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

Percentage Accurate: 67.8% → 87.9%

Time: 35.8s

Alternatives: 30

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+74} \lor \neg \left(t \leq 2.7 \cdot 10^{+75}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e+74) (not (<= t 2.7e+75)))
   (+ y (/ (- x y) (/ t (- z a))))
   (fma (/ (- z t) (- a t)) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+74) || !(t <= 2.7e+75)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e+74) || !(t <= 2.7e+75))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e+74], N[Not[LessEqual[t, 2.7e+75]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e74 or 2.69999999999999998e75 < t

   1. Initial program 33.5%

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

      1. associate-*l/ 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in t around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. associate-*r/ 69.7%

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

      3. associate-*r/ 69.7%

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

      4. div-sub 69.7%

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

      5. distribute-lft-out-- 69.7%

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

      6. associate-*r/ 69.7%

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

      7. mul-1-neg 69.7%

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

      8. unsub-neg 69.7%

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

      9. distribute-rgt-out-- 71.0%

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

      10. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   if -7.5e74 < t < 2.69999999999999998e75

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-/l* 91.3%

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

      4. associate-/r/ 91.4%

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

      5. fma-def 91.4%

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

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+74} \lor \neg \left(t \leq 2.7 \cdot 10^{+75}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 44.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{a - t}\\ t_2 := \frac{-y}{\frac{t}{z - t}}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -102:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) (- a t)))) (t_2 (/ (- y) (/ t (- z t)))))
   (if (<= a -4.5e+91)
     x
     (if (<= a -8.5e+35)
       (/ (- t) (/ (- a t) y))
       (if (<= a -102.0)
         x
         (if (<= a -7.6e-134)
           t_2
           (if (<= a -1.02e-210)
             t_1
             (if (<= a 2.7e-234)
               t_2
               (if (<= a 1.04e-181)
                 (/ x (/ t (- z a)))
                 (if (<= a 5.8e-123)
                   t_2
                   (if (<= a 6.8e-53)
                     t_1
                     (if (<= a 5.6e-12)
                       x
                       (if (<= a 2.8e+128)
                         (/ z (/ a (- y x)))
                         (* x (+ (/ t (- a t)) 1.0)))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-z / (a - t));
	double t_2 = -y / (t / (z - t));
	double tmp;
	if (a <= -4.5e+91) {
		tmp = x;
	} else if (a <= -8.5e+35) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -102.0) {
		tmp = x;
	} else if (a <= -7.6e-134) {
		tmp = t_2;
	} else if (a <= -1.02e-210) {
		tmp = t_1;
	} else if (a <= 2.7e-234) {
		tmp = t_2;
	} else if (a <= 1.04e-181) {
		tmp = x / (t / (z - a));
	} else if (a <= 5.8e-123) {
		tmp = t_2;
	} else if (a <= 6.8e-53) {
		tmp = t_1;
	} else if (a <= 5.6e-12) {
		tmp = x;
	} else if (a <= 2.8e+128) {
		tmp = z / (a / (y - x));
	} else {
		tmp = x * ((t / (a - t)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (-z / (a - t))
    t_2 = -y / (t / (z - t))
    if (a <= (-4.5d+91)) then
        tmp = x
    else if (a <= (-8.5d+35)) then
        tmp = -t / ((a - t) / y)
    else if (a <= (-102.0d0)) then
        tmp = x
    else if (a <= (-7.6d-134)) then
        tmp = t_2
    else if (a <= (-1.02d-210)) then
        tmp = t_1
    else if (a <= 2.7d-234) then
        tmp = t_2
    else if (a <= 1.04d-181) then
        tmp = x / (t / (z - a))
    else if (a <= 5.8d-123) then
        tmp = t_2
    else if (a <= 6.8d-53) then
        tmp = t_1
    else if (a <= 5.6d-12) then
        tmp = x
    else if (a <= 2.8d+128) then
        tmp = z / (a / (y - x))
    else
        tmp = x * ((t / (a - t)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-z / (a - t));
	double t_2 = -y / (t / (z - t));
	double tmp;
	if (a <= -4.5e+91) {
		tmp = x;
	} else if (a <= -8.5e+35) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -102.0) {
		tmp = x;
	} else if (a <= -7.6e-134) {
		tmp = t_2;
	} else if (a <= -1.02e-210) {
		tmp = t_1;
	} else if (a <= 2.7e-234) {
		tmp = t_2;
	} else if (a <= 1.04e-181) {
		tmp = x / (t / (z - a));
	} else if (a <= 5.8e-123) {
		tmp = t_2;
	} else if (a <= 6.8e-53) {
		tmp = t_1;
	} else if (a <= 5.6e-12) {
		tmp = x;
	} else if (a <= 2.8e+128) {
		tmp = z / (a / (y - x));
	} else {
		tmp = x * ((t / (a - t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-z / (a - t))
	t_2 = -y / (t / (z - t))
	tmp = 0
	if a <= -4.5e+91:
		tmp = x
	elif a <= -8.5e+35:
		tmp = -t / ((a - t) / y)
	elif a <= -102.0:
		tmp = x
	elif a <= -7.6e-134:
		tmp = t_2
	elif a <= -1.02e-210:
		tmp = t_1
	elif a <= 2.7e-234:
		tmp = t_2
	elif a <= 1.04e-181:
		tmp = x / (t / (z - a))
	elif a <= 5.8e-123:
		tmp = t_2
	elif a <= 6.8e-53:
		tmp = t_1
	elif a <= 5.6e-12:
		tmp = x
	elif a <= 2.8e+128:
		tmp = z / (a / (y - x))
	else:
		tmp = x * ((t / (a - t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(-z) / Float64(a - t)))
	t_2 = Float64(Float64(-y) / Float64(t / Float64(z - t)))
	tmp = 0.0
	if (a <= -4.5e+91)
		tmp = x;
	elseif (a <= -8.5e+35)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (a <= -102.0)
		tmp = x;
	elseif (a <= -7.6e-134)
		tmp = t_2;
	elseif (a <= -1.02e-210)
		tmp = t_1;
	elseif (a <= 2.7e-234)
		tmp = t_2;
	elseif (a <= 1.04e-181)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (a <= 5.8e-123)
		tmp = t_2;
	elseif (a <= 6.8e-53)
		tmp = t_1;
	elseif (a <= 5.6e-12)
		tmp = x;
	elseif (a <= 2.8e+128)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = Float64(x * Float64(Float64(t / Float64(a - t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-z / (a - t));
	t_2 = -y / (t / (z - t));
	tmp = 0.0;
	if (a <= -4.5e+91)
		tmp = x;
	elseif (a <= -8.5e+35)
		tmp = -t / ((a - t) / y);
	elseif (a <= -102.0)
		tmp = x;
	elseif (a <= -7.6e-134)
		tmp = t_2;
	elseif (a <= -1.02e-210)
		tmp = t_1;
	elseif (a <= 2.7e-234)
		tmp = t_2;
	elseif (a <= 1.04e-181)
		tmp = x / (t / (z - a));
	elseif (a <= 5.8e-123)
		tmp = t_2;
	elseif (a <= 6.8e-53)
		tmp = t_1;
	elseif (a <= 5.6e-12)
		tmp = x;
	elseif (a <= 2.8e+128)
		tmp = z / (a / (y - x));
	else
		tmp = x * ((t / (a - t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+91], x, If[LessEqual[a, -8.5e+35], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -102.0], x, If[LessEqual[a, -7.6e-134], t$95$2, If[LessEqual[a, -1.02e-210], t$95$1, If[LessEqual[a, 2.7e-234], t$95$2, If[LessEqual[a, 1.04e-181], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-123], t$95$2, If[LessEqual[a, 6.8e-53], t$95$1, If[LessEqual[a, 5.6e-12], x, If[LessEqual[a, 2.8e+128], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -4.5e91 or -8.4999999999999995e35 < a < -102 or 6.8e-53 < a < 5.6000000000000004e-12

