Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.6% → 90.9%

Time: 27.5s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.6% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-236} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-236) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

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 <= -1e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-236)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-236) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-236) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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 <= -1e-236) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-236], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.4%

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

   if -1e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.8%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. distribute-lft-out-- 67.2%

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

      3. div-sub 67.2%

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

      4. mul-1-neg 67.2%

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

      5. unsub-neg 67.2%

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

      6. distribute-rgt-out-- 67.3%

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

      7. associate-/l* 90.8%

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

   4. Simplified 90.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-236} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{z}{x - t}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\left(y - a\right) \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ z (- x t)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -5e+104)
     t
     (if (<= z -2.25e-88)
       t_2
       (if (<= z -1.12e-148)
         t_1
         (if (<= z 6.5e+67)
           t_2
           (if (<= z 1.4e+99)
             (/ (* z (- t)) (- a z))
             (if (<= z 3.5e+111)
               t_1
               (if (<= z 6.5e+233) (* (- y a) (* x (/ 1.0 z))) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z / (x - t));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+104) {
		tmp = t;
	} else if (z <= -2.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 6.5e+67) {
		tmp = t_2;
	} else if (z <= 1.4e+99) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 3.5e+111) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = (y - a) * (x * (1.0 / z));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y / (z / (x - t))
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-5d+104)) then
        tmp = t
    else if (z <= (-2.25d-88)) then
        tmp = t_2
    else if (z <= (-1.12d-148)) then
        tmp = t_1
    else if (z <= 6.5d+67) then
        tmp = t_2
    else if (z <= 1.4d+99) then
        tmp = (z * -t) / (a - z)
    else if (z <= 3.5d+111) then
        tmp = t_1
    else if (z <= 6.5d+233) then
        tmp = (y - a) * (x * (1.0d0 / z))
    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 = y / (z / (x - t));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5e+104) {
		tmp = t;
	} else if (z <= -2.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 6.5e+67) {
		tmp = t_2;
	} else if (z <= 1.4e+99) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 3.5e+111) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = (y - a) * (x * (1.0 / z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z / (x - t))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5e+104:
		tmp = t
	elif z <= -2.25e-88:
		tmp = t_2
	elif z <= -1.12e-148:
		tmp = t_1
	elif z <= 6.5e+67:
		tmp = t_2
	elif z <= 1.4e+99:
		tmp = (z * -t) / (a - z)
	elif z <= 3.5e+111:
		tmp = t_1
	elif z <= 6.5e+233:
		tmp = (y - a) * (x * (1.0 / z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z / Float64(x - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5e+104)
		tmp = t;
	elseif (z <= -2.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 6.5e+67)
		tmp = t_2;
	elseif (z <= 1.4e+99)
		tmp = Float64(Float64(z * Float64(-t)) / Float64(a - z));
	elseif (z <= 3.5e+111)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = Float64(Float64(y - a) * Float64(x * Float64(1.0 / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z / (x - t));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5e+104)
		tmp = t;
	elseif (z <= -2.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 6.5e+67)
		tmp = t_2;
	elseif (z <= 1.4e+99)
		tmp = (z * -t) / (a - z);
	elseif (z <= 3.5e+111)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = (y - a) * (x * (1.0 / z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+104], t, If[LessEqual[z, -2.25e-88], t$95$2, If[LessEqual[z, -1.12e-148], t$95$1, If[LessEqual[z, 6.5e+67], t$95$2, If[LessEqual[z, 1.4e+99], N[(N[(z * (-t)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+111], t$95$1, If[LessEqual[z, 6.5e+233], N[(N[(y - a), $MachinePrecision] * N[(x * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.9999999999999997e104 or 6.50000000000000038e233 < z

   1. Initial program 59.5%

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

   2. Taylor expanded in z around inf 65.1%

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

   if -4.9999999999999997e104 < z < -2.24999999999999996e-88 or -1.1199999999999999e-148 < z < 6.4999999999999995e67

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 54.5%

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

   if -2.24999999999999996e-88 < z < -1.1199999999999999e-148 or 1.4e99 < z < 3.5000000000000002e111

   1. Initial program 83.9%

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

   2. Taylor expanded in y around inf 68.0%

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

   3. Taylor expanded in z around inf 56.9%

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

      1. associate-/l* 62.2%

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

      2. sub-neg 62.2%

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

      3. neg-mul-1 62.2%

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

      4. neg-mul-1 62.2%

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

      5. remove-double-neg 62.2%

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

   5. Simplified 62.2%

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

   if 6.4999999999999995e67 < z < 1.4e99

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 86.8%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

   7. Simplified 73.6%

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

   if 3.5000000000000002e111 < z < 6.50000000000000038e233

   1. Initial program 63.7%

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

   2. Taylor expanded in x around inf 30.1%

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

      1. mul-1-neg 30.1%

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

      2. unsub-neg 30.1%

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

   4. Simplified 30.1%

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

   5. Taylor expanded in z around inf 26.7%

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

      1. associate-*r/ 26.7%

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

      2. mul-1-neg 26.7%

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

      3. sub-neg 26.7%

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

      4. mul-1-neg 26.7%

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

   7. Simplified 26.7%

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

   8. Taylor expanded in x around inf 26.7%

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

      1. div-inv 26.5%

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

      2. *-commutative 26.5%

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

      3. associate-*l* 45.5%

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

   10. Applied egg-rr 45.5%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\left(y - a\right) \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 290000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= y -6.5e-85)
     t_2
     (if (<= y -5.2e-136)
       t_1
       (if (<= y -4.5e-143)
         (/ t (/ a (- y z)))
         (if (<= y -4.5e-259)
           t
           (if (<= y -9.5e-274)
             x
             (if (<= y 3.45e-69) t (if (<= y 290000000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -6.5e-85) {
		tmp = t_2;
	} else if (y <= -5.2e-136) {
		tmp = t_1;
	} else if (y <= -4.5e-143) {
		tmp = t / (a / (y - z));
	} else if (y <= -4.5e-259) {
		tmp = t;
	} else if (y <= -9.5e-274) {
		tmp = x;
	} else if (y <= 3.45e-69) {
		tmp = t;
	} else if (y <= 290000000.0) {
		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) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = (t - x) * (y / (a - z))
    if (y <= (-6.5d-85)) then
        tmp = t_2
    else if (y <= (-5.2d-136)) then
        tmp = t_1
    else if (y <= (-4.5d-143)) then
        tmp = t / (a / (y - z))
    else if (y <= (-4.5d-259)) then
        tmp = t
    else if (y <= (-9.5d-274)) then
        tmp = x
    else if (y <= 3.45d-69) then
        tmp = t
    else if (y <= 290000000.0d0) 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 = x * (1.0 - (y / a));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -6.5e-85) {
		tmp = t_2;
	} else if (y <= -5.2e-136) {
		tmp = t_1;
	} else if (y <= -4.5e-143) {
		tmp = t / (a / (y - z));
	} else if (y <= -4.5e-259) {
		tmp = t;
	} else if (y <= -9.5e-274) {
		tmp = x;
	} else if (y <= 3.45e-69) {
		tmp = t;
	} else if (y <= 290000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -6.5e-85:
		tmp = t_2
	elif y <= -5.2e-136:
		tmp = t_1
	elif y <= -4.5e-143:
		tmp = t / (a / (y - z))
	elif y <= -4.5e-259:
		tmp = t
	elif y <= -9.5e-274:
		tmp = x
	elif y <= 3.45e-69:
		tmp = t
	elif y <= 290000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -6.5e-85)
		tmp = t_2;
	elseif (y <= -5.2e-136)
		tmp = t_1;
	elseif (y <= -4.5e-143)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (y <= -4.5e-259)
		tmp = t;
	elseif (y <= -9.5e-274)
		tmp = x;
	elseif (y <= 3.45e-69)
		tmp = t;
	elseif (y <= 290000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -6.5e-85)
		tmp = t_2;
	elseif (y <= -5.2e-136)
		tmp = t_1;
	elseif (y <= -4.5e-143)
		tmp = t / (a / (y - z));
	elseif (y <= -4.5e-259)
		tmp = t;
	elseif (y <= -9.5e-274)
		tmp = x;
	elseif (y <= 3.45e-69)
		tmp = t;
	elseif (y <= 290000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-85], t$95$2, If[LessEqual[y, -5.2e-136], t$95$1, If[LessEqual[y, -4.5e-143], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-259], t, If[LessEqual[y, -9.5e-274], x, If[LessEqual[y, 3.45e-69], t, If[LessEqual[y, 290000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.5e-85 or 2.9e8 < y

