (z <= -3.1e-220) {
		tmp = y * ((t - x) / a);
	} else if (z <= -6.5e-235) {
		tmp = t_1;
	} else if (z <= 8.6e-267) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.4e-28) {
		tmp = t_1;
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 8.2e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5e+50:
		tmp = t
	elif z <= -7.5e-117:
		tmp = t_1
	elif z <= -3.1e-220:
		tmp = y * ((t - x) / a)
	elif z <= -6.5e-235:
		tmp = t_1
	elif z <= 8.6e-267:
		tmp = x + ((y * t) / a)
	elif z <= 4.4e-28:
		tmp = t_1
	elif z <= 2.05e+125:
		tmp = t
	elif z <= 8.2e+190:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5e+50)
		tmp = t;
	elseif (z <= -7.5e-117)
		tmp = t_1;
	elseif (z <= -3.1e-220)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= -6.5e-235)
		tmp = t_1;
	elseif (z <= 8.6e-267)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 4.4e-28)
		tmp = t_1;
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 8.2e+190)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5e+50)
		tmp = t;
	elseif (z <= -7.5e-117)
		tmp = t_1;
	elseif (z <= -3.1e-220)
		tmp = y * ((t - x) / a);
	elseif (z <= -6.5e-235)
		tmp = t_1;
	elseif (z <= 8.6e-267)
		tmp = x + ((y * t) / a);
	elseif (z <= 4.4e-28)
		tmp = t_1;
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 8.2e+190)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+50], t, If[LessEqual[z, -7.5e-117], t$95$1, If[LessEqual[z, -3.1e-220], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-235], t$95$1, If[LessEqual[z, 8.6e-267], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-28], t$95$1, If[LessEqual[z, 2.05e+125], t, If[LessEqual[z, 8.2e+190], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5e50 or 4.39999999999999992e-28 < z < 2.04999999999999996e125 or 8.2000000000000004e190 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 53.3%

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

   if -5e50 < z < -7.50000000000000066e-117 or -3.10000000000000011e-220 < z < -6.49999999999999973e-235 or 8.5999999999999992e-267 < z < 4.39999999999999992e-28

   1. Initial program 92.7%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 69.0%

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

   6. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. sub-neg 58.7%

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

   8. Simplified 58.7%

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

   if -7.50000000000000066e-117 < z < -3.10000000000000011e-220

   1. Initial program 84.8%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around 0 62.1%

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

   6. Taylor expanded in y around inf 62.6%

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

      1. div-sub 62.6%

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

   8. Simplified 62.6%

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

   if -6.49999999999999973e-235 < z < 8.5999999999999992e-267

   1. Initial program 91.9%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around 0 85.2%

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

   6. Taylor expanded in t around inf 77.0%

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

   if 2.04999999999999996e125 < z < 8.2000000000000004e190

   1. Initial program 55.0%

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

      1. clear-num 55.1%

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

      2. associate-/r/ 55.0%

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

   4. Applied egg-rr 55.0%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in a around inf 52.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-263}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -5.7e+50)
     t
     (if (<= z -1.35e-113)
       t_1
       (if (<= z -1.14e-218)
         (* y (/ (- t x) a))
         (if (<= z -4.2e-234)
           t_1
           (if (<= z 1.3e-263)
             (+ x (/ (* y t) a))
             (if (<= z 1.8e-24)
               (- x (/ x (/ a y)))
               (if (<= z 2.05e+125)
                 t
                 (if (<= z 5.3e+190) (* t (/ (- y z) a)) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5.7e+50) {
		tmp = t;
	} else if (z <= -1.35e-113) {
		tmp = t_1;
	} else if (z <= -1.14e-218) {
		tmp = y * ((t - x) / a);
	} else if (z <= -4.2e-234) {
		tmp = t_1;
	} else if (z <= 1.3e-263) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.8e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = 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 * (1.0d0 - (y / a))
    if (z <= (-5.7d+50)) then
        tmp = t
    else if (z <= (-1.35d-113)) then
        tmp = t_1
    else if (z <= (-1.14d-218)) then
        tmp = y * ((t - x) / a)
    else if (z <= (-4.2d-234)) then
        tmp = t_1
    else if (z <= 1.3d-263) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.8d-24) then
        tmp = x - (x / (a / y))
    else if (z <= 2.05d+125) then
        tmp = t
    else if (z <= 5.3d+190) then
        tmp = t * ((y - z) / a)
    else
        tmp = 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 * (1.0 - (y / a));
	double tmp;
	if (z <= -5.7e+50) {
		tmp = t;
	} else if (z <= -1.35e-113) {
		tmp = t_1;
	} else if (z <= -1.14e-218) {
		tmp = y * ((t - x) / a);
	} else if (z <= -4.2e-234) {
		tmp = t_1;
	} else if (z <= 1.3e-263) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.8e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5.7e+50:
		tmp = t
	elif z <= -1.35e-113:
		tmp = t_1
	elif z <= -1.14e-218:
		tmp = y * ((t - x) / a)
	elif z <= -4.2e-234:
		tmp = t_1
	elif z <= 1.3e-263:
		tmp = x + ((y * t) / a)
	elif z <= 1.8e-24:
		tmp = x - (x / (a / y))
	elif z <= 2.05e+125:
		tmp = t
	elif z <= 5.3e+190:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5.7e+50)
		tmp = t;
	elseif (z <= -1.35e-113)
		tmp = t_1;
	elseif (z <= -1.14e-218)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= -4.2e-234)
		tmp = t_1;
	elseif (z <= 1.3e-263)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.8e-24)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5.7e+50)
		tmp = t;
	elseif (z <= -1.35e-113)
		tmp = t_1;
	elseif (z <= -1.14e-218)
		tmp = y * ((t - x) / a);
	elseif (z <= -4.2e-234)
		tmp = t_1;
	elseif (z <= 1.3e-263)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.8e-24)
		tmp = x - (x / (a / y));
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e+50], t, If[LessEqual[z, -1.35e-113], t$95$1, If[LessEqual[z, -1.14e-218], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-234], t$95$1, If[LessEqual[z, 1.3e-263], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-24], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+125], t, If[LessEqual[z, 5.3e+190], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.7000000000000002e50 or 1.8e-24 < z < 2.04999999999999996e125 or 5.30000000000000015e190 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 53.3%

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

   if -5.7000000000000002e50 < z < -1.34999999999999998e-113 or -1.14000000000000001e-218 < z < -4.19999999999999982e-234