   1. Initial program 76.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 56.0%

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

   if -4.5e91 < a < -8.4999999999999995e35

   1. Initial program 74.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 47.8%

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

   6. Taylor expanded in z around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. associate-/l* 56.6%

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

      3. distribute-neg-frac 56.6%

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

   8. Simplified 56.6%

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

   if -102 < a < -7.60000000000000006e-134 or -1.02000000000000002e-210 < a < 2.7000000000000002e-234 or 1.04000000000000002e-181 < a < 5.80000000000000007e-123

   1. Initial program 72.0%

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

      1. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x around 0 65.3%

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

   6. Taylor expanded in a around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate-/l* 66.5%

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

      3. distribute-neg-frac 66.5%

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

   8. Simplified 66.5%

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

   if -7.60000000000000006e-134 < a < -1.02000000000000002e-210 or 5.80000000000000007e-123 < a < 6.8e-53

   1. Initial program 64.8%

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

      1. associate-*l/ 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. associate--r+ 64.2%

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

      5. sub-neg 64.2%

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

      6. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around inf 68.8%

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

   if 2.7000000000000002e-234 < a < 1.04000000000000002e-181

   1. Initial program 47.4%

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

      1. associate-*l/ 47.8%

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

   3. Simplified 47.8%

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

   5. Taylor expanded in x around -inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. *-commutative 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. associate--r+ 40.0%

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

      5. sub-neg 40.0%

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

      6. metadata-eval 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in t around -inf 70.2%

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

      1. associate-/l* 77.2%

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

   10. Simplified 77.2%

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

   if 5.6000000000000004e-12 < a < 2.79999999999999983e128

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-*l/ 85.4%

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

      3. fma-def 85.8%

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

   3. Simplified 85.8%

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

      1. fma-udef 85.4%

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

      2. associate-/r/ 85.4%

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

      3. div-inv 85.4%

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

      4. clear-num 85.5%

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

   6. Applied egg-rr 85.5%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.4%

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

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in z around -inf 49.1%

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

       1. associate-/l* 58.1%

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

   11. Simplified 58.1%

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

   12. Taylor expanded in a around inf 48.4%

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

   if 2.79999999999999983e128 < a

   1. Initial program 63.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. *-commutative 62.5%

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

      3. distribute-rgt-neg-in 62.5%

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

      4. associate--r+ 62.5%

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

      5. sub-neg 62.5%

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

      6. metadata-eval 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in z around 0 55.5%

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

      1. +-commutative 55.5%

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

   10. Simplified 55.5%

       \[\leadsto \color{blue}{x \cdot \left(\frac{t}{a - t} + 1\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -102:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-234}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{a - t}\\ t_2 := \frac{-y}{\frac{t}{z - t}}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -0.245:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) (- a t)))) (t_2 (/ (- y) (/ t (- z t)))))
   (if (<= a -4.5e+91)
     x
     (if (<= a -5.2e+35)
       (/ (- t) (/ (- a t) y))
       (if (<= a -0.245)
         x
         (if (<= a -1.4e-129)
           t_2
           (if (<= a -4.8e-210)
             t_1
             (if (<= a 2.8e-235)
               t_2
               (if (<= a 2.9e-181)
                 (/ x (/ t (- z a)))
                 (if (<= a 2.8e-122)
                   t_2
                   (if (<= a 2.2e-53)
                     t_1
                     (if (<= a 4.5e-9)
                       x
                       (if (<= a 1.8e+127) (/ z (/ a (- y x))) x)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-z / (a - t));
	double t_2 = -y / (t / (z - t));
	double tmp;
	if (a <= -4.5e+91) {
		tmp = x;
	} else if (a <= -5.2e+35) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -0.245) {
		tmp = x;
	} else if (a <= -1.4e-129) {
		tmp = t_2;
	} else if (a <= -4.8e-210) {
		tmp = t_1;
	} else if (a <= 2.8e-235) {
		tmp = t_2;
	} else if (a <= 2.9e-181) {
		tmp = x / (t / (z - a));
	} else if (a <= 2.8e-122) {
		tmp = t_2;
	} else if (a <= 2.2e-53) {
		tmp = t_1;
	} else if (a <= 4.5e-9) {
		tmp = x;
	} else if (a <= 1.8e+127) {
		tmp = z / (a / (y - x));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * (-z / (a - t))
    t_2 = -y / (t / (z - t))
    if (a <= (-4.5d+91)) then
        tmp = x
    else if (a <= (-5.2d+35)) then
        tmp = -t / ((a - t) / y)
    else if (a <= (-0.245d0)) then
        tmp = x
    else if (a <= (-1.4d-129)) then
        tmp = t_2
    else if (a <= (-4.8d-210)) then
        tmp = t_1
    else if (a <= 2.8d-235) then
        tmp = t_2
    else if (a <= 2.9d-181) then
        tmp = x / (t / (z - a))
    else if (a <= 2.8d-122) then
        tmp = t_2
    else if (a <= 2.2d-53) then
        tmp = t_1
    else if (a <= 4.5d-9) then
        tmp = x
    else if (a <= 1.8d+127) then
        tmp = z / (a / (y - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-z / (a - t));
	double t_2 = -y / (t / (z - t));
	double tmp;
	if (a <= -4.5e+91) {
		tmp = x;
	} else if (a <= -5.2e+35) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -0.245) {
		tmp = x;
	} else if (a <= -1.4e-129) {
		tmp = t_2;
	} else if (a <= -4.8e-210) {
		tmp = t_1;
	} else if (a <= 2.8e-235) {
		tmp = t_2;
	} else if (a <= 2.9e-181) {
		tmp = x / (t / (z - a));
	} else if (a <= 2.8e-122) {
		tmp = t_2;
	} else if (a <= 2.2e-53) {
		tmp = t_1;
	} else if (a <= 4.5e-9) {
		tmp = x;
	} else if (a <= 1.8e+127) {
		tmp = z / (a / (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-z / (a - t))
	t_2 = -y / (t / (z - t))
	tmp = 0
	if a <= -4.5e+91:
		tmp = x
	elif a <= -5.2e+35:
		tmp = -t / ((a - t) / y)
	elif a <= -0.245:
		tmp = x
	elif a <= -1.4e-129:
		tmp = t_2
	elif a <= -4.8e-210:
		tmp = t_1
	elif a <= 2.8e-235:
		tmp = t_2
	elif a <= 2.9e-181:
		tmp = x / (t / (z - a))
	elif a <= 2.8e-122:
		tmp = t_2
	elif a <= 2.2e-53:
		tmp = t_1
	elif a <= 4.5e-9:
		tmp = x
	elif a <= 1.8e+127:
		tmp = z / (a / (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(-z) / Float64(a - t)))
	t_2 = Float64(Float64(-y) / Float64(t / Float64(z - t)))
	tmp = 0.0
	if (a <= -4.5e+91)
		tmp = x;
	elseif (a <= -5.2e+35)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (a <= -0.245)
		tmp = x;
	elseif (a <= -1.4e-129)
		tmp = t_2;
	elseif (a <= -4.8e-210)
		tmp = t_1;
	elseif (a <= 2.8e-235)
		tmp = t_2;
	elseif (a <= 2.9e-181)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (a <= 2.8e-122)
		tmp = t_2;
	elseif (a <= 2.2e-53)
		tmp = t_1;
	elseif (a <= 4.5e-9)
		tmp = x;
	elseif (a <= 1.8e+127)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-z / (a - t));
	t_2 = -y / (t / (z - t));
	tmp = 0.0;
	if (a <= -4.5e+91)
		tmp = x;
	elseif (a <= -5.2e+35)
		tmp = -t / ((a - t) / y);
	elseif (a <= -0.245)
		tmp = x;
	elseif (a <= -1.4e-129)
		tmp = t_2;
	elseif (a <= -4.8e-210)
		tmp = t_1;
	elseif (a <= 2.8e-235)
		tmp = t_2;
	elseif (a <= 2.9e-181)
		tmp = x / (t / (z - a));
	elseif (a <= 2.8e-122)
		tmp = t_2;
	elseif (a <= 2.2e-53)
		tmp = t_1;
	elseif (a <= 4.5e-9)
		tmp = x;
	elseif (a <= 1.8e+127)
		tmp = z / (a / (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+91], x, If[LessEqual[a, -5.2e+35], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.245], x, If[LessEqual[a, -1.4e-129], t$95$2, If[LessEqual[a, -4.8e-210], t$95$1, If[LessEqual[a, 2.8e-235], t$95$2, If[LessEqual[a, 2.9e-181], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-122], t$95$2, If[LessEqual[a, 2.2e-53], t$95$1, If[LessEqual[a, 4.5e-9], x, If[LessEqual[a, 1.8e+127], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.5e91 or -5.20000000000000013e35 < a < -0.245 or 2.20000000000000018e-53 < a < 4.49999999999999976e-9 or 1.79999999999999989e127 < a