   1. Initial program 81.3%

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

   2. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 57.3%

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

      3. associate-/l* 68.3%

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

      4. associate-/r/ 69.1%

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

   4. Simplified 69.1%

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

   if -6.5e-85 < y < -5.19999999999999993e-136 or 3.44999999999999985e-69 < y < 2.9e8

   1. Initial program 83.8%

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

   2. Taylor expanded in x around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   4. Simplified 60.7%

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

   5. Taylor expanded in z around 0 55.5%

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

   if -5.19999999999999993e-136 < y < -4.5e-143

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 80.9%

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

      1. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

   if -4.5e-143 < y < -4.49999999999999974e-259 or -9.5000000000000009e-274 < y < 3.44999999999999985e-69

   1. Initial program 75.6%

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

   2. Taylor expanded in z around inf 53.3%

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

   if -4.49999999999999974e-259 < y < -9.5000000000000009e-274

   1. Initial program 69.2%

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

   2. Taylor expanded in a around inf 84.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-85}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-136}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 290000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 4: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\left(y - a\right) \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= z -5.2e+104)
     t
     (if (<= z -1.25e-88)
       t_2
       (if (<= z -1.12e-148)
         t_1
         (if (<= z 2.8e+81)
           t_2
           (if (<= z 6.6e+123)
             (/ (* z (- t)) (- a z))
             (if (<= z 5.2e+149)
               t_1
               (if (<= z 6.5e+233) (* (- y a) (* x (/ 1.0 z))) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -5.2e+104) {
		tmp = t;
	} else if (z <= -1.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 2.8e+81) {
		tmp = t_2;
	} else if (z <= 6.6e+123) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 5.2e+149) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = (y - a) * (x * (1.0 / z));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = x + ((t - x) * (y / a))
    if (z <= (-5.2d+104)) then
        tmp = t
    else if (z <= (-1.25d-88)) then
        tmp = t_2
    else if (z <= (-1.12d-148)) then
        tmp = t_1
    else if (z <= 2.8d+81) then
        tmp = t_2
    else if (z <= 6.6d+123) then
        tmp = (z * -t) / (a - z)
    else if (z <= 5.2d+149) then
        tmp = t_1
    else if (z <= 6.5d+233) then
        tmp = (y - a) * (x * (1.0d0 / z))
    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 = (t - x) * (y / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -5.2e+104) {
		tmp = t;
	} else if (z <= -1.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 2.8e+81) {
		tmp = t_2;
	} else if (z <= 6.6e+123) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 5.2e+149) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = (y - a) * (x * (1.0 / z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if z <= -5.2e+104:
		tmp = t
	elif z <= -1.25e-88:
		tmp = t_2
	elif z <= -1.12e-148:
		tmp = t_1
	elif z <= 2.8e+81:
		tmp = t_2
	elif z <= 6.6e+123:
		tmp = (z * -t) / (a - z)
	elif z <= 5.2e+149:
		tmp = t_1
	elif z <= 6.5e+233:
		tmp = (y - a) * (x * (1.0 / z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (z <= -5.2e+104)
		tmp = t;
	elseif (z <= -1.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 2.8e+81)
		tmp = t_2;
	elseif (z <= 6.6e+123)
		tmp = Float64(Float64(z * Float64(-t)) / Float64(a - z));
	elseif (z <= 5.2e+149)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = Float64(Float64(y - a) * Float64(x * Float64(1.0 / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (z <= -5.2e+104)
		tmp = t;
	elseif (z <= -1.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 2.8e+81)
		tmp = t_2;
	elseif (z <= 6.6e+123)
		tmp = (z * -t) / (a - z);
	elseif (z <= 5.2e+149)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = (y - a) * (x * (1.0 / z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+104], t, If[LessEqual[z, -1.25e-88], t$95$2, If[LessEqual[z, -1.12e-148], t$95$1, If[LessEqual[z, 2.8e+81], t$95$2, If[LessEqual[z, 6.6e+123], N[(N[(z * (-t)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+149], t$95$1, If[LessEqual[z, 6.5e+233], N[(N[(y - a), $MachinePrecision] * N[(x * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.20000000000000001e104 or 6.50000000000000038e233 < z

   1. Initial program 59.5%

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

   2. Taylor expanded in z around inf 65.1%

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

   if -5.20000000000000001e104 < z < -1.25000000000000002e-88 or -1.1199999999999999e-148 < z < 2.79999999999999995e81

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 67.4%

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

      1. associate-/l* 70.0%

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

      2. associate-/r/ 72.3%

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

   4. Simplified 72.3%

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

   if -1.25000000000000002e-88 < z < -1.1199999999999999e-148 or 6.60000000000000006e123 < z < 5.19999999999999957e149