   1. Initial program 93.3%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 69.4%

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

   6. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. sub-neg 62.9%

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

   8. Simplified 62.9%

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

   if -1.34999999999999998e-113 < z < -1.14000000000000001e-218

   1. Initial program 84.8%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around 0 62.1%

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

   6. Taylor expanded in y around inf 62.6%

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

      1. div-sub 62.6%

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

   8. Simplified 62.6%

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

   if -4.19999999999999982e-234 < z < 1.3e-263

   1. Initial program 91.9%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around 0 85.2%

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

   6. Taylor expanded in t around inf 77.0%

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

   if 1.3e-263 < z < 1.8e-24

   1. Initial program 92.2%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around 0 68.8%

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

   6. Taylor expanded in t around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-/l* 55.4%

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

   8. Simplified 55.4%

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

   if 2.04999999999999996e125 < z < 5.30000000000000015e190

   1. Initial program 55.0%

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

      1. clear-num 55.1%

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

      2. associate-/r/ 55.0%

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

   4. Applied egg-rr 55.0%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in a around inf 52.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-263}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := x \cdot \frac{-y}{a - z}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 32000:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))) (t_2 (* x (/ (- y) (- a z)))))
   (if (<= a -1.35e+153)
     t_1
     (if (<= a -2.1e+123)
       (/ t (- 1.0 (/ a z)))
       (if (<= a -6.2e-80)
         t_1
         (if (<= a -1.6e-189)
           t_2
           (if (<= a 9.5e-219)
             (* t (- 1.0 (/ y z)))
             (if (<= a 9e-158)
               t_2
               (if (<= a 32000.0) (* t (+ (/ (- a y) z) 1.0)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double t_2 = x * (-y / (a - z));
	double tmp;
	if (a <= -1.35e+153) {
		tmp = t_1;
	} else if (a <= -2.1e+123) {
		tmp = t / (1.0 - (a / z));
	} else if (a <= -6.2e-80) {
		tmp = t_1;
	} else if (a <= -1.6e-189) {
		tmp = t_2;
	} else if (a <= 9.5e-219) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 9e-158) {
		tmp = t_2;
	} else if (a <= 32000.0) {
		tmp = t * (((a - y) / z) + 1.0);
	} 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 = x + (t / (a / y))
    t_2 = x * (-y / (a - z))
    if (a <= (-1.35d+153)) then
        tmp = t_1
    else if (a <= (-2.1d+123)) then
        tmp = t / (1.0d0 - (a / z))
    else if (a <= (-6.2d-80)) then
        tmp = t_1
    else if (a <= (-1.6d-189)) then
        tmp = t_2
    else if (a <= 9.5d-219) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 9d-158) then
        tmp = t_2
    else if (a <= 32000.0d0) then
        tmp = t * (((a - y) / z) + 1.0d0)
    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 + (t / (a / y));
	double t_2 = x * (-y / (a - z));
	double tmp;
	if (a <= -1.35e+153) {
		tmp = t_1;
	} else if (a <= -2.1e+123) {
		tmp = t / (1.0 - (a / z));
	} else if (a <= -6.2e-80) {
		tmp = t_1;
	} else if (a <= -1.6e-189) {
		tmp = t_2;
	} else if (a <= 9.5e-219) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 9e-158) {
		tmp = t_2;
	} else if (a <= 32000.0) {
		tmp = t * (((a - y) / z) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	t_2 = x * (-y / (a - z))
	tmp = 0
	if a <= -1.35e+153:
		tmp = t_1
	elif a <= -2.1e+123:
		tmp = t / (1.0 - (a / z))
	elif a <= -6.2e-80:
		tmp = t_1
	elif a <= -1.6e-189:
		tmp = t_2
	elif a <= 9.5e-219:
		tmp = t * (1.0 - (y / z))
	elif a <= 9e-158:
		tmp = t_2
	elif a <= 32000.0:
		tmp = t * (((a - y) / z) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	t_2 = Float64(x * Float64(Float64(-y) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.35e+153)
		tmp = t_1;
	elseif (a <= -2.1e+123)
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	elseif (a <= -6.2e-80)
		tmp = t_1;
	elseif (a <= -1.6e-189)
		tmp = t_2;
	elseif (a <= 9.5e-219)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 9e-158)
		tmp = t_2;
	elseif (a <= 32000.0)
		tmp = Float64(t * Float64(Float64(Float64(a - y) / z) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	t_2 = x * (-y / (a - z));
	tmp = 0.0;
	if (a <= -1.35e+153)
		tmp = t_1;
	elseif (a <= -2.1e+123)
		tmp = t / (1.0 - (a / z));
	elseif (a <= -6.2e-80)
		tmp = t_1;
	elseif (a <= -1.6e-189)
		tmp = t_2;
	elseif (a <= 9.5e-219)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 9e-158)
		tmp = t_2;
	elseif (a <= 32000.0)
		tmp = t * (((a - y) / z) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-y) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+153], t$95$1, If[LessEqual[a, -2.1e+123], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-80], t$95$1, If[LessEqual[a, -1.6e-189], t$95$2, If[LessEqual[a, 9.5e-219], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-158], t$95$2, If[LessEqual[a, 32000.0], N[(t * N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35e153 or -2.09999999999999994e123 < a < -6.20000000000000032e-80 or 32000 < a

   1. Initial program 72.1%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 59.1%

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

   6. Taylor expanded in t around inf 51.3%

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

      1. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

   if -1.35e153 < a < -2.09999999999999994e123

   1. Initial program 59.3%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 31.8%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. div-sub 72.3%

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

      3. sub-neg 72.3%

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

      4. *-inverses 72.3%

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

      5. metadata-eval 72.3%

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

   10. Simplified 72.3%

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

   if -6.20000000000000032e-80 < a < -1.6e-189 or 9.4999999999999997e-219 < a < 9e-158

   1. Initial program 69.4%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. mul-1-neg 60.7%

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

   10. Simplified 60.7%

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

   if -1.6e-189 < a < 9.4999999999999997e-219

   1. Initial program 69.3%

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

      1. clear-num 69.3%

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

      2. associate-/r/ 69.2%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in t around inf 76.4%

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

      1. div-sub 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in a around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. div-sub 72.7%

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

      3. sub-neg 72.7%

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

      4. *-inverses 72.7%

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

      5. metadata-eval 72.7%

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

   10. Simplified 72.7%

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

   if 9e-158 < a < 32000

   1. Initial program 64.4%

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

      1. clear-num 64.3%

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

      2. associate-/r/ 64.4%

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

   4. Applied egg-rr 64.4%

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

   5. Taylor expanded in t around inf 70.4%

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

      1. div-sub 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in z around inf 74.0%

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

      1. associate--l+ 74.0%

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

      2. associate-*r/ 74.0%

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

      3. associate-*r/ 74.0%

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

      4. div-sub 74.0%

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

      5. distribute-lft-out-- 74.0%

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

      6. associate-*r/ 74.0%

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

      7. mul-1-neg 74.0%

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

      8. unsub-neg 74.0%

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

   10. Simplified 74.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 32000:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-138}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.45 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -7e+130)
     (* x (/ (- y) a))
     (if (<= y -4.4e+96)
       (+ x t)
       (if (<= y -9.5e+57)
         (/ (- x) (/ a y))
         (if (<= y -2.85e+17)
           t_1
           (if (<= y 2.6e-138)
             (+ x t)
             (if (<= y 9.5e-67) t (if (<= y 4.45e+77) x t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -7e+130) {
		tmp = x * (-y / a);
	} else if (y <= -4.4e+96) {
		tmp = x + t;
	} else if (y <= -9.5e+57) {
		tmp = -x / (a / y);
	} else if (y <= -2.85e+17) {
		tmp = t_1;
	} else if (y <= 2.6e-138) {
		tmp = x + t;
	} else if (y <= 9.5e-67) {
		tmp = t;
	} else if (y <= 4.45e+77) {
		tmp = 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 = t * (y / (a - z))
    if (y <= (-7d+130)) then
        tmp = x * (-y / a)
    else if (y <= (-4.4d+96)) then
        tmp = x + t
    else if (y <= (-9.5d+57)) then
        tmp = -x / (a / y)
    else if (y <= (-2.85d+17)) then
        tmp = t_1
    else if (y <= 2.6d-138) then
        tmp = x + t
    else if (y <= 9.5d-67) then
        tmp = t
    else if (y <= 4.45d+77) then
        tmp = 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 = t * (y / (a - z));
	double tmp;
	if (y <= -7e+130) {
		tmp = x * (-y / a);
	} else if (y <= -4.4e+96) {
		tmp = x + t;
	} else if (y <= -9.5e+57) {
		tmp = -x / (a / y);
	} else if (y <= -2.85e+17) {
		tmp = t_1;
	} else if (y <= 2.6e-138) {
		tmp = x + t;
	} else if (y <= 9.5e-67) {
		tmp = t;
	} else if (y <= 4.45e+77) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -7e+130:
		tmp = x * (-y / a)
	elif y <= -4.4e+96:
		tmp = x + t
	elif y <= -9.5e+57:
		tmp = -x / (a / y)
	elif y <= -2.85e+17:
		tmp = t_1
	elif y <= 2.6e-138:
		tmp = x + t
	elif y <= 9.5e-67:
		tmp = t
	elif y <= 4.45e+77:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -7e+130)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (y <= -4.4e+96)
		tmp = Float64(x + t);
	elseif (y <= -9.5e+57)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (y <= -2.85e+17)
		tmp = t_1;
	elseif (y <= 2.6e-138)
		tmp = Float64(x + t);
	elseif (y <= 9.5e-67)
		tmp = t;
	elseif (y <= 4.45e+77)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -7e+130)
		tmp = x * (-y / a);
	elseif (y <= -4.4e+96)
		tmp = x + t;
	elseif (y <= -9.5e+57)
		tmp = -x / (a / y);
	elseif (y <= -2.85e+17)
		tmp = t_1;
	elseif (y <= 2.6e-138)
		tmp = x + t;
	elseif (y <= 9.5e-67)
		tmp = t;
	elseif (y <= 4.45e+77)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+130], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e+96], N[(x + t), $MachinePrecision], If[LessEqual[y, -9.5e+57], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.85e+17], t$95$1, If[LessEqual[y, 2.6e-138], N[(x + t), $MachinePrecision], If[LessEqual[y, 9.5e-67], t, If[LessEqual[y, 4.45e+77], x, t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.0000000000000002e130