   1. Initial program 72.3%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 54.8%

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

   if -4.5e91 < a < -5.20000000000000013e35

   1. Initial program 74.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 47.8%

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

   6. Taylor expanded in z around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. associate-/l* 56.6%

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

      3. distribute-neg-frac 56.6%

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

   8. Simplified 56.6%

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

   if -0.245 < a < -1.4e-129 or -4.80000000000000008e-210 < a < 2.79999999999999995e-235 or 2.8999999999999998e-181 < a < 2.7999999999999999e-122

   1. Initial program 72.0%

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

      1. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x around 0 65.3%

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

   6. Taylor expanded in a around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate-/l* 66.5%

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

      3. distribute-neg-frac 66.5%

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

   8. Simplified 66.5%

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

   if -1.4e-129 < a < -4.80000000000000008e-210 or 2.7999999999999999e-122 < a < 2.20000000000000018e-53

   1. Initial program 64.8%

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

      1. associate-*l/ 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. associate--r+ 64.2%

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

      5. sub-neg 64.2%

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

      6. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around inf 68.8%

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

   if 2.79999999999999995e-235 < a < 2.8999999999999998e-181

   1. Initial program 47.4%

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

      1. associate-*l/ 47.8%

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

   3. Simplified 47.8%

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

   5. Taylor expanded in x around -inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. *-commutative 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. associate--r+ 40.0%

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

      5. sub-neg 40.0%

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

      6. metadata-eval 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in t around -inf 70.2%

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

      1. associate-/l* 77.2%

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

   10. Simplified 77.2%

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

   if 4.49999999999999976e-9 < a < 1.79999999999999989e127

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-*l/ 85.4%

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

      3. fma-def 85.8%

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

   3. Simplified 85.8%

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

      1. fma-udef 85.4%

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

      2. associate-/r/ 85.4%

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

      3. div-inv 85.4%

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

      4. clear-num 85.5%

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

   6. Applied egg-rr 85.5%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.4%

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

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in z around -inf 49.1%

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

       1. associate-/l* 58.1%

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

   11. Simplified 58.1%

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

   12. Taylor expanded in a around inf 48.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -0.245:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+195}:\\ \;\;\;\;\frac{-t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -9.2e-54)
       (* y (+ (/ a t) 1.0))
       (if (<= t -2.4e-122)
         x
         (if (<= t -4.8e-287)
           (/ z (/ a (- y x)))
           (if (<= t 2.9e-94)
             x
             (if (<= t 1.48e-27)
               (* x (/ (- z) (- a t)))
               (if (<= t 8e+45)
                 (/ y (/ a (- z t)))
                 (if (<= t 1.2e+192)
                   t_1
                   (if (<= t 5.5e+195) (/ (- t) (/ a y)) y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -9.2e-54) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -2.4e-122) {
		tmp = x;
	} else if (t <= -4.8e-287) {
		tmp = z / (a / (y - x));
	} else if (t <= 2.9e-94) {
		tmp = x;
	} else if (t <= 1.48e-27) {
		tmp = x * (-z / (a - t));
	} else if (t <= 8e+45) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.2e+192) {
		tmp = t_1;
	} else if (t <= 5.5e+195) {
		tmp = -t / (a / y);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-9.2d-54)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-2.4d-122)) then
        tmp = x
    else if (t <= (-4.8d-287)) then
        tmp = z / (a / (y - x))
    else if (t <= 2.9d-94) then
        tmp = x
    else if (t <= 1.48d-27) then
        tmp = x * (-z / (a - t))
    else if (t <= 8d+45) then
        tmp = y / (a / (z - t))
    else if (t <= 1.2d+192) then
        tmp = t_1
    else if (t <= 5.5d+195) then
        tmp = -t / (a / y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -9.2e-54) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -2.4e-122) {
		tmp = x;
	} else if (t <= -4.8e-287) {
		tmp = z / (a / (y - x));
	} else if (t <= 2.9e-94) {
		tmp = x;
	} else if (t <= 1.48e-27) {
		tmp = x * (-z / (a - t));
	} else if (t <= 8e+45) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.2e+192) {
		tmp = t_1;
	} else if (t <= 5.5e+195) {
		tmp = -t / (a / y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -9.2e-54:
		tmp = y * ((a / t) + 1.0)
	elif t <= -2.4e-122:
		tmp = x
	elif t <= -4.8e-287:
		tmp = z / (a / (y - x))
	elif t <= 2.9e-94:
		tmp = x
	elif t <= 1.48e-27:
		tmp = x * (-z / (a - t))
	elif t <= 8e+45:
		tmp = y / (a / (z - t))
	elif t <= 1.2e+192:
		tmp = t_1
	elif t <= 5.5e+195:
		tmp = -t / (a / y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -9.2e-54)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -2.4e-122)
		tmp = x;
	elseif (t <= -4.8e-287)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 2.9e-94)
		tmp = x;
	elseif (t <= 1.48e-27)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (t <= 8e+45)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.2e+192)
		tmp = t_1;
	elseif (t <= 5.5e+195)
		tmp = Float64(Float64(-t) / Float64(a / y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -9.2e-54)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -2.4e-122)
		tmp = x;
	elseif (t <= -4.8e-287)
		tmp = z / (a / (y - x));
	elseif (t <= 2.9e-94)
		tmp = x;
	elseif (t <= 1.48e-27)
		tmp = x * (-z / (a - t));
	elseif (t <= 8e+45)
		tmp = y / (a / (z - t));
	elseif (t <= 1.2e+192)
		tmp = t_1;
	elseif (t <= 5.5e+195)
		tmp = -t / (a / y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -9.2e-54], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-122], x, If[LessEqual[t, -4.8e-287], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-94], x, If[LessEqual[t, 1.48e-27], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+45], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+192], t$95$1, If[LessEqual[t, 5.5e+195], N[((-t) / N[(a / y), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -5.7999999999999995e279 or 7.9999999999999994e45 < t < 1.1999999999999999e192

   1. Initial program 39.2%

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

      1. associate-*l/ 45.6%

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

   3. Simplified 45.6%

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

   5. Taylor expanded in x around -inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. *-commutative 49.9%

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

      3. distribute-rgt-neg-in 49.9%

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

      4. associate--r+ 21.4%

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

      5. sub-neg 21.4%

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

      6. metadata-eval 21.4%

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

   7. Simplified 21.4%

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

   8. Taylor expanded in t around -inf 34.6%

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

      1. associate-/l* 54.2%

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

   10. Simplified 54.2%

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

   if -5.7999999999999995e279 < t < -9.1999999999999996e-54

   1. Initial program 59.6%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-*r/ 69.2%

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

      3. associate-*r/ 69.2%

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

      4. div-sub 69.3%

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

      5. distribute-lft-out-- 69.3%

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

      6. associate-*r/ 69.3%

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

      7. mul-1-neg 69.3%

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

      8. unsub-neg 69.3%

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

      9. distribute-rgt-out-- 69.4%

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

      10. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in z around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around inf 39.8%