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 67.8%

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

      3. associate-/l* 72.4%

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

      4. associate-/r/ 72.3%

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

   4. Simplified 72.3%

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

   if 2.79999999999999995e81 < z < 6.60000000000000006e123

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 60.3%

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

      1. associate-/l* 75.7%

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

   4. Simplified 75.7%

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

   5. Taylor expanded in y around 0 59.8%

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

      1. associate-*r/ 59.8%

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

      2. associate-*r* 59.8%

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

      3. neg-mul-1 59.8%

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

   7. Simplified 59.8%

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

   if 5.19999999999999957e149 < z < 6.50000000000000038e233

   1. Initial program 52.8%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in z around inf 29.6%

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

      1. associate-*r/ 29.6%

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

      2. mul-1-neg 29.6%

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

      3. sub-neg 29.6%

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

      4. mul-1-neg 29.6%

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

   7. Simplified 29.6%

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

   8. Taylor expanded in x around inf 29.6%

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

      1. div-inv 29.4%

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

      2. *-commutative 29.4%

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

      3. associate-*l* 61.2%

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

   10. Applied egg-rr 61.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+81}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\left(y - a\right) \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 36.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2700000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -2.9e-69)
     t_1
     (if (<= y -4.8e-136)
       x
       (if (<= y -4.2e-143)
         (/ (* y t) a)
         (if (<= y -4.1e-259)
           t
           (if (<= y -5.4e-275)
             x
             (if (<= y 1.05e-14) t (if (<= y 2700000.0) 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 <= -2.9e-69) {
		tmp = t_1;
	} else if (y <= -4.8e-136) {
		tmp = x;
	} else if (y <= -4.2e-143) {
		tmp = (y * t) / a;
	} else if (y <= -4.1e-259) {
		tmp = t;
	} else if (y <= -5.4e-275) {
		tmp = x;
	} else if (y <= 1.05e-14) {
		tmp = t;
	} else if (y <= 2700000.0) {
		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 <= (-2.9d-69)) then
        tmp = t_1
    else if (y <= (-4.8d-136)) then
        tmp = x
    else if (y <= (-4.2d-143)) then
        tmp = (y * t) / a
    else if (y <= (-4.1d-259)) then
        tmp = t
    else if (y <= (-5.4d-275)) then
        tmp = x
    else if (y <= 1.05d-14) then
        tmp = t
    else if (y <= 2700000.0d0) 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 <= -2.9e-69) {
		tmp = t_1;
	} else if (y <= -4.8e-136) {
		tmp = x;
	} else if (y <= -4.2e-143) {
		tmp = (y * t) / a;
	} else if (y <= -4.1e-259) {
		tmp = t;
	} else if (y <= -5.4e-275) {
		tmp = x;
	} else if (y <= 1.05e-14) {
		tmp = t;
	} else if (y <= 2700000.0) {
		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 <= -2.9e-69:
		tmp = t_1
	elif y <= -4.8e-136:
		tmp = x
	elif y <= -4.2e-143:
		tmp = (y * t) / a
	elif y <= -4.1e-259:
		tmp = t
	elif y <= -5.4e-275:
		tmp = x
	elif y <= 1.05e-14:
		tmp = t
	elif y <= 2700000.0:
		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 <= -2.9e-69)
		tmp = t_1;
	elseif (y <= -4.8e-136)
		tmp = x;
	elseif (y <= -4.2e-143)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= -4.1e-259)
		tmp = t;
	elseif (y <= -5.4e-275)
		tmp = x;
	elseif (y <= 1.05e-14)
		tmp = t;
	elseif (y <= 2700000.0)
		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 <= -2.9e-69)
		tmp = t_1;
	elseif (y <= -4.8e-136)
		tmp = x;
	elseif (y <= -4.2e-143)
		tmp = (y * t) / a;
	elseif (y <= -4.1e-259)
		tmp = t;
	elseif (y <= -5.4e-275)
		tmp = x;
	elseif (y <= 1.05e-14)
		tmp = t;
	elseif (y <= 2700000.0)
		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, -2.9e-69], t$95$1, If[LessEqual[y, -4.8e-136], x, If[LessEqual[y, -4.2e-143], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -4.1e-259], t, If[LessEqual[y, -5.4e-275], x, If[LessEqual[y, 1.05e-14], t, If[LessEqual[y, 2700000.0], x, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.8999999999999998e-69 or 2.7e6 < y

   1. Initial program 81.9%

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

   2. Taylor expanded in x around 0 40.1%

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

      1. associate-/l* 48.5%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in y around inf 32.0%

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

      1. associate-/l* 37.3%

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

   7. Simplified 37.3%

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

      1. div-inv 37.3%

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

      2. clear-num 37.3%

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

   9. Applied egg-rr 37.3%

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

   if -2.8999999999999998e-69 < y < -4.7999999999999997e-136 or -4.0999999999999998e-259 < y < -5.39999999999999987e-275 or 1.0499999999999999e-14 < y < 2.7e6

   1. Initial program 84.0%

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

   2. Taylor expanded in a around inf 58.4%

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

   if -4.7999999999999997e-136 < y < -4.2000000000000002e-143

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 80.9%

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

      1. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 61.7%

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

   if -4.2000000000000002e-143 < y < -4.0999999999999998e-259 or -5.39999999999999987e-275 < y < 1.0499999999999999e-14

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 49.8%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2700000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 45.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -5.4e+104)
     t
     (if (<= z -1.45e-88)
       t_1
       (if (<= z -1.12e-148)
         (/ y (/ z (- x t)))
         (if (<= z 6.5e+71)
           t_1
           (if (<= z 1.6e+124)
             t
             (if (<= z 1.6e+150)
               (* t (/ y (- a z)))
               (if (<= z 6.5e+233) (* x (/ (- y a) z)) 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 <= -5.4e+104) {
		tmp = t;
	} else if (z <= -1.45e-88) {
		tmp = t_1;
	} else if (z <= -1.12e-148) {
		tmp = y / (z / (x - t));
	} else if (z <= 6.5e+71) {
		tmp = t_1;
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 1.6e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} 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 <= (-5.4d+104)) then
        tmp = t
    else if (z <= (-1.45d-88)) then
        tmp = t_1
    else if (z <= (-1.12d-148)) then
        tmp = y / (z / (x - t))
    else if (z <= 6.5d+71) then
        tmp = t_1
    else if (z <= 1.6d+124) then
        tmp = t
    else if (z <= 1.6d+150) then
        tmp = t * (y / (a - z))
    else if (z <= 6.5d+233) then
        tmp = x * ((y - a) / z)
    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 <= -5.4e+104) {
		tmp = t;
	} else if (z <= -1.45e-88) {
		tmp = t_1;
	} else if (z <= -1.12e-148) {
		tmp = y / (z / (x - t));
	} else if (z <= 6.5e+71) {
		tmp = t_1;
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 1.6e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5.4e+104:
		tmp = t
	elif z <= -1.45e-88:
		tmp = t_1
	elif z <= -1.12e-148:
		tmp = y / (z / (x - t))
	elif z <= 6.5e+71:
		tmp = t_1
	elif z <= 1.6e+124:
		tmp = t
	elif z <= 1.6e+150:
		tmp = t * (y / (a - z))
	elif z <= 6.5e+233:
		tmp = x * ((y - a) / z)
	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 <= -5.4e+104)
		tmp = t;
	elseif (z <= -1.45e-88)
		tmp = t_1;
	elseif (z <= -1.12e-148)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	elseif (z <= 6.5e+71)
		tmp = t_1;
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 1.6e+150)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6.5e+233)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	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 <= -5.4e+104)
		tmp = t;
	elseif (z <= -1.45e-88)
		tmp = t_1;
	elseif (z <= -1.12e-148)
		tmp = y / (z / (x - t));
	elseif (z <= 6.5e+71)
		tmp = t_1;
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 1.6e+150)
		tmp = t * (y / (a - z));
	elseif (z <= 6.5e+233)
		tmp = x * ((y - a) / z);
	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, -5.4e+104], t, If[LessEqual[z, -1.45e-88], t$95$1, If[LessEqual[z, -1.12e-148], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+71], t$95$1, If[LessEqual[z, 1.6e+124], t, If[LessEqual[z, 1.6e+150], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+233], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.39999999999999969e104 or 6.49999999999999954e71 < z < 1.59999999999999996e124 or 6.50000000000000038e233 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 61.1%

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

   if -5.39999999999999969e104 < z < -1.4500000000000001e-88 or -1.1199999999999999e-148 < z < 6.49999999999999954e71