   1. Initial program 71.9%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. unsub-neg 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in y around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. mul-1-neg 54.4%

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

   10. Simplified 54.4%

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

   11. Taylor expanded in a around inf 42.1%

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

       1. associate-*r/ 42.1%

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

       2. mul-1-neg 42.1%

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

   13. Simplified 42.1%

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

   if -7.0000000000000002e130 < y < -4.3999999999999998e96 or -2.85e17 < y < 2.6e-138

   1. Initial program 67.4%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in t around inf 71.6%

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

   6. Taylor expanded in z around inf 49.9%

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

   if -4.3999999999999998e96 < y < -9.4999999999999997e57

   1. Initial program 87.8%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 74.8%

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

   6. Taylor expanded in y around inf 62.8%

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

      1. div-sub 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in t around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. associate-/l* 51.4%

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

       3. distribute-neg-frac 51.4%

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

   11. Simplified 51.4%

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

   if -9.4999999999999997e57 < y < -2.85e17 or 4.4499999999999999e77 < y

   1. Initial program 73.7%

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

      1. clear-num 73.6%

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

      2. associate-/r/ 73.6%

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

   4. Applied egg-rr 73.6%

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

   5. Taylor expanded in t around inf 59.8%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in y around inf 50.5%

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

   if 2.6e-138 < y < 9.4999999999999994e-67

   1. Initial program 37.4%

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

      1. associate-*l/ 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in z around inf 78.6%

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

   if 9.4999999999999994e-67 < y < 4.4499999999999999e77

   1. Initial program 74.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around inf 30.9%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-138}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.45 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-141}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -2e+130)
     (* x (/ (- y) a))
     (if (<= y -3.2e+95)
       (+ x t)
       (if (<= y -1.95e+59)
         (/ (- x) (/ a y))
         (if (<= y -7e+17)
           t_1
           (if (<= y 7e-141)
             (+ x t)
             (if (<= y 1.75e-68)
               t
               (if (<= y 8.5e+77) (* t (/ (- y z) a)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -2e+130) {
		tmp = x * (-y / a);
	} else if (y <= -3.2e+95) {
		tmp = x + t;
	} else if (y <= -1.95e+59) {
		tmp = -x / (a / y);
	} else if (y <= -7e+17) {
		tmp = t_1;
	} else if (y <= 7e-141) {
		tmp = x + t;
	} else if (y <= 1.75e-68) {
		tmp = t;
	} else if (y <= 8.5e+77) {
		tmp = t * ((y - z) / 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 = t * (y / (a - z))
    if (y <= (-2d+130)) then
        tmp = x * (-y / a)
    else if (y <= (-3.2d+95)) then
        tmp = x + t
    else if (y <= (-1.95d+59)) then
        tmp = -x / (a / y)
    else if (y <= (-7d+17)) then
        tmp = t_1
    else if (y <= 7d-141) then
        tmp = x + t
    else if (y <= 1.75d-68) then
        tmp = t
    else if (y <= 8.5d+77) then
        tmp = t * ((y - z) / 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 = t * (y / (a - z));
	double tmp;
	if (y <= -2e+130) {
		tmp = x * (-y / a);
	} else if (y <= -3.2e+95) {
		tmp = x + t;
	} else if (y <= -1.95e+59) {
		tmp = -x / (a / y);
	} else if (y <= -7e+17) {
		tmp = t_1;
	} else if (y <= 7e-141) {
		tmp = x + t;
	} else if (y <= 1.75e-68) {
		tmp = t;
	} else if (y <= 8.5e+77) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -2e+130:
		tmp = x * (-y / a)
	elif y <= -3.2e+95:
		tmp = x + t
	elif y <= -1.95e+59:
		tmp = -x / (a / y)
	elif y <= -7e+17:
		tmp = t_1
	elif y <= 7e-141:
		tmp = x + t
	elif y <= 1.75e-68:
		tmp = t
	elif y <= 8.5e+77:
		tmp = t * ((y - z) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -2e+130)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (y <= -3.2e+95)
		tmp = Float64(x + t);
	elseif (y <= -1.95e+59)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (y <= -7e+17)
		tmp = t_1;
	elseif (y <= 7e-141)
		tmp = Float64(x + t);
	elseif (y <= 1.75e-68)
		tmp = t;
	elseif (y <= 8.5e+77)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -2e+130)
		tmp = x * (-y / a);
	elseif (y <= -3.2e+95)
		tmp = x + t;
	elseif (y <= -1.95e+59)
		tmp = -x / (a / y);
	elseif (y <= -7e+17)
		tmp = t_1;
	elseif (y <= 7e-141)
		tmp = x + t;
	elseif (y <= 1.75e-68)
		tmp = t;
	elseif (y <= 8.5e+77)
		tmp = t * ((y - z) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+130], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e+95], N[(x + t), $MachinePrecision], If[LessEqual[y, -1.95e+59], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e+17], t$95$1, If[LessEqual[y, 7e-141], N[(x + t), $MachinePrecision], If[LessEqual[y, 1.75e-68], t, If[LessEqual[y, 8.5e+77], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.0000000000000001e130

   1. Initial program 71.9%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. unsub-neg 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in y around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. mul-1-neg 54.4%

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

   10. Simplified 54.4%

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

   11. Taylor expanded in a around inf 42.1%

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

       1. associate-*r/ 42.1%

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

       2. mul-1-neg 42.1%

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

   13. Simplified 42.1%

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

   if -2.0000000000000001e130 < y < -3.2000000000000001e95 or -7e17 < y < 7.0000000000000006e-141

   1. Initial program 67.4%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in t around inf 71.6%

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

   6. Taylor expanded in z around inf 49.9%

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

   if -3.2000000000000001e95 < y < -1.95000000000000011e59

   1. Initial program 87.8%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 74.8%

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

   6. Taylor expanded in y around inf 62.8%

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

      1. div-sub 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in t around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. associate-/l* 51.4%

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

       3. distribute-neg-frac 51.4%

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

   11. Simplified 51.4%

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

   if -1.95000000000000011e59 < y < -7e17 or 8.50000000000000018e77 < y

   1. Initial program 73.7%

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

      1. clear-num 73.6%

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

      2. associate-/r/ 73.6%

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

   4. Applied egg-rr 73.6%

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

   5. Taylor expanded in t around inf 59.8%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in y around inf 50.5%

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

   if 7.0000000000000006e-141 < y < 1.75000000000000006e-68

   1. Initial program 37.4%

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

      1. associate-*l/ 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in z around inf 78.6%