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

       1. sub-neg 39.8%

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

       2. mul-1-neg 39.8%

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

       3. remove-double-neg 39.8%

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

   13. Simplified 39.8%

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

   if -9.1999999999999996e-54 < t < -2.39999999999999987e-122 or -4.79999999999999999e-287 < t < 2.89999999999999995e-94

   1. Initial program 89.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around inf 53.0%

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

   if -2.39999999999999987e-122 < t < -4.79999999999999999e-287

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 94.8%

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

      2. associate-/r/ 92.4%

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

      3. div-inv 92.4%

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

      4. clear-num 92.5%

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

   6. Applied egg-rr 92.5%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.4%

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

   8. Applied egg-rr 92.4%

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

   9. Taylor expanded in z around -inf 65.4%

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

       1. associate-/l* 67.8%

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

   11. Simplified 67.8%

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

   12. Taylor expanded in a around inf 52.6%

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

   if 2.89999999999999995e-94 < t < 1.48000000000000008e-27

   1. Initial program 79.5%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around -inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. associate--r+ 58.7%

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

      5. sub-neg 58.7%

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

      6. metadata-eval 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around inf 58.9%

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

   if 1.48000000000000008e-27 < t < 7.9999999999999994e45

   1. Initial program 94.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in a around inf 51.6%

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

      1. associate-/l* 51.7%

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

   8. Simplified 51.7%

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

   if 1.1999999999999999e192 < t < 5.49999999999999994e195

   1. Initial program 4.9%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 4.9%

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

   6. Taylor expanded in z around 0 4.9%

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

      1. associate-*r/ 4.9%

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

      2. mul-1-neg 4.9%

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

      3. distribute-lft-neg-out 4.9%

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

      4. *-commutative 4.9%

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

   8. Simplified 4.9%

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

   9. Taylor expanded in t around 0 4.9%

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

       1. mul-1-neg 4.9%

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

       2. associate-/l* 99.2%

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

       3. distribute-neg-frac 99.2%

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

   11. Simplified 99.2%

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

   if 5.49999999999999994e195 < t

   1. Initial program 23.1%

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

      1. associate-*l/ 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in t around inf 76.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+195}:\\ \;\;\;\;\frac{-t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a - t}{y}}\\ t_2 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ (- a t) y))) (t_2 (/ x (/ t (- z a)))))
   (if (<= t -5e+279)
     t_2
     (if (<= t -3.8e-58)
       t_1
       (if (<= t -2.7e-122)
         x
         (if (<= t -4.1e-285)
           (/ z (/ a (- y x)))
           (if (<= t 6e-93)
             x
             (if (<= t 1.5e-27)
               (* x (/ (- z) (- a t)))
               (if (<= t 3.5e+46)
                 (/ y (/ a (- z t)))
                 (if (<= t 1.7e+190) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - t) / y);
	double t_2 = x / (t / (z - a));
	double tmp;
	if (t <= -5e+279) {
		tmp = t_2;
	} else if (t <= -3.8e-58) {
		tmp = t_1;
	} else if (t <= -2.7e-122) {
		tmp = x;
	} else if (t <= -4.1e-285) {
		tmp = z / (a / (y - x));
	} else if (t <= 6e-93) {
		tmp = x;
	} else if (t <= 1.5e-27) {
		tmp = x * (-z / (a - t));
	} else if (t <= 3.5e+46) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.7e+190) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -t / ((a - t) / y)
    t_2 = x / (t / (z - a))
    if (t <= (-5d+279)) then
        tmp = t_2
    else if (t <= (-3.8d-58)) then
        tmp = t_1
    else if (t <= (-2.7d-122)) then
        tmp = x
    else if (t <= (-4.1d-285)) then
        tmp = z / (a / (y - x))
    else if (t <= 6d-93) then
        tmp = x
    else if (t <= 1.5d-27) then
        tmp = x * (-z / (a - t))
    else if (t <= 3.5d+46) then
        tmp = y / (a / (z - t))
    else if (t <= 1.7d+190) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - t) / y);
	double t_2 = x / (t / (z - a));
	double tmp;
	if (t <= -5e+279) {
		tmp = t_2;
	} else if (t <= -3.8e-58) {
		tmp = t_1;
	} else if (t <= -2.7e-122) {
		tmp = x;
	} else if (t <= -4.1e-285) {
		tmp = z / (a / (y - x));
	} else if (t <= 6e-93) {
		tmp = x;
	} else if (t <= 1.5e-27) {
		tmp = x * (-z / (a - t));
	} else if (t <= 3.5e+46) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.7e+190) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / ((a - t) / y)
	t_2 = x / (t / (z - a))
	tmp = 0
	if t <= -5e+279:
		tmp = t_2
	elif t <= -3.8e-58:
		tmp = t_1
	elif t <= -2.7e-122:
		tmp = x
	elif t <= -4.1e-285:
		tmp = z / (a / (y - x))
	elif t <= 6e-93:
		tmp = x
	elif t <= 1.5e-27:
		tmp = x * (-z / (a - t))
	elif t <= 3.5e+46:
		tmp = y / (a / (z - t))
	elif t <= 1.7e+190:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(Float64(a - t) / y))
	t_2 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -5e+279)
		tmp = t_2;
	elseif (t <= -3.8e-58)
		tmp = t_1;
	elseif (t <= -2.7e-122)
		tmp = x;
	elseif (t <= -4.1e-285)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 6e-93)
		tmp = x;
	elseif (t <= 1.5e-27)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (t <= 3.5e+46)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.7e+190)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / ((a - t) / y);
	t_2 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -5e+279)
		tmp = t_2;
	elseif (t <= -3.8e-58)
		tmp = t_1;
	elseif (t <= -2.7e-122)
		tmp = x;
	elseif (t <= -4.1e-285)
		tmp = z / (a / (y - x));
	elseif (t <= 6e-93)
		tmp = x;
	elseif (t <= 1.5e-27)
		tmp = x * (-z / (a - t));
	elseif (t <= 3.5e+46)
		tmp = y / (a / (z - t));
	elseif (t <= 1.7e+190)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+279], t$95$2, If[LessEqual[t, -3.8e-58], t$95$1, If[LessEqual[t, -2.7e-122], x, If[LessEqual[t, -4.1e-285], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-93], x, If[LessEqual[t, 1.5e-27], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+46], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+190], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.0000000000000002e279 or 3.49999999999999985e46 < t < 1.7e190

   1. Initial program 39.2%

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

      1. associate-*l/ 45.6%

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

   3. Simplified 45.6%

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

   5. Taylor expanded in x around -inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. *-commutative 49.9%

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

      3. distribute-rgt-neg-in 49.9%

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

      4. associate--r+ 21.4%

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

      5. sub-neg 21.4%

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

      6. metadata-eval 21.4%

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

   7. Simplified 21.4%

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

   8. Taylor expanded in t around -inf 34.6%

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

      1. associate-/l* 54.2%

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

   10. Simplified 54.2%

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

   if -5.0000000000000002e279 < t < -3.7999999999999997e-58 or 1.7e190 < t

   1. Initial program 50.2%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in x around 0 45.5%

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

   6. Taylor expanded in z around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 51.1%

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

      3. distribute-neg-frac 51.1%

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

   8. Simplified 51.1%

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

   if -3.7999999999999997e-58 < t < -2.70000000000000009e-122 or -4.1e-285 < t < 6.0000000000000003e-93