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 54.5%

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

   if -1.4500000000000001e-88 < z < -1.1199999999999999e-148

   1. Initial program 87.2%

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

   2. Taylor expanded in y around inf 67.9%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. associate-/l* 61.2%

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

      2. sub-neg 61.2%

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

      3. neg-mul-1 61.2%

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

      4. neg-mul-1 61.2%

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

      5. remove-double-neg 61.2%

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

   5. Simplified 61.2%

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

   if 1.59999999999999996e124 < z < 1.60000000000000008e150

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 21.6%

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

      1. associate-/l* 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in y around inf 21.6%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

      1. div-inv 52.8%

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

      2. clear-num 53.0%

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

   9. Applied egg-rr 53.0%

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

   if 1.60000000000000008e150 < z < 6.50000000000000038e233

   1. Initial program 52.8%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in z around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. sub-neg 60.0%

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

      3. mul-1-neg 60.0%

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

   7. Simplified 60.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{z}{x - t}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+98}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ z (- x t)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -7e+104)
     t
     (if (<= z -1.25e-88)
       t_2
       (if (<= z -1.12e-148)
         t_1
         (if (<= z 5.2e+71)
           t_2
           (if (<= z 7e+98)
             (/ (* z (- t)) (- a z))
             (if (<= z 6.8e+110)
               t_1
               (if (<= z 6.5e+233) (* x (/ (- y a) z)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z / (x - t));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7e+104) {
		tmp = t;
	} else if (z <= -1.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 5.2e+71) {
		tmp = t_2;
	} else if (z <= 7e+98) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 6.8e+110) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y / (z / (x - t))
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-7d+104)) then
        tmp = t
    else if (z <= (-1.25d-88)) then
        tmp = t_2
    else if (z <= (-1.12d-148)) then
        tmp = t_1
    else if (z <= 5.2d+71) then
        tmp = t_2
    else if (z <= 7d+98) then
        tmp = (z * -t) / (a - z)
    else if (z <= 6.8d+110) then
        tmp = t_1
    else if (z <= 6.5d+233) then
        tmp = x * ((y - a) / z)
    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 = y / (z / (x - t));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7e+104) {
		tmp = t;
	} else if (z <= -1.25e-88) {
		tmp = t_2;
	} else if (z <= -1.12e-148) {
		tmp = t_1;
	} else if (z <= 5.2e+71) {
		tmp = t_2;
	} else if (z <= 7e+98) {
		tmp = (z * -t) / (a - z);
	} else if (z <= 6.8e+110) {
		tmp = t_1;
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z / (x - t))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -7e+104:
		tmp = t
	elif z <= -1.25e-88:
		tmp = t_2
	elif z <= -1.12e-148:
		tmp = t_1
	elif z <= 5.2e+71:
		tmp = t_2
	elif z <= 7e+98:
		tmp = (z * -t) / (a - z)
	elif z <= 6.8e+110:
		tmp = t_1
	elif z <= 6.5e+233:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z / Float64(x - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -7e+104)
		tmp = t;
	elseif (z <= -1.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 5.2e+71)
		tmp = t_2;
	elseif (z <= 7e+98)
		tmp = Float64(Float64(z * Float64(-t)) / Float64(a - z));
	elseif (z <= 6.8e+110)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z / (x - t));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -7e+104)
		tmp = t;
	elseif (z <= -1.25e-88)
		tmp = t_2;
	elseif (z <= -1.12e-148)
		tmp = t_1;
	elseif (z <= 5.2e+71)
		tmp = t_2;
	elseif (z <= 7e+98)
		tmp = (z * -t) / (a - z);
	elseif (z <= 6.8e+110)
		tmp = t_1;
	elseif (z <= 6.5e+233)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+104], t, If[LessEqual[z, -1.25e-88], t$95$2, If[LessEqual[z, -1.12e-148], t$95$1, If[LessEqual[z, 5.2e+71], t$95$2, If[LessEqual[z, 7e+98], N[(N[(z * (-t)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+110], t$95$1, If[LessEqual[z, 6.5e+233], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.0000000000000003e104 or 6.50000000000000038e233 < z

   1. Initial program 59.5%

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

   2. Taylor expanded in z around inf 65.1%

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

   if -7.0000000000000003e104 < z < -1.25000000000000002e-88 or -1.1199999999999999e-148 < z < 5.19999999999999983e71

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 54.5%

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

   if -1.25000000000000002e-88 < z < -1.1199999999999999e-148 or 7e98 < z < 6.8000000000000003e110

   1. Initial program 83.9%

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

   2. Taylor expanded in y around inf 68.0%

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

   3. Taylor expanded in z around inf 56.9%

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

      1. associate-/l* 62.2%

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

      2. sub-neg 62.2%

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

      3. neg-mul-1 62.2%

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

      4. neg-mul-1 62.2%

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

      5. remove-double-neg 62.2%

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

   5. Simplified 62.2%

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

   if 5.19999999999999983e71 < z < 7e98

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 86.8%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

   7. Simplified 73.6%

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

   if 6.8000000000000003e110 < z < 6.50000000000000038e233

   1. Initial program 63.7%

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

   2. Taylor expanded in x around inf 30.1%

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

      1. mul-1-neg 30.1%

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

      2. unsub-neg 30.1%

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

   4. Simplified 30.1%

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

   5. Taylor expanded in z around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. sub-neg 44.8%

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

      3. mul-1-neg 44.8%

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

   7. Simplified 44.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+98}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+110}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-216}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+149)
   x
   (if (<= a -9.5e-142)
     t
     (if (<= a -2.8e-206)
       (/ x (/ z y))
       (if (<= a -1.6e-216)
         (+ x (- t x))
         (if (<= a -5.5e-253)
           (/ (- t) (/ z y))
           (if (<= a -2.1e-278)
             t
             (if (<= a 2.62e-285)
               (* x (/ y z))
               (if (<= a 2.85e+82) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -9.5e-142) {
		tmp = t;
	} else if (a <= -2.8e-206) {
		tmp = x / (z / y);
	} else if (a <= -1.6e-216) {
		tmp = x + (t - x);
	} else if (a <= -5.5e-253) {
		tmp = -t / (z / y);
	} else if (a <= -2.1e-278) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = x * (y / z);
	} else if (a <= 2.85e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+149)) then
        tmp = x
    else if (a <= (-9.5d-142)) then
        tmp = t
    else if (a <= (-2.8d-206)) then
        tmp = x / (z / y)
    else if (a <= (-1.6d-216)) then
        tmp = x + (t - x)
    else if (a <= (-5.5d-253)) then
        tmp = -t / (z / y)
    else if (a <= (-2.1d-278)) then
        tmp = t
    else if (a <= 2.62d-285) then
        tmp = x * (y / z)
    else if (a <= 2.85d+82) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -9.5e-142) {
		tmp = t;
	} else if (a <= -2.8e-206) {
		tmp = x / (z / y);
	} else if (a <= -1.6e-216) {
		tmp = x + (t - x);
	} else if (a <= -5.5e-253) {
		tmp = -t / (z / y);
	} else if (a <= -2.1e-278) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = x * (y / z);
	} else if (a <= 2.85e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+149:
		tmp = x
	elif a <= -9.5e-142:
		tmp = t
	elif a <= -2.8e-206:
		tmp = x / (z / y)
	elif a <= -1.6e-216:
		tmp = x + (t - x)
	elif a <= -5.5e-253:
		tmp = -t / (z / y)
	elif a <= -2.1e-278:
		tmp = t
	elif a <= 2.62e-285:
		tmp = x * (y / z)
	elif a <= 2.85e+82:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -9.5e-142)
		tmp = t;
	elseif (a <= -2.8e-206)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= -1.6e-216)
		tmp = Float64(x + Float64(t - x));
	elseif (a <= -5.5e-253)
		tmp = Float64(Float64(-t) / Float64(z / y));
	elseif (a <= -2.1e-278)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.85e+82)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -9.5e-142)
		tmp = t;
	elseif (a <= -2.8e-206)
		tmp = x / (z / y);
	elseif (a <= -1.6e-216)
		tmp = x + (t - x);
	elseif (a <= -5.5e-253)
		tmp = -t / (z / y);
	elseif (a <= -2.1e-278)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = x * (y / z);
	elseif (a <= 2.85e+82)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+149], x, If[LessEqual[a, -9.5e-142], t, If[LessEqual[a, -2.8e-206], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-216], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-253], N[((-t) / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-278], t, If[LessEqual[a, 2.62e-285], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.85e+82], t, x]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.19999999999999974e149 or 2.85000000000000008e82 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 56.8%