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

   if 1.75000000000000006e-68 < y < 8.50000000000000018e77

   1. Initial program 74.2%

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

      1. clear-num 74.2%

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

      2. associate-/r/ 74.3%

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

   4. Applied egg-rr 74.3%

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

   5. Taylor expanded in t around inf 47.4%

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

      1. div-sub 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in a around inf 32.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-141}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := x \cdot \frac{-y}{a - z}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-188}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-157}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 36000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (* x (/ (- y) (- a z)))))
   (if (<= a -3.6e+153)
     t_2
     (if (<= a -2.1e+123)
       (/ t (- 1.0 (/ a z)))
       (if (<= a -2.4e-76)
         t_2
         (if (<= a -1.7e-188)
           t_3
           (if (<= a 9.5e-219)
             t_1
             (if (<= a 1e-157) t_3 (if (<= a 36000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double t_3 = x * (-y / (a - z));
	double tmp;
	if (a <= -3.6e+153) {
		tmp = t_2;
	} else if (a <= -2.1e+123) {
		tmp = t / (1.0 - (a / z));
	} else if (a <= -2.4e-76) {
		tmp = t_2;
	} else if (a <= -1.7e-188) {
		tmp = t_3;
	} else if (a <= 9.5e-219) {
		tmp = t_1;
	} else if (a <= 1e-157) {
		tmp = t_3;
	} else if (a <= 36000.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t / (a / y))
    t_3 = x * (-y / (a - z))
    if (a <= (-3.6d+153)) then
        tmp = t_2
    else if (a <= (-2.1d+123)) then
        tmp = t / (1.0d0 - (a / z))
    else if (a <= (-2.4d-76)) then
        tmp = t_2
    else if (a <= (-1.7d-188)) then
        tmp = t_3
    else if (a <= 9.5d-219) then
        tmp = t_1
    else if (a <= 1d-157) then
        tmp = t_3
    else if (a <= 36000.0d0) 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 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double t_3 = x * (-y / (a - z));
	double tmp;
	if (a <= -3.6e+153) {
		tmp = t_2;
	} else if (a <= -2.1e+123) {
		tmp = t / (1.0 - (a / z));
	} else if (a <= -2.4e-76) {
		tmp = t_2;
	} else if (a <= -1.7e-188) {
		tmp = t_3;
	} else if (a <= 9.5e-219) {
		tmp = t_1;
	} else if (a <= 1e-157) {
		tmp = t_3;
	} else if (a <= 36000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t / (a / y))
	t_3 = x * (-y / (a - z))
	tmp = 0
	if a <= -3.6e+153:
		tmp = t_2
	elif a <= -2.1e+123:
		tmp = t / (1.0 - (a / z))
	elif a <= -2.4e-76:
		tmp = t_2
	elif a <= -1.7e-188:
		tmp = t_3
	elif a <= 9.5e-219:
		tmp = t_1
	elif a <= 1e-157:
		tmp = t_3
	elif a <= 36000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(x * Float64(Float64(-y) / Float64(a - z)))
	tmp = 0.0
	if (a <= -3.6e+153)
		tmp = t_2;
	elseif (a <= -2.1e+123)
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	elseif (a <= -2.4e-76)
		tmp = t_2;
	elseif (a <= -1.7e-188)
		tmp = t_3;
	elseif (a <= 9.5e-219)
		tmp = t_1;
	elseif (a <= 1e-157)
		tmp = t_3;
	elseif (a <= 36000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t / (a / y));
	t_3 = x * (-y / (a - z));
	tmp = 0.0;
	if (a <= -3.6e+153)
		tmp = t_2;
	elseif (a <= -2.1e+123)
		tmp = t / (1.0 - (a / z));
	elseif (a <= -2.4e-76)
		tmp = t_2;
	elseif (a <= -1.7e-188)
		tmp = t_3;
	elseif (a <= 9.5e-219)
		tmp = t_1;
	elseif (a <= 1e-157)
		tmp = t_3;
	elseif (a <= 36000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[((-y) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+153], t$95$2, If[LessEqual[a, -2.1e+123], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-76], t$95$2, If[LessEqual[a, -1.7e-188], t$95$3, If[LessEqual[a, 9.5e-219], t$95$1, If[LessEqual[a, 1e-157], t$95$3, If[LessEqual[a, 36000.0], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6000000000000001e153 or -2.09999999999999994e123 < a < -2.40000000000000013e-76 or 36000 < a

   1. Initial program 72.1%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 59.1%

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

   6. Taylor expanded in t around inf 51.3%

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

      1. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

   if -3.6000000000000001e153 < a < -2.09999999999999994e123

   1. Initial program 59.3%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 31.8%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. div-sub 72.3%

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

      3. sub-neg 72.3%

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

      4. *-inverses 72.3%

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

      5. metadata-eval 72.3%

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

   10. Simplified 72.3%

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

   if -2.40000000000000013e-76 < a < -1.70000000000000014e-188 or 9.4999999999999997e-219 < a < 9.99999999999999943e-158

   1. Initial program 69.4%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. mul-1-neg 60.7%

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

   10. Simplified 60.7%

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

   if -1.70000000000000014e-188 < a < 9.4999999999999997e-219 or 9.99999999999999943e-158 < a < 36000

   1. Initial program 67.3%

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

      1. clear-num 67.4%

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

      2. associate-/r/ 67.3%

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

   4. Applied egg-rr 67.3%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in a around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. div-sub 73.2%

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

      3. sub-neg 73.2%

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

      4. *-inverses 73.2%

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

      5. metadata-eval 73.2%

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

   10. Simplified 73.2%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 10^{-157}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 36000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.5e+50)
     t
     (if (<= z -1.4e-116)
       t_1
       (if (<= z -2.85e-272)
         (* y (/ (- t x) a))
         (if (<= z 4.2e-25)
           t_1
           (if (<= z 2.05e+125)
             t
             (if (<= z 5.3e+190) (* t (/ (- y z) a)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+50) {
		tmp = t;
	} else if (z <= -1.4e-116) {
		tmp = t_1;
	} else if (z <= -2.85e-272) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.2e-25) {
		tmp = t_1;
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = 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 * (1.0d0 - (y / a))
    if (z <= (-6.5d+50)) then
        tmp = t
    else if (z <= (-1.4d-116)) then
        tmp = t_1
    else if (z <= (-2.85d-272)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.2d-25) then
        tmp = t_1
    else if (z <= 2.05d+125) then
        tmp = t
    else if (z <= 5.3d+190) then
        tmp = t * ((y - z) / a)
    else
        tmp = 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 * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+50) {
		tmp = t;
	} else if (z <= -1.4e-116) {
		tmp = t_1;
	} else if (z <= -2.85e-272) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.2e-25) {
		tmp = t_1;
	} else if (z <= 2.05e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.5e+50:
		tmp = t
	elif z <= -1.4e-116:
		tmp = t_1
	elif z <= -2.85e-272:
		tmp = y * ((t - x) / a)
	elif z <= 4.2e-25:
		tmp = t_1
	elif z <= 2.05e+125:
		tmp = t
	elif z <= 5.3e+190:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.5e+50)
		tmp = t;
	elseif (z <= -1.4e-116)
		tmp = t_1;
	elseif (z <= -2.85e-272)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.2e-25)
		tmp = t_1;
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.5e+50)
		tmp = t;
	elseif (z <= -1.4e-116)
		tmp = t_1;
	elseif (z <= -2.85e-272)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.2e-25)
		tmp = t_1;
	elseif (z <= 2.05e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+50], t, If[LessEqual[z, -1.4e-116], t$95$1, If[LessEqual[z, -2.85e-272], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-25], t$95$1, If[LessEqual[z, 2.05e+125], t, If[LessEqual[z, 5.3e+190], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5000000000000003e50 or 4.20000000000000005e-25 < z < 2.04999999999999996e125 or 5.30000000000000015e190 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 53.3%

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

   if -6.5000000000000003e50 < z < -1.3999999999999999e-116 or -2.8499999999999999e-272 < z < 4.20000000000000005e-25