   1. Initial program 89.6%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in a around inf 53.8%

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

   if -2.70000000000000009e-122 < t < -4.1e-285

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 94.8%

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

      2. associate-/r/ 92.4%

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

      3. div-inv 92.4%

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

      4. clear-num 92.5%

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

   6. Applied egg-rr 92.5%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.4%

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

   8. Applied egg-rr 92.4%

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

   9. Taylor expanded in z around -inf 65.4%

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

       1. associate-/l* 67.8%

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

   11. Simplified 67.8%

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

   12. Taylor expanded in a around inf 52.6%

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

   if 6.0000000000000003e-93 < t < 1.5000000000000001e-27

   1. Initial program 79.5%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around -inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. associate--r+ 58.7%

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

      5. sub-neg 58.7%

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

      6. metadata-eval 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around inf 58.9%

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

   if 1.5000000000000001e-27 < t < 3.49999999999999985e46

   1. Initial program 94.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in a around inf 51.6%

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

      1. associate-/l* 51.7%

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

   8. Simplified 51.7%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+190}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-285}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -1.1e-53)
       (* y (+ (/ a t) 1.0))
       (if (<= t -1.4e-122)
         x
         (if (<= t -3e-285)
           (/ z (/ a (- y x)))
           (if (<= t 2.05e-91)
             x
             (if (<= t 5e-26)
               (* x (/ z t))
               (if (<= t 9.2e+45)
                 (/ y (/ a (- z t)))
                 (if (<= t 1.5e+195) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -1.1e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -1.4e-122) {
		tmp = x;
	} else if (t <= -3e-285) {
		tmp = z / (a / (y - x));
	} else if (t <= 2.05e-91) {
		tmp = x;
	} else if (t <= 5e-26) {
		tmp = x * (z / t);
	} else if (t <= 9.2e+45) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.5e+195) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-1.1d-53)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-1.4d-122)) then
        tmp = x
    else if (t <= (-3d-285)) then
        tmp = z / (a / (y - x))
    else if (t <= 2.05d-91) then
        tmp = x
    else if (t <= 5d-26) then
        tmp = x * (z / t)
    else if (t <= 9.2d+45) then
        tmp = y / (a / (z - t))
    else if (t <= 1.5d+195) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -1.1e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -1.4e-122) {
		tmp = x;
	} else if (t <= -3e-285) {
		tmp = z / (a / (y - x));
	} else if (t <= 2.05e-91) {
		tmp = x;
	} else if (t <= 5e-26) {
		tmp = x * (z / t);
	} else if (t <= 9.2e+45) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.5e+195) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -1.1e-53:
		tmp = y * ((a / t) + 1.0)
	elif t <= -1.4e-122:
		tmp = x
	elif t <= -3e-285:
		tmp = z / (a / (y - x))
	elif t <= 2.05e-91:
		tmp = x
	elif t <= 5e-26:
		tmp = x * (z / t)
	elif t <= 9.2e+45:
		tmp = y / (a / (z - t))
	elif t <= 1.5e+195:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -1.1e-53)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -1.4e-122)
		tmp = x;
	elseif (t <= -3e-285)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 2.05e-91)
		tmp = x;
	elseif (t <= 5e-26)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 9.2e+45)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.5e+195)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -1.1e-53)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -1.4e-122)
		tmp = x;
	elseif (t <= -3e-285)
		tmp = z / (a / (y - x));
	elseif (t <= 2.05e-91)
		tmp = x;
	elseif (t <= 5e-26)
		tmp = x * (z / t);
	elseif (t <= 9.2e+45)
		tmp = y / (a / (z - t));
	elseif (t <= 1.5e+195)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -1.1e-53], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-122], x, If[LessEqual[t, -3e-285], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-91], x, If[LessEqual[t, 5e-26], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+45], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+195], t$95$1, y]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.7999999999999995e279 or 9.20000000000000049e45 < t < 1.5e195

   1. Initial program 38.2%

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

      1. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   5. Taylor expanded in x around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. *-commutative 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

      4. associate--r+ 21.0%

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

      5. sub-neg 21.0%

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

      6. metadata-eval 21.0%

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

   7. Simplified 21.0%

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

   8. Taylor expanded in t around -inf 33.5%

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

      1. associate-/l* 52.5%

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

   10. Simplified 52.5%

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

   if -5.7999999999999995e279 < t < -1.10000000000000009e-53

   1. Initial program 59.6%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-*r/ 69.2%

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

      3. associate-*r/ 69.2%

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

      4. div-sub 69.3%

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

      5. distribute-lft-out-- 69.3%

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

      6. associate-*r/ 69.3%

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

      7. mul-1-neg 69.3%

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

      8. unsub-neg 69.3%

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

      9. distribute-rgt-out-- 69.4%

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

      10. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in z around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around inf 39.8%

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

       1. sub-neg 39.8%

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

       2. mul-1-neg 39.8%

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

       3. remove-double-neg 39.8%

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

   13. Simplified 39.8%

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

   if -1.10000000000000009e-53 < t < -1.3999999999999999e-122 or -3.00000000000000003e-285 < t < 2.05000000000000012e-91

   1. Initial program 89.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around inf 53.0%

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

   if -1.3999999999999999e-122 < t < -3.00000000000000003e-285

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 94.8%

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

      2. associate-/r/ 92.4%

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

      3. div-inv 92.4%

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

      4. clear-num 92.5%

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

   6. Applied egg-rr 92.5%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.4%

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

   8. Applied egg-rr 92.4%

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

   9. Taylor expanded in z around -inf 65.4%

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

       1. associate-/l* 67.8%

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

   11. Simplified 67.8%

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

   12. Taylor expanded in a around inf 52.6%

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

   if 2.05000000000000012e-91 < t < 5.00000000000000019e-26

   1. Initial program 80.5%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around -inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. *-commutative 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