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

   if -6.19999999999999974e149 < a < -9.49999999999999967e-142 or -5.49999999999999974e-253 < a < -2.10000000000000014e-278 or 2.62000000000000002e-285 < a < 2.85000000000000008e82

   1. Initial program 74.3%

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

   2. Taylor expanded in z around inf 34.8%

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

   if -9.49999999999999967e-142 < a < -2.8000000000000001e-206

   1. Initial program 64.7%

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

   2. Taylor expanded in x around inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. unsub-neg 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in a around 0 47.9%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   if -2.8000000000000001e-206 < a < -1.60000000000000013e-216

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -1.60000000000000013e-216 < a < -5.49999999999999974e-253

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 86.6%

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

      1. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in y around inf 86.1%

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

      1. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in a around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-/l* 75.2%

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

   10. Simplified 75.2%

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

   if -2.10000000000000014e-278 < a < 2.62000000000000002e-285

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in a around 0 58.9%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-216}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -950000000000:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+189}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= x -2.3e+80)
     t_1
     (if (<= x -950000000000.0)
       (* x (/ (- y) (- a z)))
       (if (<= x 4e+82)
         (/ t (/ (- a z) (- y z)))
         (if (<= x 1.85e+189)
           (/ x (/ z (- y a)))
           (if (<= x 7.5e+260) t_1 (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (x <= -2.3e+80) {
		tmp = t_1;
	} else if (x <= -950000000000.0) {
		tmp = x * (-y / (a - z));
	} else if (x <= 4e+82) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 1.85e+189) {
		tmp = x / (z / (y - a));
	} else if (x <= 7.5e+260) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (x <= (-2.3d+80)) then
        tmp = t_1
    else if (x <= (-950000000000.0d0)) then
        tmp = x * (-y / (a - z))
    else if (x <= 4d+82) then
        tmp = t / ((a - z) / (y - z))
    else if (x <= 1.85d+189) then
        tmp = x / (z / (y - a))
    else if (x <= 7.5d+260) then
        tmp = t_1
    else
        tmp = x * ((y - a) / 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 + ((t - x) * (y / a));
	double tmp;
	if (x <= -2.3e+80) {
		tmp = t_1;
	} else if (x <= -950000000000.0) {
		tmp = x * (-y / (a - z));
	} else if (x <= 4e+82) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 1.85e+189) {
		tmp = x / (z / (y - a));
	} else if (x <= 7.5e+260) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if x <= -2.3e+80:
		tmp = t_1
	elif x <= -950000000000.0:
		tmp = x * (-y / (a - z))
	elif x <= 4e+82:
		tmp = t / ((a - z) / (y - z))
	elif x <= 1.85e+189:
		tmp = x / (z / (y - a))
	elif x <= 7.5e+260:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (x <= -2.3e+80)
		tmp = t_1;
	elseif (x <= -950000000000.0)
		tmp = Float64(x * Float64(Float64(-y) / Float64(a - z)));
	elseif (x <= 4e+82)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (x <= 1.85e+189)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (x <= 7.5e+260)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (x <= -2.3e+80)
		tmp = t_1;
	elseif (x <= -950000000000.0)
		tmp = x * (-y / (a - z));
	elseif (x <= 4e+82)
		tmp = t / ((a - z) / (y - z));
	elseif (x <= 1.85e+189)
		tmp = x / (z / (y - a));
	elseif (x <= 7.5e+260)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+80], t$95$1, If[LessEqual[x, -950000000000.0], N[(x * N[((-y) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+82], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+189], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+260], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.30000000000000004e80 or 1.8500000000000001e189 < x < 7.49999999999999947e260

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0 54.2%

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

      1. associate-/l* 61.7%

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

      2. associate-/r/ 63.5%

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

   4. Simplified 63.5%

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

   if -2.30000000000000004e80 < x < -9.5e11

   1. Initial program 78.5%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. associate-*r/ 78.3%

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

      2. mul-1-neg 78.3%

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

   7. Simplified 78.3%

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

   if -9.5e11 < x < 3.9999999999999999e82

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if 3.9999999999999999e82 < x < 1.8500000000000001e189

   1. Initial program 69.7%

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

   2. Taylor expanded in x around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in z around inf 55.3%

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

      1. associate-*r/ 55.3%

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

      2. mul-1-neg 55.3%

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

      3. sub-neg 55.3%

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

      4. mul-1-neg 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in x around inf 55.3%

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

      1. associate-/l* 62.6%

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

   10. Simplified 62.6%

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

   if 7.49999999999999947e260 < x

   1. Initial program 45.6%

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

   2. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. sub-neg 62.0%

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

      3. mul-1-neg 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -950000000000:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+189}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+260}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 10: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -350000000000:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+190}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= x -4.1e+96)
     t_1
     (if (<= x -350000000000.0)
       (/ y (/ (- a z) (- t x)))
       (if (<= x 1.46e+82)
         (/ t (/ (- a z) (- y z)))
         (if (<= x 6.4e+190)
           (/ x (/ z (- y a)))
           (if (<= x 4.7e+260) t_1 (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (x <= -4.1e+96) {
		tmp = t_1;
	} else if (x <= -350000000000.0) {
		tmp = y / ((a - z) / (t - x));
	} else if (x <= 1.46e+82) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 6.4e+190) {
		tmp = x / (z / (y - a));
	} else if (x <= 4.7e+260) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (x <= (-4.1d+96)) then
        tmp = t_1
    else if (x <= (-350000000000.0d0)) then
        tmp = y / ((a - z) / (t - x))
    else if (x <= 1.46d+82) then
        tmp = t / ((a - z) / (y - z))
    else if (x <= 6.4d+190) then
        tmp = x / (z / (y - a))
    else if (x <= 4.7d+260) then
        tmp = t_1
    else
        tmp = x * ((y - a) / 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 + ((t - x) * (y / a));
	double tmp;
	if (x <= -4.1e+96) {
		tmp = t_1;
	} else if (x <= -350000000000.0) {
		tmp = y / ((a - z) / (t - x));
	} else if (x <= 1.46e+82) {
		tmp = t / ((a - z) / (y - z));
	} else if (x <= 6.4e+190) {
		tmp = x / (z / (y - a));
	} else if (x <= 4.7e+260) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if x <= -4.1e+96:
		tmp = t_1
	elif x <= -350000000000.0:
		tmp = y / ((a - z) / (t - x))
	elif x <= 1.46e+82:
		tmp = t / ((a - z) / (y - z))
	elif x <= 6.4e+190:
		tmp = x / (z / (y - a))
	elif x <= 4.7e+260:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (x <= -4.1e+96)
		tmp = t_1;
	elseif (x <= -350000000000.0)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (x <= 1.46e+82)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (x <= 6.4e+190)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (x <= 4.7e+260)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (x <= -4.1e+96)
		tmp = t_1;
	elseif (x <= -350000000000.0)
		tmp = y / ((a - z) / (t - x));
	elseif (x <= 1.46e+82)
		tmp = t / ((a - z) / (y - z));
	elseif (x <= 6.4e+190)
		tmp = x / (z / (y - a));
	elseif (x <= 4.7e+260)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+96], t$95$1, If[LessEqual[x, -350000000000.0], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.46e+82], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+190], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e+260], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.09999999999999998e96 or 6.4000000000000001e190 < x < 4.70000000000000021e260