   1. Initial program 92.6%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. sub-neg 57.1%

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

   8. Simplified 57.1%

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

   if -1.3999999999999999e-116 < z < -2.8499999999999999e-272

   1. Initial program 87.8%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 74.2%

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

   6. Taylor expanded in y around inf 67.8%

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

      1. div-sub 67.8%

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

   8. Simplified 67.8%

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

   if 2.04999999999999996e125 < z < 5.30000000000000015e190

   1. Initial program 55.0%

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

      1. clear-num 55.1%

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

      2. associate-/r/ 55.0%

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

   4. Applied egg-rr 55.0%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in a around inf 52.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- z y) (/ (- a z) t)))))
   (if (<= t -1.35e-123)
     t_1
     (if (<= t -1.05e-230)
       (* y (/ (- t x) (- a z)))
       (if (<= t 4.8e-138)
         (* x (+ (/ (- z y) (- a z)) 1.0))
         (if (<= t 4.3e-41)
           (+ x (* (- t x) (/ (- y z) a)))
           (if (<= t 1.9e-28) (* x (/ (- y) (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - y) / ((a - z) / t));
	double tmp;
	if (t <= -1.35e-123) {
		tmp = t_1;
	} else if (t <= -1.05e-230) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4.8e-138) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (t <= 4.3e-41) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (t <= 1.9e-28) {
		tmp = x * (-y / (a - z));
	} 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 - y) / ((a - z) / t))
    if (t <= (-1.35d-123)) then
        tmp = t_1
    else if (t <= (-1.05d-230)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 4.8d-138) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else if (t <= 4.3d-41) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (t <= 1.9d-28) then
        tmp = x * (-y / (a - z))
    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 - y) / ((a - z) / t));
	double tmp;
	if (t <= -1.35e-123) {
		tmp = t_1;
	} else if (t <= -1.05e-230) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4.8e-138) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (t <= 4.3e-41) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (t <= 1.9e-28) {
		tmp = x * (-y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - y) / ((a - z) / t))
	tmp = 0
	if t <= -1.35e-123:
		tmp = t_1
	elif t <= -1.05e-230:
		tmp = y * ((t - x) / (a - z))
	elif t <= 4.8e-138:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	elif t <= 4.3e-41:
		tmp = x + ((t - x) * ((y - z) / a))
	elif t <= 1.9e-28:
		tmp = x * (-y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - y) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -1.35e-123)
		tmp = t_1;
	elseif (t <= -1.05e-230)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 4.8e-138)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	elseif (t <= 4.3e-41)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (t <= 1.9e-28)
		tmp = Float64(x * Float64(Float64(-y) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - y) / ((a - z) / t));
	tmp = 0.0;
	if (t <= -1.35e-123)
		tmp = t_1;
	elseif (t <= -1.05e-230)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 4.8e-138)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	elseif (t <= 4.3e-41)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (t <= 1.9e-28)
		tmp = x * (-y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-123], t$95$1, If[LessEqual[t, -1.05e-230], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-138], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-41], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-28], N[(x * N[((-y) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.35e-123 or 1.90000000000000005e-28 < t

   1. Initial program 64.6%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in t around inf 79.4%

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

   if -1.35e-123 < t < -1.0499999999999999e-230

   1. Initial program 57.4%

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

      1. associate-*l/ 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   7. Simplified 68.4%

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

   if -1.0499999999999999e-230 < t < 4.7999999999999998e-138

   1. Initial program 83.3%

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

      1. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in x around inf 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   7. Simplified 81.2%

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

   if 4.7999999999999998e-138 < t < 4.2999999999999999e-41

   1. Initial program 91.0%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 73.2%

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

   if 4.2999999999999999e-41 < t < 1.90000000000000005e-28

   1. Initial program 83.1%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in x around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in y around inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. mul-1-neg 83.5%

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

   10. Simplified 83.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.65e-36)
     t_1
     (if (<= a -4.4e-188)
       (/ x (/ z (- y a)))
       (if (<= a 7.6e-219)
         t_2
         (if (<= a 1.2e-171) (/ (* x (- y a)) z) (if (<= a 1.0) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.65e-36) {
		tmp = t_1;
	} else if (a <= -4.4e-188) {
		tmp = x / (z / (y - a));
	} else if (a <= 7.6e-219) {
		tmp = t_2;
	} else if (a <= 1.2e-171) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.0) {
		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 = x + (t / (a / y))
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-1.65d-36)) then
        tmp = t_1
    else if (a <= (-4.4d-188)) then
        tmp = x / (z / (y - a))
    else if (a <= 7.6d-219) then
        tmp = t_2
    else if (a <= 1.2d-171) then
        tmp = (x * (y - a)) / z
    else if (a <= 1.0d0) 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 = x + (t / (a / y));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.65e-36) {
		tmp = t_1;
	} else if (a <= -4.4e-188) {
		tmp = x / (z / (y - a));
	} else if (a <= 7.6e-219) {
		tmp = t_2;
	} else if (a <= 1.2e-171) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.65e-36:
		tmp = t_1
	elif a <= -4.4e-188:
		tmp = x / (z / (y - a))
	elif a <= 7.6e-219:
		tmp = t_2
	elif a <= 1.2e-171:
		tmp = (x * (y - a)) / z
	elif a <= 1.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.65e-36)
		tmp = t_1;
	elseif (a <= -4.4e-188)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (a <= 7.6e-219)
		tmp = t_2;
	elseif (a <= 1.2e-171)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.65e-36)
		tmp = t_1;
	elseif (a <= -4.4e-188)
		tmp = x / (z / (y - a));
	elseif (a <= 7.6e-219)
		tmp = t_2;
	elseif (a <= 1.2e-171)
		tmp = (x * (y - a)) / z;
	elseif (a <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-36], t$95$1, If[LessEqual[a, -4.4e-188], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-219], t$95$2, If[LessEqual[a, 1.2e-171], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.0], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.64999999999999995e-36 or 1 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around 0 58.6%

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

   6. Taylor expanded in t around inf 50.3%

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

      1. associate-/l* 55.0%

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

   8. Simplified 55.0%

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

   if -1.64999999999999995e-36 < a < -4.3999999999999999e-188

   1. Initial program 66.8%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in x around -inf 56.9%

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

      1. associate-*r* 56.9%

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

      2. neg-mul-1 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in z around -inf 38.9%

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

      1. associate-/l* 47.8%

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

   10. Simplified 47.8%

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

   if -4.3999999999999999e-188 < a < 7.60000000000000049e-219 or 1.19999999999999993e-171 < a < 1

   1. Initial program 67.3%

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

      1. clear-num 67.4%

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

      2. associate-/r/ 67.3%

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

   4. Applied egg-rr 67.3%

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

   5. Taylor expanded in t around inf 69.9%

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

      1. div-sub 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in a around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. div-sub 69.2%

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

      3. sub-neg 69.2%

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

      4. *-inverses 69.2%

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

      5. metadata-eval 69.2%

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

   10. Simplified 69.2%

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

   if 7.60000000000000049e-219 < a < 1.19999999999999993e-171

   1. Initial program 67.6%

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

      1. associate-*l/ 57.7%

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

   3. Simplified 57.7%

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

   5. Taylor expanded in x around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in z around -inf 68.1%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-y}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 50:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y) (- a z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.9e-78)
     t_2
     (if (<= a -6e-189)
       t_1
       (if (<= a 9.5e-219)
         t_3
         (if (<= a 2.05e-151) t_1 (if (<= a 50.0) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-y / (a - z));
	double t_2 = x + (t / (a / y));
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.9e-78) {
		tmp = t_2;
	} else if (a <= -6e-189) {
		tmp = t_1;
	} else if (a <= 9.5e-219) {
		tmp = t_3;
	} else if (a <= 2.05e-151) {
		tmp = t_1;
	} else if (a <= 50.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (-y / (a - z))
    t_2 = x + (t / (a / y))
    t_3 = t * (1.0d0 - (y / z))
    if (a <= (-2.9d-78)) then
        tmp = t_2
    else if (a <= (-6d-189)) then
        tmp = t_1
    else if (a <= 9.5d-219) then
        tmp = t_3
    else if (a <= 2.05d-151) then
        tmp = t_1
    else if (a <= 50.0d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-y / (a - z));
	double t_2 = x + (t / (a / y));
	double t_3 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.9e-78) {
		tmp = t_2;
	} else if (a <= -6e-189) {
		tmp = t_1;
	} else if (a <= 9.5e-219) {
		tmp = t_3;
	} else if (a <= 2.05e-151) {
		tmp = t_1;
	} else if (a <= 50.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-y / (a - z))
	t_2 = x + (t / (a / y))
	t_3 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.9e-78:
		tmp = t_2
	elif a <= -6e-189:
		tmp = t_1
	elif a <= 9.5e-219:
		tmp = t_3
	elif a <= 2.05e-151:
		tmp = t_1
	elif a <= 50.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(-y) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -2.9e-78)
		tmp = t_2;
	elseif (a <= -6e-189)
		tmp = t_1;
	elseif (a <= 9.5e-219)
		tmp = t_3;
	elseif (a <= 2.05e-151)
		tmp = t_1;
	elseif (a <= 50.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-y / (a - z));
	t_2 = x + (t / (a / y));
	t_3 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.9e-78)
		tmp = t_2;
	elseif (a <= -6e-189)
		tmp = t_1;
	elseif (a <= 9.5e-219)
		tmp = t_3;
	elseif (a <= 2.05e-151)
		tmp = t_1;
	elseif (a <= 50.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[((-y) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e-78], t$95$2, If[LessEqual[a, -6e-189], t$95$1, If[LessEqual[a, 9.5e-219], t$95$3, If[LessEqual[a, 2.05e-151], t$95$1, If[LessEqual[a, 50.0], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9000000000000001e-78 or 50 < a