      4. associate--r+ 60.8%

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

      5. sub-neg 60.8%

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

      6. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in a around 0 51.3%

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

      1. associate-*r/ 51.3%

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

      2. mul-1-neg 51.3%

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

   10. Simplified 51.3%

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

   if 5.00000000000000019e-26 < t < 9.20000000000000049e45

   1. Initial program 93.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 60.5%

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

   6. Taylor expanded in a around inf 54.7%

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

      1. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   if 1.5e195 < t

   1. Initial program 22.2%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-285}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+195}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 33.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ t_2 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))) (t_2 (/ y (/ a z))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -8.8e-57)
       (* y (+ (/ a t) 1.0))
       (if (<= t -2.25e-237)
         x
         (if (<= t -1.8e-279)
           t_2
           (if (<= t 1.05e-91)
             x
             (if (<= t 7.5e-28)
               t_1
               (if (<= t 2.3e+134) t_2 (if (<= t 5.2e+192) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double t_2 = y / (a / z);
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -8.8e-57) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -2.25e-237) {
		tmp = x;
	} else if (t <= -1.8e-279) {
		tmp = t_2;
	} else if (t <= 1.05e-91) {
		tmp = x;
	} else if (t <= 7.5e-28) {
		tmp = t_1;
	} else if (t <= 2.3e+134) {
		tmp = t_2;
	} else if (t <= 5.2e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z / t)
    t_2 = y / (a / z)
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-8.8d-57)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-2.25d-237)) then
        tmp = x
    else if (t <= (-1.8d-279)) then
        tmp = t_2
    else if (t <= 1.05d-91) then
        tmp = x
    else if (t <= 7.5d-28) then
        tmp = t_1
    else if (t <= 2.3d+134) then
        tmp = t_2
    else if (t <= 5.2d+192) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double t_2 = y / (a / z);
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -8.8e-57) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -2.25e-237) {
		tmp = x;
	} else if (t <= -1.8e-279) {
		tmp = t_2;
	} else if (t <= 1.05e-91) {
		tmp = x;
	} else if (t <= 7.5e-28) {
		tmp = t_1;
	} else if (t <= 2.3e+134) {
		tmp = t_2;
	} else if (t <= 5.2e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	t_2 = y / (a / z)
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -8.8e-57:
		tmp = y * ((a / t) + 1.0)
	elif t <= -2.25e-237:
		tmp = x
	elif t <= -1.8e-279:
		tmp = t_2
	elif t <= 1.05e-91:
		tmp = x
	elif t <= 7.5e-28:
		tmp = t_1
	elif t <= 2.3e+134:
		tmp = t_2
	elif t <= 5.2e+192:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	t_2 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -8.8e-57)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -2.25e-237)
		tmp = x;
	elseif (t <= -1.8e-279)
		tmp = t_2;
	elseif (t <= 1.05e-91)
		tmp = x;
	elseif (t <= 7.5e-28)
		tmp = t_1;
	elseif (t <= 2.3e+134)
		tmp = t_2;
	elseif (t <= 5.2e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	t_2 = y / (a / z);
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -8.8e-57)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -2.25e-237)
		tmp = x;
	elseif (t <= -1.8e-279)
		tmp = t_2;
	elseif (t <= 1.05e-91)
		tmp = x;
	elseif (t <= 7.5e-28)
		tmp = t_1;
	elseif (t <= 2.3e+134)
		tmp = t_2;
	elseif (t <= 5.2e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -8.8e-57], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.25e-237], x, If[LessEqual[t, -1.8e-279], t$95$2, If[LessEqual[t, 1.05e-91], x, If[LessEqual[t, 7.5e-28], t$95$1, If[LessEqual[t, 2.3e+134], t$95$2, If[LessEqual[t, 5.2e+192], t$95$1, y]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.7999999999999995e279 or 1.05e-91 < t < 7.5000000000000003e-28 or 2.2999999999999998e134 < t < 5.20000000000000006e192

   1. Initial program 52.7%

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

      1. associate-*l/ 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in x around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. associate--r+ 38.8%

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

      5. sub-neg 38.8%

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

      6. metadata-eval 38.8%

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

   7. Simplified 38.8%

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

   8. Taylor expanded in a around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. mul-1-neg 58.1%

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

   10. Simplified 58.1%

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

   if -5.7999999999999995e279 < t < -8.79999999999999994e-57

   1. Initial program 59.6%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-*r/ 69.2%

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

      3. associate-*r/ 69.2%

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

      4. div-sub 69.3%

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

      5. distribute-lft-out-- 69.3%

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

      6. associate-*r/ 69.3%

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

      7. mul-1-neg 69.3%

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

      8. unsub-neg 69.3%

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

      9. distribute-rgt-out-- 69.4%

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

      10. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in z around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around inf 39.8%

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

       1. sub-neg 39.8%

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

       2. mul-1-neg 39.8%

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

       3. remove-double-neg 39.8%

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

   13. Simplified 39.8%

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

   if -8.79999999999999994e-57 < t < -2.25000000000000005e-237 or -1.7999999999999998e-279 < t < 1.05e-91

   1. Initial program 90.8%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 47.4%

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

   if -2.25000000000000005e-237 < t < -1.7999999999999998e-279 or 7.5000000000000003e-28 < t < 2.2999999999999998e134

   1. Initial program 78.4%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0 49.5%

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

   6. Taylor expanded in t around 0 29.4%

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

      1. associate-/l* 35.6%

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

   8. Simplified 35.6%

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

   if 5.20000000000000006e192 < t

   1. Initial program 22.2%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 72.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-283}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{z}}{y}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -9.5e-56)
       (* y (+ (/ a t) 1.0))
       (if (<= t -6.4e-240)
         x
         (if (<= t -3.1e-283)
           (/ 1.0 (/ (/ a z) y))
           (if (<= t 3.9e-92)
             x
             (if (<= t 3.2e-28)
               t_1
               (if (<= t 2.5e+134)
                 (/ y (/ a z))
                 (if (<= t 5.2e+192) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -9.5e-56) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -6.4e-240) {
		tmp = x;
	} else if (t <= -3.1e-283) {
		tmp = 1.0 / ((a / z) / y);
	} else if (t <= 3.9e-92) {
		tmp = x;
	} else if (t <= 3.2e-28) {
		tmp = t_1;
	} else if (t <= 2.5e+134) {
		tmp = y / (a / z);
	} else if (t <= 5.2e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-9.5d-56)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-6.4d-240)) then
        tmp = x
    else if (t <= (-3.1d-283)) then
        tmp = 1.0d0 / ((a / z) / y)
    else if (t <= 3.9d-92) then
        tmp = x
    else if (t <= 3.2d-28) then
        tmp = t_1
    else if (t <= 2.5d+134) then
        tmp = y / (a / z)
    else if (t <= 5.2d+192) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -9.5e-56) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -6.4e-240) {
		tmp = x;
	} else if (t <= -3.1e-283) {
		tmp = 1.0 / ((a / z) / y);
	} else if (t <= 3.9e-92) {
		tmp = x;
	} else if (t <= 3.2e-28) {
		tmp = t_1;
	} else if (t <= 2.5e+134) {
		tmp = y / (a / z);
	} else if (t <= 5.2e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -9.5e-56:
		tmp = y * ((a / t) + 1.0)
	elif t <= -6.4e-240:
		tmp = x
	elif t <= -3.1e-283:
		tmp = 1.0 / ((a / z) / y)
	elif t <= 3.9e-92:
		tmp = x
	elif t <= 3.2e-28:
		tmp = t_1
	elif t <= 2.5e+134:
		tmp = y / (a / z)
	elif t <= 5.2e+192:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -9.5e-56)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -6.4e-240)
		tmp = x;
	elseif (t <= -3.1e-283)
		tmp = Float64(1.0 / Float64(Float64(a / z) / y));
	elseif (t <= 3.9e-92)
		tmp = x;
	elseif (t <= 3.2e-28)
		tmp = t_1;
	elseif (t <= 2.5e+134)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.2e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -9.5e-56)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -6.4e-240)
		tmp = x;
	elseif (t <= -3.1e-283)
		tmp = 1.0 / ((a / z) / y);
	elseif (t <= 3.9e-92)
		tmp = x;
	elseif (t <= 3.2e-28)
		tmp = t_1;
	elseif (t <= 2.5e+134)
		tmp = y / (a / z);
	elseif (t <= 5.2e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -9.5e-56], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.4e-240], x, If[LessEqual[t, -3.1e-283], N[(1.0 / N[(N[(a / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-92], x, If[LessEqual[t, 3.2e-28], t$95$1, If[LessEqual[t, 2.5e+134], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+192], t$95$1, y]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.7999999999999995e279 or 3.8999999999999997e-92 < t < 3.19999999999999982e-28 or 2.4999999999999999e134 < t < 5.20000000000000006e192

   1. Initial program 52.7%

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

      1. associate-*l/ 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in x around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. associate--r+ 38.8%

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

      5. sub-neg 38.8%

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

      6. metadata-eval 38.8%

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

   7. Simplified 38.8%

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

   8. Taylor expanded in a around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. mul-1-neg 58.1%

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

   10. Simplified 58.1%

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

   if -5.7999999999999995e279 < t < -9.4999999999999991e-56

   1. Initial program 59.6%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-*r/ 69.2%

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

      3. associate-*r/ 69.2%

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

      4. div-sub 69.3%

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

      5. distribute-lft-out-- 69.3%

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

      6. associate-*r/ 69.3%

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

      7. mul-1-neg 69.3%

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

      8. unsub-neg 69.3%

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

      9. distribute-rgt-out-- 69.4%

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

      10. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in z around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around inf 39.8%