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0 54.2%

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

      1. associate-/l* 61.7%

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

      2. associate-/r/ 63.5%

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

   4. Simplified 63.5%

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

   if -4.09999999999999998e96 < x < -3.5e11

   1. Initial program 78.5%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. div-sub 78.5%

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

      2. associate-*r/ 57.5%

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

      3. associate-/l* 78.5%

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

   4. Simplified 78.5%

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

   if -3.5e11 < x < 1.4599999999999999e82

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if 1.4599999999999999e82 < x < 6.4000000000000001e190

   1. Initial program 69.7%

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

   2. Taylor expanded in x around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in z around inf 55.3%

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

      1. associate-*r/ 55.3%

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

      2. mul-1-neg 55.3%

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

      3. sub-neg 55.3%

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

      4. mul-1-neg 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in x around inf 55.3%

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

      1. associate-/l* 62.6%

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

   10. Simplified 62.6%

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

   if 4.70000000000000021e260 < x

   1. Initial program 45.6%

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

   2. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. sub-neg 62.0%

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

      3. mul-1-neg 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -350000000000:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+190}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+260}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 11: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{if}\;x \leq -4:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-130}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z))))
        (t_2 (* x (+ (/ (- z y) (- a z)) 1.0))))
   (if (<= x -4.0)
     t_2
     (if (<= x 1.4e-185)
       t_1
       (if (<= x 7.2e-130)
         (+ x (* (- z y) (/ (- x t) a)))
         (if (<= x 4.5e+51) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double t_2 = x * (((z - y) / (a - z)) + 1.0);
	double tmp;
	if (x <= -4.0) {
		tmp = t_2;
	} else if (x <= 1.4e-185) {
		tmp = t_1;
	} else if (x <= 7.2e-130) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (x <= 4.5e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    t_2 = x * (((z - y) / (a - z)) + 1.0d0)
    if (x <= (-4.0d0)) then
        tmp = t_2
    else if (x <= 1.4d-185) then
        tmp = t_1
    else if (x <= 7.2d-130) then
        tmp = x + ((z - y) * ((x - t) / a))
    else if (x <= 4.5d+51) 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 / ((a - z) / (y - z));
	double t_2 = x * (((z - y) / (a - z)) + 1.0);
	double tmp;
	if (x <= -4.0) {
		tmp = t_2;
	} else if (x <= 1.4e-185) {
		tmp = t_1;
	} else if (x <= 7.2e-130) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (x <= 4.5e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	t_2 = x * (((z - y) / (a - z)) + 1.0)
	tmp = 0
	if x <= -4.0:
		tmp = t_2
	elif x <= 1.4e-185:
		tmp = t_1
	elif x <= 7.2e-130:
		tmp = x + ((z - y) * ((x - t) / a))
	elif x <= 4.5e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	t_2 = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0))
	tmp = 0.0
	if (x <= -4.0)
		tmp = t_2;
	elseif (x <= 1.4e-185)
		tmp = t_1;
	elseif (x <= 7.2e-130)
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)));
	elseif (x <= 4.5e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	t_2 = x * (((z - y) / (a - z)) + 1.0);
	tmp = 0.0;
	if (x <= -4.0)
		tmp = t_2;
	elseif (x <= 1.4e-185)
		tmp = t_1;
	elseif (x <= 7.2e-130)
		tmp = x + ((z - y) * ((x - t) / a));
	elseif (x <= 4.5e+51)
		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[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.0], t$95$2, If[LessEqual[x, 1.4e-185], t$95$1, If[LessEqual[x, 7.2e-130], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4 or 4.5e51 < x

   1. Initial program 70.8%

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

   2. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   4. Simplified 64.9%

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

   if -4 < x < 1.39999999999999996e-185 or 7.2000000000000003e-130 < x < 4.5e51

   1. Initial program 86.3%

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

   2. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 75.7%

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

   4. Simplified 75.7%

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

   if 1.39999999999999996e-185 < x < 7.2000000000000003e-130

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf 78.8%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 78.9%

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

   4. Simplified 78.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-185}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-130}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \end{array} \]

Alternative 12: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -8300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-149}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 225000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -8300000000.0)
     t_1
     (if (<= z -1.7e-88)
       (+ x (* (- z y) (/ (- x t) a)))
       (if (<= z -3.35e-149)
         (/ (* y (- t x)) (- a z))
         (if (<= z 225000.0) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -8300000000.0) {
		tmp = t_1;
	} else if (z <= -1.7e-88) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (z <= -3.35e-149) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 225000.0) {
		tmp = x + ((t - x) * (y / 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 + ((x - t) / (z / (y - a)))
    if (z <= (-8300000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.7d-88)) then
        tmp = x + ((z - y) * ((x - t) / a))
    else if (z <= (-3.35d-149)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 225000.0d0) then
        tmp = x + ((t - x) * (y / 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 + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -8300000000.0) {
		tmp = t_1;
	} else if (z <= -1.7e-88) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (z <= -3.35e-149) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 225000.0) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -8300000000.0:
		tmp = t_1
	elif z <= -1.7e-88:
		tmp = x + ((z - y) * ((x - t) / a))
	elif z <= -3.35e-149:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 225000.0:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -8300000000.0)
		tmp = t_1;
	elseif (z <= -1.7e-88)
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)));
	elseif (z <= -3.35e-149)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 225000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -8300000000.0)
		tmp = t_1;
	elseif (z <= -1.7e-88)
		tmp = x + ((z - y) * ((x - t) / a));
	elseif (z <= -3.35e-149)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 225000.0)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8300000000.0], t$95$1, If[LessEqual[z, -1.7e-88], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.35e-149], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 225000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.3e9 or 225000 < z