   1. Initial program 71.4%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 57.6%

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

   6. Taylor expanded in t around inf 48.7%

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

      1. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

   if -2.9000000000000001e-78 < a < -6e-189 or 9.4999999999999997e-219 < a < 2.0500000000000001e-151

   1. Initial program 69.4%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. mul-1-neg 60.7%

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

   10. Simplified 60.7%

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

   if -6e-189 < a < 9.4999999999999997e-219 or 2.0500000000000001e-151 < a < 50

   1. Initial program 67.3%

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

      1. clear-num 67.4%

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

      2. associate-/r/ 67.3%

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

   4. Applied egg-rr 67.3%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in a around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. div-sub 73.2%

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

      3. sub-neg 73.2%

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

      4. *-inverses 73.2%

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

      5. metadata-eval 73.2%

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

   10. Simplified 73.2%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 50:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+62} \lor \neg \left(z \leq 1.95 \cdot 10^{+83}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -6.8e+50)
     t_1
     (if (<= z 2.3e-26)
       (- x (* (/ y a) (- x t)))
       (if (or (<= z 4e+62) (not (<= z 1.95e+83)))
         t_1
         (* x (+ (/ (- z y) (- a z)) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.8e+50) {
		tmp = t_1;
	} else if (z <= 2.3e-26) {
		tmp = x - ((y / a) * (x - t));
	} else if ((z <= 4e+62) || !(z <= 1.95e+83)) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / (a - z)) + 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 = t * ((y - z) / (a - z))
    if (z <= (-6.8d+50)) then
        tmp = t_1
    else if (z <= 2.3d-26) then
        tmp = x - ((y / a) * (x - t))
    else if ((z <= 4d+62) .or. (.not. (z <= 1.95d+83))) then
        tmp = t_1
    else
        tmp = x * (((z - y) / (a - z)) + 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.8e+50) {
		tmp = t_1;
	} else if (z <= 2.3e-26) {
		tmp = x - ((y / a) * (x - t));
	} else if ((z <= 4e+62) || !(z <= 1.95e+83)) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -6.8e+50:
		tmp = t_1
	elif z <= 2.3e-26:
		tmp = x - ((y / a) * (x - t))
	elif (z <= 4e+62) or not (z <= 1.95e+83):
		tmp = t_1
	else:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.8e+50)
		tmp = t_1;
	elseif (z <= 2.3e-26)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	elseif ((z <= 4e+62) || !(z <= 1.95e+83))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -6.8e+50)
		tmp = t_1;
	elseif (z <= 2.3e-26)
		tmp = x - ((y / a) * (x - t));
	elseif ((z <= 4e+62) || ~((z <= 1.95e+83)))
		tmp = t_1;
	else
		tmp = x * (((z - y) / (a - z)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+50], t$95$1, If[LessEqual[z, 2.3e-26], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4e+62], N[Not[LessEqual[z, 1.95e+83]], $MachinePrecision]], t$95$1, N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999997e50 or 2.30000000000000009e-26 < z < 4.00000000000000014e62 or 1.9500000000000001e83 < z

   1. Initial program 40.4%

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

      1. clear-num 40.4%

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

      2. associate-/r/ 40.4%

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

   4. Applied egg-rr 40.4%

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

   5. Taylor expanded in t around inf 73.9%

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

      1. div-sub 73.9%

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

   7. Simplified 73.9%

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

   if -6.7999999999999997e50 < z < 2.30000000000000009e-26

   1. Initial program 91.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 73.7%

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

   if 4.00000000000000014e62 < z < 1.9500000000000001e83

   1. Initial program 91.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+62} \lor \neg \left(z \leq 1.95 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4e+37)
     t_1
     (if (<= z 3.2e-7)
       (+ x (* (- t x) (/ (- y z) a)))
       (if (<= z 9e+61)
         (/ t (- 1.0 (/ a z)))
         (if (<= z 2.9e+83) (* x (+ (/ (- z y) (- a z)) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4e+37) {
		tmp = t_1;
	} else if (z <= 3.2e-7) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 9e+61) {
		tmp = t / (1.0 - (a / z));
	} else if (z <= 2.9e+83) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} 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 = t * ((y - z) / (a - z))
    if (z <= (-4d+37)) then
        tmp = t_1
    else if (z <= 3.2d-7) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (z <= 9d+61) then
        tmp = t / (1.0d0 - (a / z))
    else if (z <= 2.9d+83) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4e+37) {
		tmp = t_1;
	} else if (z <= 3.2e-7) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 9e+61) {
		tmp = t / (1.0 - (a / z));
	} else if (z <= 2.9e+83) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4e+37:
		tmp = t_1
	elif z <= 3.2e-7:
		tmp = x + ((t - x) * ((y - z) / a))
	elif z <= 9e+61:
		tmp = t / (1.0 - (a / z))
	elif z <= 2.9e+83:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4e+37)
		tmp = t_1;
	elseif (z <= 3.2e-7)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (z <= 9e+61)
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	elseif (z <= 2.9e+83)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4e+37)
		tmp = t_1;
	elseif (z <= 3.2e-7)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (z <= 9e+61)
		tmp = t / (1.0 - (a / z));
	elseif (z <= 2.9e+83)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+37], t$95$1, If[LessEqual[z, 3.2e-7], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+61], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+83], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999982e37 or 2.89999999999999999e83 < z

   1. Initial program 39.3%

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

      1. clear-num 39.2%

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

      2. associate-/r/ 39.2%

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

   4. Applied egg-rr 39.2%

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

   5. Taylor expanded in t around inf 71.4%

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

      1. div-sub 71.4%

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

   7. Simplified 71.4%

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

   if -3.99999999999999982e37 < z < 3.2000000000000001e-7

   1. Initial program 91.5%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 78.5%

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

   if 3.2000000000000001e-7 < z < 9e61

   1. Initial program 55.5%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in x around 0 68.1%

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

      1. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in y around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. div-sub 80.3%

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

      3. sub-neg 80.3%

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

      4. *-inverses 80.3%

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

      5. metadata-eval 80.3%

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

   10. Simplified 80.3%

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

   if 9e61 < z < 2.89999999999999999e83

   1. Initial program 91.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- t x) (- a y)) z))))
   (if (<= a -1.55e-45)
     (- x (/ (- z y) (/ (- a z) t)))
     (if (<= a -6.8e-72)
       t_1
       (if (<= a -4.2e-97)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.8e-48) t_1 (+ x (* (- t x) (/ (- y z) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (a <= -1.55e-45) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else if (a <= -6.8e-72) {
		tmp = t_1;
	} else if (a <= -4.2e-97) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.8e-48) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) * ((y - 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 = t + (((t - x) * (a - y)) / z)
    if (a <= (-1.55d-45)) then
        tmp = x - ((z - y) / ((a - z) / t))
    else if (a <= (-6.8d-72)) then
        tmp = t_1
    else if (a <= (-4.2d-97)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.8d-48) then
        tmp = t_1
    else
        tmp = x + ((t - x) * ((y - 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 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (a <= -1.55e-45) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else if (a <= -6.8e-72) {
		tmp = t_1;
	} else if (a <= -4.2e-97) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.8e-48) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) * (a - y)) / z)
	tmp = 0
	if a <= -1.55e-45:
		tmp = x - ((z - y) / ((a - z) / t))
	elif a <= -6.8e-72:
		tmp = t_1
	elif a <= -4.2e-97:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.8e-48:
		tmp = t_1
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z))
	tmp = 0.0
	if (a <= -1.55e-45)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(Float64(a - z) / t)));
	elseif (a <= -6.8e-72)
		tmp = t_1;
	elseif (a <= -4.2e-97)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.8e-48)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) * (a - y)) / z);
	tmp = 0.0;
	if (a <= -1.55e-45)
		tmp = x - ((z - y) / ((a - z) / t));
	elseif (a <= -6.8e-72)
		tmp = t_1;
	elseif (a <= -4.2e-97)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.8e-48)
		tmp = t_1;
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-45], N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e-72], t$95$1, If[LessEqual[a, -4.2e-97], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-48], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e-45