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

       1. sub-neg 39.8%

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

       2. mul-1-neg 39.8%

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

       3. remove-double-neg 39.8%

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

   13. Simplified 39.8%

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

   if -9.4999999999999991e-56 < t < -6.3999999999999998e-240 or -3.10000000000000004e-283 < t < 3.8999999999999997e-92

   1. Initial program 90.8%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 47.4%

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

   if -6.3999999999999998e-240 < t < -3.10000000000000004e-283

   1. Initial program 91.2%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 48.1%

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

   6. Taylor expanded in t around 0 48.1%

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

      1. associate-/l* 56.5%

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

   8. Simplified 56.5%

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

      1. clear-num 56.6%

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

      2. inv-pow 56.6%

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

   10. Applied egg-rr 56.6%

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

       1. unpow-1 56.6%

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

   12. Simplified 56.6%

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

   if 3.19999999999999982e-28 < t < 2.4999999999999999e134

   1. Initial program 74.3%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in x around 0 49.9%

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

   6. Taylor expanded in t around 0 23.4%

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

      1. associate-/l* 28.9%

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

   8. Simplified 28.9%

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

   if 5.20000000000000006e192 < t

   1. Initial program 22.2%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 72.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-283}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{z}}{y}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (- x (/ (- x y) (/ a (- z t))))))
   (if (<= a -3.2e+56)
     t_2
     (if (<= a -3.8e+35)
       t_1
       (if (<= a -6.8e-13)
         (* x (+ (/ (- t z) (- a t)) 1.0))
         (if (<= a -1.7e-127)
           (* y (/ (- z t) (- a t)))
           (if (<= a -4.2e-231)
             (/ z (/ (- a t) (- y x)))
             (if (<= a 2.7e-39) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -3.2e+56) {
		tmp = t_2;
	} else if (a <= -3.8e+35) {
		tmp = t_1;
	} else if (a <= -6.8e-13) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (a <= -1.7e-127) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= -4.2e-231) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 2.7e-39) {
		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 = y + ((x - y) / (t / z))
    t_2 = x - ((x - y) / (a / (z - t)))
    if (a <= (-3.2d+56)) then
        tmp = t_2
    else if (a <= (-3.8d+35)) then
        tmp = t_1
    else if (a <= (-6.8d-13)) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (a <= (-1.7d-127)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= (-4.2d-231)) then
        tmp = z / ((a - t) / (y - x))
    else if (a <= 2.7d-39) 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 = y + ((x - y) / (t / z));
	double t_2 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -3.2e+56) {
		tmp = t_2;
	} else if (a <= -3.8e+35) {
		tmp = t_1;
	} else if (a <= -6.8e-13) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (a <= -1.7e-127) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= -4.2e-231) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 2.7e-39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = x - ((x - y) / (a / (z - t)))
	tmp = 0
	if a <= -3.2e+56:
		tmp = t_2
	elif a <= -3.8e+35:
		tmp = t_1
	elif a <= -6.8e-13:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif a <= -1.7e-127:
		tmp = y * ((z - t) / (a - t))
	elif a <= -4.2e-231:
		tmp = z / ((a - t) / (y - x))
	elif a <= 2.7e-39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -3.2e+56)
		tmp = t_2;
	elseif (a <= -3.8e+35)
		tmp = t_1;
	elseif (a <= -6.8e-13)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (a <= -1.7e-127)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= -4.2e-231)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (a <= 2.7e-39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = x - ((x - y) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -3.2e+56)
		tmp = t_2;
	elseif (a <= -3.8e+35)
		tmp = t_1;
	elseif (a <= -6.8e-13)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (a <= -1.7e-127)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= -4.2e-231)
		tmp = z / ((a - t) / (y - x));
	elseif (a <= 2.7e-39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+56], t$95$2, If[LessEqual[a, -3.8e+35], t$95$1, If[LessEqual[a, -6.8e-13], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e-127], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-231], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-39], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.20000000000000003e56 or 2.7000000000000001e-39 < a

   1. Initial program 71.6%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around inf 67.6%

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

      1. associate-/l* 79.5%

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

   7. Simplified 79.5%

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

   if -3.20000000000000003e56 < a < -3.8e35 or -4.19999999999999978e-231 < a < 2.7000000000000001e-39

   1. Initial program 65.1%

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

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in t around inf 80.7%

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

      1. associate--l+ 80.7%

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

      2. associate-*r/ 80.7%

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

      3. associate-*r/ 80.7%

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

      4. div-sub 80.7%

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

      5. distribute-lft-out-- 80.7%

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

      6. associate-*r/ 80.7%

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

      7. mul-1-neg 80.7%

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

      8. unsub-neg 80.7%

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

      9. distribute-rgt-out-- 80.7%

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

      10. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in z around inf 83.4%

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

   if -3.8e35 < a < -6.80000000000000031e-13

   1. Initial program 85.2%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

   7. Simplified 77.5%

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

   if -6.80000000000000031e-13 < a < -1.6999999999999999e-127

   1. Initial program 73.6%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. associate-/l* 79.1%

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

      2. div-inv 79.2%

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

      3. clear-num 79.2%

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

   7. Applied egg-rr 79.2%

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

   if -1.6999999999999999e-127 < a < -4.19999999999999978e-231

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-*l/ 69.2%

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

      3. fma-def 69.1%

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

   3. Simplified 69.1%

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

      1. fma-udef 69.2%

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

      2. associate-/r/ 64.5%

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

      3. div-inv 64.4%

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

      4. clear-num 64.6%

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

   6. Applied egg-rr 64.6%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.5%

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

   8. Applied egg-rr 64.5%

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

   9. Taylor expanded in z around -inf 74.8%

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

       1. associate-/l* 84.8%

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

   11. Simplified 84.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-54} \lor \neg \left(t \leq 2.05 \cdot 10^{-91}\right) \land \left(t \leq 1.48 \cdot 10^{-27} \lor \neg \left(t \leq 370000000\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -4.2e+75)
     t_1
     (if (<= t -3.4e-31)
       (* y (/ (- z t) (- a t)))
       (if (or (<= t -2.5e-54)
               (and (not (<= t 2.05e-91))
                    (or (<= t 1.48e-27) (not (<= t 370000000.0)))))
         t_1
         (+ x (/ z (/ a (- y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -4.2e+75) {
		tmp = t_1;
	} else if (t <= -3.4e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if ((t <= -2.5e-54) || (!(t <= 2.05e-91) && ((t <= 1.48e-27) || !(t <= 370000000.0)))) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * ((x - y) / t))
    if (t <= (-4.2d+75)) then
        tmp = t_1
    else if (t <= (-3.4d-31)) then
        tmp = y * ((z - t) / (a - t))
    else if ((t <= (-2.5d-54)) .or. (.not. (t <= 2.05d-91)) .and. (t <= 1.48d-27) .or. (.not. (t <= 370000000.0d0))) then
        tmp = t_1
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -4.2e+75) {
		tmp = t_1;
	} else if (t <= -3.4e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if ((t <= -2.5e-54) || (!(t <= 2.05e-91) && ((t <= 1.48e-27) || !(t <= 370000000.0)))) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if t <= -4.2e+75:
		tmp = t_1
	elif t <= -3.4e-31:
		tmp = y * ((z - t) / (a - t))
	elif (t <= -2.5e-54) or (not (t <= 2.05e-91) and ((t <= 1.48e-27) or not (t <= 370000000.0))):
		tmp = t_1
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -4.2e+75)
		tmp = t_1;
	elseif (t <= -3.4e-31)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif ((t <= -2.5e-54) || (!(t <= 2.05e-91) && ((t <= 1.48e-27) || !(t <= 370000000.0))))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -4.2e+75)
		tmp = t_1;
	elseif (t <= -3.4e-31)
		tmp = y * ((z - t) / (a - t));
	elseif ((t <= -2.5e-54) || (~((t <= 2.05e-91)) && ((t <= 1.48e-27) || ~((t <= 370000000.0)))))
		tmp = t_1;
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+75], t$95$1, If[LessEqual[t, -3.4e-31], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.5e-54], And[N[Not[LessEqual[t, 2.05e-91]], $MachinePrecision], Or[LessEqual[t, 1.48e-27], N[Not[LessEqual[t, 370000000.0]], $MachinePrecision]]]], t$95$1, N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999997e75 or -3.4000000000000001e-31 < t < -2.50000000000000008e-54 or 2.05000000000000012e-91 < t < 1.48000000000000008e-27 or 3.7e8 < t