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf 61.2%

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

      1. associate--l+ 61.2%

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

      2. distribute-lft-out-- 61.2%

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

      3. div-sub 61.2%

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

      4. mul-1-neg 61.2%

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

      5. unsub-neg 61.2%

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

      6. distribute-rgt-out-- 61.3%

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

      7. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

   if -8.3e9 < z < -1.69999999999999987e-88

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf 71.2%

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

      1. associate-/l* 75.3%

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

      2. associate-/r/ 75.4%

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

   4. Simplified 75.4%

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

   if -1.69999999999999987e-88 < z < -3.3499999999999998e-149

   1. Initial program 87.2%

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

   2. Taylor expanded in y around -inf 74.1%

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

   if -3.3499999999999998e-149 < z < 225000

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 79.3%

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

      1. associate-/l* 80.6%

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

      2. associate-/r/ 84.0%

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

   4. Simplified 84.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8300000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-149}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 225000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 13: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+104)
   t
   (if (<= z 1.6e+71)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.6e+124)
       t
       (if (<= z 1.6e+149)
         (* t (/ y (- a z)))
         (if (<= z 6.5e+233) (/ x (/ z (- y a))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+104) {
		tmp = t;
	} else if (z <= 1.6e+71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 1.6e+149) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x / (z / (y - 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 <= (-4.6d+104)) then
        tmp = t
    else if (z <= 1.6d+71) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d+124) then
        tmp = t
    else if (z <= 1.6d+149) then
        tmp = t * (y / (a - z))
    else if (z <= 6.5d+233) then
        tmp = x / (z / (y - 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 <= -4.6e+104) {
		tmp = t;
	} else if (z <= 1.6e+71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 1.6e+149) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+104:
		tmp = t
	elif z <= 1.6e+71:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e+124:
		tmp = t
	elif z <= 1.6e+149:
		tmp = t * (y / (a - z))
	elif z <= 6.5e+233:
		tmp = x / (z / (y - a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+104)
		tmp = t;
	elseif (z <= 1.6e+71)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 1.6e+149)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6.5e+233)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+104)
		tmp = t;
	elseif (z <= 1.6e+71)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 1.6e+149)
		tmp = t * (y / (a - z));
	elseif (z <= 6.5e+233)
		tmp = x / (z / (y - a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+104], t, If[LessEqual[z, 1.6e+71], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+124], t, If[LessEqual[z, 1.6e+149], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+233], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.59999999999999969e104 or 1.60000000000000012e71 < z < 1.59999999999999996e124 or 6.50000000000000038e233 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 61.1%

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

   if -4.59999999999999969e104 < z < 1.60000000000000012e71

   1. Initial program 88.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around 0 51.6%

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

   if 1.59999999999999996e124 < z < 1.6000000000000001e149

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 21.6%

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

      1. associate-/l* 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in y around inf 21.6%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

      1. div-inv 52.8%

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

      2. clear-num 53.0%

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

   9. Applied egg-rr 53.0%

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

   if 1.6000000000000001e149 < z < 6.50000000000000038e233

   1. Initial program 52.8%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in z around inf 29.6%

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

      1. associate-*r/ 29.6%

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

      2. mul-1-neg 29.6%

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

      3. sub-neg 29.6%

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

      4. mul-1-neg 29.6%

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

   7. Simplified 29.6%

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

   8. Taylor expanded in x around inf 29.6%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+104)
   t
   (if (<= z 9e+68)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.6e+124)
       t
       (if (<= z 4e+150)
         (* t (/ y (- a z)))
         (if (<= z 6.5e+233) (* x (/ (- y a) z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+104) {
		tmp = t;
	} else if (z <= 9e+68) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 4e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} 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 <= (-4.9d+104)) then
        tmp = t
    else if (z <= 9d+68) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d+124) then
        tmp = t
    else if (z <= 4d+150) then
        tmp = t * (y / (a - z))
    else if (z <= 6.5d+233) then
        tmp = x * ((y - a) / z)
    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 <= -4.9e+104) {
		tmp = t;
	} else if (z <= 9e+68) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 4e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e+104:
		tmp = t
	elif z <= 9e+68:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e+124:
		tmp = t
	elif z <= 4e+150:
		tmp = t * (y / (a - z))
	elif z <= 6.5e+233:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+104)
		tmp = t;
	elseif (z <= 9e+68)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 4e+150)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6.5e+233)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e+104)
		tmp = t;
	elseif (z <= 9e+68)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 4e+150)
		tmp = t * (y / (a - z));
	elseif (z <= 6.5e+233)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+104], t, If[LessEqual[z, 9e+68], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+124], t, If[LessEqual[z, 4e+150], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+233], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.89999999999999985e104 or 9.0000000000000007e68 < z < 1.59999999999999996e124 or 6.50000000000000038e233 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 61.1%

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

   if -4.89999999999999985e104 < z < 9.0000000000000007e68

   1. Initial program 88.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around 0 51.6%

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

   if 1.59999999999999996e124 < z < 3.99999999999999992e150

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 21.6%

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

      1. associate-/l* 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in y around inf 21.6%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

      1. div-inv 52.8%

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

      2. clear-num 53.0%

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

   9. Applied egg-rr 53.0%

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

   if 3.99999999999999992e150 < z < 6.50000000000000038e233

   1. Initial program 52.8%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in z around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. sub-neg 60.0%

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

      3. mul-1-neg 60.0%

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

   7. Simplified 60.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-146}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-275}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -6.2e+149)
     x
     (if (<= a -4.9e-146)
       t
       (if (<= a -5.5e-203)
         t_1
         (if (<= a -4.8e-275)
           t
           (if (<= a 2.62e-285) t_1 (if (<= a 2.35e+82) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -4.9e-146) {
		tmp = t;
	} else if (a <= -5.5e-203) {
		tmp = t_1;
	} else if (a <= -4.8e-275) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = t_1;
	} else if (a <= 2.35e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-6.2d+149)) then
        tmp = x
    else if (a <= (-4.9d-146)) then
        tmp = t
    else if (a <= (-5.5d-203)) then
        tmp = t_1
    else if (a <= (-4.8d-275)) then
        tmp = t
    else if (a <= 2.62d-285) then
        tmp = t_1
    else if (a <= 2.35d+82) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -4.9e-146) {
		tmp = t;
	} else if (a <= -5.5e-203) {
		tmp = t_1;
	} else if (a <= -4.8e-275) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = t_1;
	} else if (a <= 2.35e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -6.2e+149:
		tmp = x
	elif a <= -4.9e-146:
		tmp = t
	elif a <= -5.5e-203:
		tmp = t_1
	elif a <= -4.8e-275:
		tmp = t
	elif a <= 2.62e-285:
		tmp = t_1
	elif a <= 2.35e+82:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -4.9e-146)
		tmp = t;
	elseif (a <= -5.5e-203)
		tmp = t_1;
	elseif (a <= -4.8e-275)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = t_1;
	elseif (a <= 2.35e+82)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -4.9e-146)
		tmp = t;
	elseif (a <= -5.5e-203)
		tmp = t_1;
	elseif (a <= -4.8e-275)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = t_1;
	elseif (a <= 2.35e+82)
		tmp = t;
	else
		tmp = x;
	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[a, -6.2e+149], x, If[LessEqual[a, -4.9e-146], t, If[LessEqual[a, -5.5e-203], t$95$1, If[LessEqual[a, -4.8e-275], t, If[LessEqual[a, 2.62e-285], t$95$1, If[LessEqual[a, 2.35e+82], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999974e149 or 2.35e82 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 56.8%

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

   if -6.19999999999999974e149 < a < -4.9000000000000004e-146 or -5.5000000000000002e-203 < a < -4.79999999999999981e-275 or 2.62000000000000002e-285 < a < 2.35e82