   1. Initial program 74.2%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in t around inf 76.6%

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

   if -1.55e-45 < a < -6.7999999999999997e-72 or -4.2000000000000002e-97 < a < 1.8000000000000001e-48

   1. Initial program 64.4%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

      6. associate-*r/ 77.9%

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

      7. mul-1-neg 77.9%

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

      8. unsub-neg 77.9%

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

      9. distribute-rgt-out-- 77.9%

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

   7. Simplified 77.9%

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

   if -6.7999999999999997e-72 < a < -4.2000000000000002e-97

   1. Initial program 72.9%

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

      1. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in y around inf 90.8%

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

      1. div-sub 90.8%

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

   7. Simplified 90.8%

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

   if 1.8000000000000001e-48 < a

   1. Initial program 74.6%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf 83.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-72}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-48}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+50)
   t
   (if (<= z 2.3e-24)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.6e+125) t (if (<= z 5.3e+190) (* t (/ (- y z) a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+50) {
		tmp = t;
	} else if (z <= 2.3e-24) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.6d+50)) then
        tmp = t
    else if (z <= 2.3d-24) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d+125) then
        tmp = t
    else if (z <= 5.3d+190) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+50) {
		tmp = t;
	} else if (z <= 2.3e-24) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+50:
		tmp = t
	elif z <= 2.3e-24:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e+125:
		tmp = t
	elif z <= 5.3e+190:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+50)
		tmp = t;
	elseif (z <= 2.3e-24)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+50)
		tmp = t;
	elseif (z <= 2.3e-24)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+50], t, If[LessEqual[z, 2.3e-24], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+125], t, If[LessEqual[z, 5.3e+190], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000001e50 or 2.3000000000000001e-24 < z < 1.59999999999999992e125 or 5.30000000000000015e190 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 53.3%

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

   if -6.6000000000000001e50 < z < 2.3000000000000001e-24

   1. Initial program 91.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 70.9%

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

   6. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. sub-neg 55.7%

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

   8. Simplified 55.7%

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

   if 1.59999999999999992e125 < z < 5.30000000000000015e190

   1. Initial program 55.0%

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

      1. clear-num 55.1%

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

      2. associate-/r/ 55.0%

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

   4. Applied egg-rr 55.0%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in a around inf 52.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-138}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-70}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= y -2.2e+136)
     t_1
     (if (<= y 2.9e-138)
       (+ x t)
       (if (<= y 4.8e-70) t (if (<= y 9e+57) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -2.2e+136) {
		tmp = t_1;
	} else if (y <= 2.9e-138) {
		tmp = x + t;
	} else if (y <= 4.8e-70) {
		tmp = t;
	} else if (y <= 9e+57) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (y <= (-2.2d+136)) then
        tmp = t_1
    else if (y <= 2.9d-138) then
        tmp = x + t
    else if (y <= 4.8d-70) then
        tmp = t
    else if (y <= 9d+57) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -2.2e+136) {
		tmp = t_1;
	} else if (y <= 2.9e-138) {
		tmp = x + t;
	} else if (y <= 4.8e-70) {
		tmp = t;
	} else if (y <= 9e+57) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if y <= -2.2e+136:
		tmp = t_1
	elif y <= 2.9e-138:
		tmp = x + t
	elif y <= 4.8e-70:
		tmp = t
	elif y <= 9e+57:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -2.2e+136)
		tmp = t_1;
	elseif (y <= 2.9e-138)
		tmp = Float64(x + t);
	elseif (y <= 4.8e-70)
		tmp = t;
	elseif (y <= 9e+57)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (y <= -2.2e+136)
		tmp = t_1;
	elseif (y <= 2.9e-138)
		tmp = x + t;
	elseif (y <= 4.8e-70)
		tmp = t;
	elseif (y <= 9e+57)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+136], t$95$1, If[LessEqual[y, 2.9e-138], N[(x + t), $MachinePrecision], If[LessEqual[y, 4.8e-70], t, If[LessEqual[y, 9e+57], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e136 or 8.99999999999999991e57 < y

   1. Initial program 74.9%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in a around 0 38.2%

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

   if -2.1999999999999999e136 < y < 2.89999999999999973e-138 or 4.8000000000000002e-70 < y < 8.99999999999999991e57

   1. Initial program 68.3%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in t around inf 70.5%

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

   6. Taylor expanded in z around inf 43.9%

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

   if 2.89999999999999973e-138 < y < 4.8000000000000002e-70

   1. Initial program 41.3%

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

      1. associate-*l/ 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in z around inf 76.0%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-138}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-70}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-139}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-70}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.3e+129)
   (* x (/ (- y) a))
   (if (<= y 4.1e-139)
     (+ x t)
     (if (<= y 3.8e-70) t (if (<= y 5.6e+57) (+ x t) (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.3e+129) {
		tmp = x * (-y / a);
	} else if (y <= 4.1e-139) {
		tmp = x + t;
	} else if (y <= 3.8e-70) {
		tmp = t;
	} else if (y <= 5.6e+57) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.3d+129)) then
        tmp = x * (-y / a)
    else if (y <= 4.1d-139) then
        tmp = x + t
    else if (y <= 3.8d-70) then
        tmp = t
    else if (y <= 5.6d+57) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.3e+129) {
		tmp = x * (-y / a);
	} else if (y <= 4.1e-139) {
		tmp = x + t;
	} else if (y <= 3.8e-70) {
		tmp = t;
	} else if (y <= 5.6e+57) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.3e+129:
		tmp = x * (-y / a)
	elif y <= 4.1e-139:
		tmp = x + t
	elif y <= 3.8e-70:
		tmp = t
	elif y <= 5.6e+57:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.3e+129)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (y <= 4.1e-139)
		tmp = Float64(x + t);
	elseif (y <= 3.8e-70)
		tmp = t;
	elseif (y <= 5.6e+57)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.3e+129)
		tmp = x * (-y / a);
	elseif (y <= 4.1e-139)
		tmp = x + t;
	elseif (y <= 3.8e-70)
		tmp = t;
	elseif (y <= 5.6e+57)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.3e+129], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-139], N[(x + t), $MachinePrecision], If[LessEqual[y, 3.8e-70], t, If[LessEqual[y, 5.6e+57], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2999999999999999e129

   1. Initial program 71.9%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. unsub-neg 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in y around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. mul-1-neg 54.4%

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

   10. Simplified 54.4%

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

   11. Taylor expanded in a around inf 42.1%

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

       1. associate-*r/ 42.1%

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

       2. mul-1-neg 42.1%

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

   13. Simplified 42.1%

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

   if -5.2999999999999999e129 < y < 4.10000000000000014e-139 or 3.7999999999999998e-70 < y < 5.59999999999999999e57

   1. Initial program 68.4%

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

      1. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around inf 44.7%

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

   if 4.10000000000000014e-139 < y < 3.7999999999999998e-70

   1. Initial program 41.3%

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

      1. associate-*l/ 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in z around inf 76.0%

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

   if 5.59999999999999999e57 < y

   1. Initial program 76.9%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. unsub-neg 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in a around 0 40.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-139}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-70}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+257}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8e+257)
   (* y (/ (- t x) (- a z)))
   (if (<= x -2.3e+73)
     (- x (/ x (/ a y)))
     (if (<= x 1.3e+89) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8e+257) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -2.3e+73) {
		tmp = x - (x / (a / y));
	} else if (x <= 1.3e+89) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / 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 <= (-8d+257)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= (-2.3d+73)) then
        tmp = x - (x / (a / y))
    else if (x <= 1.3d+89) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / 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 <= -8e+257) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -2.3e+73) {
		tmp = x - (x / (a / y));
	} else if (x <= 1.3e+89) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8e+257:
		tmp = y * ((t - x) / (a - z))
	elif x <= -2.3e+73:
		tmp = x - (x / (a / y))
	elif x <= 1.3e+89:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8e+257)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= -2.3e+73)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (x <= 1.3e+89)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8e+257)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= -2.3e+73)
		tmp = x - (x / (a / y));
	elseif (x <= 1.3e+89)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8e+257], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e+73], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+89], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.00000000000000024e257