   1. Initial program 75.9%

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

   2. Taylor expanded in z around inf 34.7%

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

   if -4.9000000000000004e-146 < a < -5.5000000000000002e-203 or -4.79999999999999981e-275 < a < 2.62000000000000002e-285

   1. Initial program 79.6%

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

   2. Taylor expanded in x around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in a around 0 61.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-146}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-275}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-145}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-276}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+149)
   x
   (if (<= a -1.45e-145)
     t
     (if (<= a -1.15e-204)
       (/ x (/ z y))
       (if (<= a -3.6e-276)
         t
         (if (<= a 2.62e-285) (* x (/ y z)) (if (<= a 8.5e+81) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -1.45e-145) {
		tmp = t;
	} else if (a <= -1.15e-204) {
		tmp = x / (z / y);
	} else if (a <= -3.6e-276) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = x * (y / z);
	} else if (a <= 8.5e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+149)) then
        tmp = x
    else if (a <= (-1.45d-145)) then
        tmp = t
    else if (a <= (-1.15d-204)) then
        tmp = x / (z / y)
    else if (a <= (-3.6d-276)) then
        tmp = t
    else if (a <= 2.62d-285) then
        tmp = x * (y / z)
    else if (a <= 8.5d+81) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= -1.45e-145) {
		tmp = t;
	} else if (a <= -1.15e-204) {
		tmp = x / (z / y);
	} else if (a <= -3.6e-276) {
		tmp = t;
	} else if (a <= 2.62e-285) {
		tmp = x * (y / z);
	} else if (a <= 8.5e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+149:
		tmp = x
	elif a <= -1.45e-145:
		tmp = t
	elif a <= -1.15e-204:
		tmp = x / (z / y)
	elif a <= -3.6e-276:
		tmp = t
	elif a <= 2.62e-285:
		tmp = x * (y / z)
	elif a <= 8.5e+81:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -1.45e-145)
		tmp = t;
	elseif (a <= -1.15e-204)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= -3.6e-276)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 8.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= -1.45e-145)
		tmp = t;
	elseif (a <= -1.15e-204)
		tmp = x / (z / y);
	elseif (a <= -3.6e-276)
		tmp = t;
	elseif (a <= 2.62e-285)
		tmp = x * (y / z);
	elseif (a <= 8.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+149], x, If[LessEqual[a, -1.45e-145], t, If[LessEqual[a, -1.15e-204], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e-276], t, If[LessEqual[a, 2.62e-285], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+81], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.19999999999999974e149 or 8.49999999999999986e81 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 56.8%

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

   if -6.19999999999999974e149 < a < -1.44999999999999992e-145 or -1.15e-204 < a < -3.59999999999999994e-276 or 2.62000000000000002e-285 < a < 8.49999999999999986e81

   1. Initial program 75.9%

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

   2. Taylor expanded in z around inf 34.7%

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

   if -1.44999999999999992e-145 < a < -1.15e-204

   1. Initial program 64.7%

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

   2. Taylor expanded in x around inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. unsub-neg 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in a around 0 47.9%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   if -3.59999999999999994e-276 < a < 2.62000000000000002e-285

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in a around 0 58.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-145}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-276}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.62 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+104)
   t
   (if (<= z 6.6e+69)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.6e+124)
       t
       (if (<= z 2e+150)
         (* t (/ y (- a z)))
         (if (<= z 6.5e+233) (/ x (/ z y)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+104) {
		tmp = t;
	} else if (z <= 6.6e+69) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 2e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x / (z / y);
	} 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 <= (-4.6d+104)) then
        tmp = t
    else if (z <= 6.6d+69) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d+124) then
        tmp = t
    else if (z <= 2d+150) then
        tmp = t * (y / (a - z))
    else if (z <= 6.5d+233) then
        tmp = x / (z / y)
    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 <= -4.6e+104) {
		tmp = t;
	} else if (z <= 6.6e+69) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+124) {
		tmp = t;
	} else if (z <= 2e+150) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.5e+233) {
		tmp = x / (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+104:
		tmp = t
	elif z <= 6.6e+69:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e+124:
		tmp = t
	elif z <= 2e+150:
		tmp = t * (y / (a - z))
	elif z <= 6.5e+233:
		tmp = x / (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+104)
		tmp = t;
	elseif (z <= 6.6e+69)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 2e+150)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6.5e+233)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+104)
		tmp = t;
	elseif (z <= 6.6e+69)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e+124)
		tmp = t;
	elseif (z <= 2e+150)
		tmp = t * (y / (a - z));
	elseif (z <= 6.5e+233)
		tmp = x / (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+104], t, If[LessEqual[z, 6.6e+69], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+124], t, If[LessEqual[z, 2e+150], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+233], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.59999999999999969e104 or 6.5999999999999997e69 < z < 1.59999999999999996e124 or 6.50000000000000038e233 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 61.1%

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

   if -4.59999999999999969e104 < z < 6.5999999999999997e69

   1. Initial program 88.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around 0 51.6%

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

   if 1.59999999999999996e124 < z < 1.99999999999999996e150

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 21.6%

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

      1. associate-/l* 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in y around inf 21.6%

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

      1. associate-/l* 53.0%

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

   7. Simplified 53.0%

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

      1. div-inv 52.8%

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

      2. clear-num 53.0%

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

   9. Applied egg-rr 53.0%

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

   if 1.99999999999999996e150 < z < 6.50000000000000038e233

   1. Initial program 52.8%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in a around 0 17.4%

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

      1. associate-/l* 33.7%

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

   7. Simplified 33.7%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8500000000 \lor \neg \left(x \leq 1.6 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8500000000.0) (not (<= x 1.6e+49)))
   (* x (+ (/ (- z y) (- a z)) 1.0))
   (/ t (/ (- a z) (- y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8500000000.0) || !(x <= 1.6e+49)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t / ((a - z) / (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 ((x <= (-8500000000.0d0)) .or. (.not. (x <= 1.6d+49))) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else
        tmp = t / ((a - z) / (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 ((x <= -8500000000.0) || !(x <= 1.6e+49)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8500000000.0) or not (x <= 1.6e+49):
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8500000000.0) || !(x <= 1.6e+49))
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8500000000.0) || ~((x <= 1.6e+49)))
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8500000000.0], N[Not[LessEqual[x, 1.6e+49]], $MachinePrecision]], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e9 or 1.60000000000000007e49 < x

   1. Initial program 70.8%

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

   2. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   4. Simplified 64.9%

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

   if -8.5e9 < x < 1.60000000000000007e49

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 59.0%

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

      1. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8500000000 \lor \neg \left(x \leq 1.6 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 19: 37.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+149) x (if (<= a 2.7e+83) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= 2.7e+83) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+149)) then
        tmp = x
    else if (a <= 2.7d+83) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+149) {
		tmp = x;
	} else if (a <= 2.7e+83) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+149:
		tmp = x
	elif a <= 2.7e+83:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= 2.7e+83)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+149)
		tmp = x;
	elseif (a <= 2.7e+83)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+149], x, If[LessEqual[a, 2.7e+83], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999974e149 or 2.70000000000000007e83 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 56.8%

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

   if -6.19999999999999974e149 < a < 2.70000000000000007e83

   1. Initial program 76.4%

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

   2. Taylor expanded in z around inf 32.5%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 24.7% 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 80.0%

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

2. Taylor expanded in z around inf 26.7%

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

3. Final simplification 26.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))