   1. Initial program 77.8%

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

      1. associate-*l/ 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 89.6%

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

      1. div-sub 89.6%

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

   7. Simplified 89.6%

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

   if -8.00000000000000024e257 < x < -2.3e73

   1. Initial program 64.2%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around 0 61.5%

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

   6. Taylor expanded in t around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

   if -2.3e73 < x < 1.3e89

   1. Initial program 71.0%

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

      1. clear-num 70.9%

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

      2. associate-/r/ 70.9%

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

   4. Applied egg-rr 70.9%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. div-sub 71.1%

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

   7. Simplified 71.1%

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

   if 1.3e89 < x

   1. Initial program 70.1%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around 0 55.6%

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

   6. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. sub-neg 53.3%

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

   8. Simplified 53.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+257}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+30} \lor \neg \left(t \leq 2.3 \cdot 10^{+14}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{a - z} \cdot \left(y \cdot \left(x - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+30) (not (<= t 2.3e+14)))
   (- x (/ (- z y) (/ (- a z) t)))
   (- x (* (/ 1.0 (- a z)) (* y (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+30) || !(t <= 2.3e+14)) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else {
		tmp = x - ((1.0 / (a - z)) * (y * (x - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.5d+30)) .or. (.not. (t <= 2.3d+14))) then
        tmp = x - ((z - y) / ((a - z) / t))
    else
        tmp = x - ((1.0d0 / (a - z)) * (y * (x - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+30) || !(t <= 2.3e+14)) {
		tmp = x - ((z - y) / ((a - z) / t));
	} else {
		tmp = x - ((1.0 / (a - z)) * (y * (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e+30) or not (t <= 2.3e+14):
		tmp = x - ((z - y) / ((a - z) / t))
	else:
		tmp = x - ((1.0 / (a - z)) * (y * (x - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+30) || !(t <= 2.3e+14))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(Float64(1.0 / Float64(a - z)) * Float64(y * Float64(x - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e+30) || ~((t <= 2.3e+14)))
		tmp = x - ((z - y) / ((a - z) / t));
	else
		tmp = x - ((1.0 / (a - z)) * (y * (x - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e+30], N[Not[LessEqual[t, 2.3e+14]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999989e30 or 2.3e14 < t

   1. Initial program 62.1%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 83.5%

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

   if -1.49999999999999989e30 < t < 2.3e14

   1. Initial program 77.1%

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

      1. clear-num 77.1%

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

      2. associate-/r/ 77.1%

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

   4. Applied egg-rr 77.1%

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

   5. Taylor expanded in y around inf 69.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+30} \lor \neg \left(t \leq 2.3 \cdot 10^{+14}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{a - z} \cdot \left(y \cdot \left(x - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+18)
   t
   (if (<= z -2e-116)
     x
     (if (<= z -2.3e-273) (* t (/ y a)) (if (<= z 1.26e-25) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+18) {
		tmp = t;
	} else if (z <= -2e-116) {
		tmp = x;
	} else if (z <= -2.3e-273) {
		tmp = t * (y / a);
	} else if (z <= 1.26e-25) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.7d+18)) then
        tmp = t
    else if (z <= (-2d-116)) then
        tmp = x
    else if (z <= (-2.3d-273)) then
        tmp = t * (y / a)
    else if (z <= 1.26d-25) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+18) {
		tmp = t;
	} else if (z <= -2e-116) {
		tmp = x;
	} else if (z <= -2.3e-273) {
		tmp = t * (y / a);
	} else if (z <= 1.26e-25) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+18:
		tmp = t
	elif z <= -2e-116:
		tmp = x
	elif z <= -2.3e-273:
		tmp = t * (y / a)
	elif z <= 1.26e-25:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+18)
		tmp = t;
	elseif (z <= -2e-116)
		tmp = x;
	elseif (z <= -2.3e-273)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.26e-25)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+18)
		tmp = t;
	elseif (z <= -2e-116)
		tmp = x;
	elseif (z <= -2.3e-273)
		tmp = t * (y / a);
	elseif (z <= 1.26e-25)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+18], t, If[LessEqual[z, -2e-116], x, If[LessEqual[z, -2.3e-273], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-25], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e18 or 1.26e-25 < z

   1. Initial program 46.4%

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

      1. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in z around inf 46.4%

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

   if -1.7e18 < z < -2e-116 or -2.29999999999999981e-273 < z < 1.26e-25

   1. Initial program 93.0%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 35.2%

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

   if -2e-116 < z < -2.29999999999999981e-273

   1. Initial program 87.8%

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

      1. clear-num 87.8%

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

      2. associate-/r/ 87.9%

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

   4. Applied egg-rr 87.9%

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

   5. Taylor expanded in t around inf 48.5%

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

      1. div-sub 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in z around 0 45.6%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+51} \lor \neg \left(z \leq 5.6 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e+51) (not (<= z 5.6e-30)))
   (* t (/ (- y z) (- a z)))
   (- x (* (/ y a) (- x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+51) || !(z <= 5.6e-30)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.6d+51)) .or. (.not. (z <= 5.6d-30))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - ((y / a) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+51) || !(z <= 5.6e-30)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e+51) or not (z <= 5.6e-30):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e+51) || !(z <= 5.6e-30))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.6e+51) || ~((z <= 5.6e-30)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e+51], N[Not[LessEqual[z, 5.6e-30]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999994e51 or 5.59999999999999977e-30 < z

   1. Initial program 43.1%

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

      1. clear-num 43.0%

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

      2. associate-/r/ 43.0%

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

   4. Applied egg-rr 43.0%

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

   5. Taylor expanded in t around inf 70.2%

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

      1. div-sub 70.2%

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

   7. Simplified 70.2%

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

   if -7.5999999999999994e51 < z < 5.59999999999999977e-30

   1. Initial program 91.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 73.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+51} \lor \neg \left(z \leq 5.6 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.5e+73)
   (- x (/ x (/ a y)))
   (if (<= x 1.3e+90) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+73) {
		tmp = x - (x / (a / y));
	} else if (x <= 1.3e+90) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / 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 <= (-7.5d+73)) then
        tmp = x - (x / (a / y))
    else if (x <= 1.3d+90) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / 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 <= -7.5e+73) {
		tmp = x - (x / (a / y));
	} else if (x <= 1.3e+90) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.5e+73:
		tmp = x - (x / (a / y))
	elif x <= 1.3e+90:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.5e+73)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (x <= 1.3e+90)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.5e+73)
		tmp = x - (x / (a / y));
	elseif (x <= 1.3e+90)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.5e+73], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+90], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5e73

   1. Initial program 66.4%

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

      1. associate-*l/ 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around 0 58.9%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 60.2%

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

   8. Simplified 60.2%

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

   if -7.5e73 < x < 1.2999999999999999e90

   1. Initial program 71.0%

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

      1. clear-num 70.9%

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

      2. associate-/r/ 70.9%

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

   4. Applied egg-rr 70.9%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. div-sub 71.1%

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

   7. Simplified 71.1%

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

   if 1.2999999999999999e90 < x

   1. Initial program 70.1%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around 0 55.6%

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

   6. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. sub-neg 53.3%

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

   8. Simplified 53.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.14e+17) t (if (<= z 5.2e-28) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.14e+17) {
		tmp = t;
	} else if (z <= 5.2e-28) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.14d+17)) then
        tmp = t
    else if (z <= 5.2d-28) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.14e+17) {
		tmp = t;
	} else if (z <= 5.2e-28) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.14e+17:
		tmp = t
	elif z <= 5.2e-28:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.14e+17)
		tmp = t;
	elseif (z <= 5.2e-28)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.14e+17)
		tmp = t;
	elseif (z <= 5.2e-28)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.14e+17], t, If[LessEqual[z, 5.2e-28], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14e17 or 5.2e-28 < z

   1. Initial program 46.4%

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

      1. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in z around inf 46.4%

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

   if -1.14e17 < z < 5.2e-28

   1. Initial program 91.8%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 30.8%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 24.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.8%

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

   1. associate-*l/ 84.4%

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

3. Simplified 84.4%

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

5. Taylor expanded in z around inf 25.1%

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

6. Final simplification 25.1%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))