   1. Initial program 49.8%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around inf 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate-*r/ 70.5%

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

      3. associate-*r/ 70.5%

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

      4. div-sub 70.5%

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

      5. distribute-lft-out-- 70.5%

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

      6. associate-*r/ 70.5%

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

      7. mul-1-neg 70.5%

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

      8. unsub-neg 70.5%

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

      9. distribute-rgt-out-- 71.4%

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

      10. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in z around inf 66.8%

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

      1. associate-*r/ 72.4%

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

   10. Simplified 72.4%

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

   if -4.19999999999999997e75 < t < -3.4000000000000001e-31

   1. Initial program 70.2%

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

      1. associate-*l/ 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around 0 63.2%

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

      1. associate-/l* 66.6%

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

      2. div-inv 66.6%

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

      3. clear-num 66.7%

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

   7. Applied egg-rr 66.7%

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

   if -2.50000000000000008e-54 < t < 2.05000000000000012e-91 or 1.48000000000000008e-27 < t < 3.7e8

   1. Initial program 90.8%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 74.7%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-54} \lor \neg \left(t \leq 2.05 \cdot 10^{-91}\right) \land \left(t \leq 1.48 \cdot 10^{-27} \lor \neg \left(t \leq 370000000\right)\right):\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-106} \lor \neg \left(y \leq 6.5 \cdot 10^{+52}\right) \land y \leq 6.6 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -6.6e-54)
     t_2
     (if (<= y -1.35e-251)
       t_1
       (if (<= y -1.8e-300)
         x
         (if (or (<= y 2.7e-106) (and (not (<= y 6.5e+52)) (<= y 6.6e+163)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -6.6e-54) {
		tmp = t_2;
	} else if (y <= -1.35e-251) {
		tmp = t_1;
	} else if (y <= -1.8e-300) {
		tmp = x;
	} else if ((y <= 2.7e-106) || (!(y <= 6.5e+52) && (y <= 6.6e+163))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-6.6d-54)) then
        tmp = t_2
    else if (y <= (-1.35d-251)) then
        tmp = t_1
    else if (y <= (-1.8d-300)) then
        tmp = x
    else if ((y <= 2.7d-106) .or. (.not. (y <= 6.5d+52)) .and. (y <= 6.6d+163)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -6.6e-54) {
		tmp = t_2;
	} else if (y <= -1.35e-251) {
		tmp = t_1;
	} else if (y <= -1.8e-300) {
		tmp = x;
	} else if ((y <= 2.7e-106) || (!(y <= 6.5e+52) && (y <= 6.6e+163))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -6.6e-54:
		tmp = t_2
	elif y <= -1.35e-251:
		tmp = t_1
	elif y <= -1.8e-300:
		tmp = x
	elif (y <= 2.7e-106) or (not (y <= 6.5e+52) and (y <= 6.6e+163)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -6.6e-54)
		tmp = t_2;
	elseif (y <= -1.35e-251)
		tmp = t_1;
	elseif (y <= -1.8e-300)
		tmp = x;
	elseif ((y <= 2.7e-106) || (!(y <= 6.5e+52) && (y <= 6.6e+163)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -6.6e-54)
		tmp = t_2;
	elseif (y <= -1.35e-251)
		tmp = t_1;
	elseif (y <= -1.8e-300)
		tmp = x;
	elseif ((y <= 2.7e-106) || (~((y <= 6.5e+52)) && (y <= 6.6e+163)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e-54], t$95$2, If[LessEqual[y, -1.35e-251], t$95$1, If[LessEqual[y, -1.8e-300], x, If[Or[LessEqual[y, 2.7e-106], And[N[Not[LessEqual[y, 6.5e+52]], $MachinePrecision], LessEqual[y, 6.6e+163]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.59999999999999986e-54 or 2.70000000000000022e-106 < y < 6.49999999999999996e52 or 6.5999999999999999e163 < y

   1. Initial program 65.8%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 70.6%

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

      2. div-inv 70.6%

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

      3. clear-num 70.6%

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

   7. Applied egg-rr 70.6%

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

   if -6.59999999999999986e-54 < y < -1.35000000000000005e-251 or -1.80000000000000008e-300 < y < 2.70000000000000022e-106 or 6.49999999999999996e52 < y < 6.5999999999999999e163

   1. Initial program 74.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 56.7%

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

      1. div-sub 56.7%

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

   7. Simplified 56.7%

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

   if -1.35000000000000005e-251 < y < -1.80000000000000008e-300

   1. Initial program 82.2%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in a around inf 58.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-251}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-106} \lor \neg \left(y \leq 6.5 \cdot 10^{+52}\right) \land y \leq 6.6 \cdot 10^{+163}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= y -2.6e-52)
     t_2
     (if (<= y -6.2e-252)
       t_1
       (if (<= y -1.65e-300)
         x
         (if (<= y 1.95e-106)
           t_1
           (if (<= y 8.8e+51)
             (* y (/ (- z t) (- a t)))
             (if (<= y 4.1e+163) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -2.6e-52) {
		tmp = t_2;
	} else if (y <= -6.2e-252) {
		tmp = t_1;
	} else if (y <= -1.65e-300) {
		tmp = x;
	} else if (y <= 1.95e-106) {
		tmp = t_1;
	} else if (y <= 8.8e+51) {
		tmp = y * ((z - t) / (a - t));
	} else if (y <= 4.1e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = (z - t) * (y / (a - t))
    if (y <= (-2.6d-52)) then
        tmp = t_2
    else if (y <= (-6.2d-252)) then
        tmp = t_1
    else if (y <= (-1.65d-300)) then
        tmp = x
    else if (y <= 1.95d-106) then
        tmp = t_1
    else if (y <= 8.8d+51) then
        tmp = y * ((z - t) / (a - t))
    else if (y <= 4.1d+163) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -2.6e-52) {
		tmp = t_2;
	} else if (y <= -6.2e-252) {
		tmp = t_1;
	} else if (y <= -1.65e-300) {
		tmp = x;
	} else if (y <= 1.95e-106) {
		tmp = t_1;
	} else if (y <= 8.8e+51) {
		tmp = y * ((z - t) / (a - t));
	} else if (y <= 4.1e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = (z - t) * (y / (a - t))
	tmp = 0
	if y <= -2.6e-52:
		tmp = t_2
	elif y <= -6.2e-252:
		tmp = t_1
	elif y <= -1.65e-300:
		tmp = x
	elif y <= 1.95e-106:
		tmp = t_1
	elif y <= 8.8e+51:
		tmp = y * ((z - t) / (a - t))
	elif y <= 4.1e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (y <= -2.6e-52)
		tmp = t_2;
	elseif (y <= -6.2e-252)
		tmp = t_1;
	elseif (y <= -1.65e-300)
		tmp = x;
	elseif (y <= 1.95e-106)
		tmp = t_1;
	elseif (y <= 8.8e+51)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (y <= 4.1e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (y <= -2.6e-52)
		tmp = t_2;
	elseif (y <= -6.2e-252)
		tmp = t_1;
	elseif (y <= -1.65e-300)
		tmp = x;
	elseif (y <= 1.95e-106)
		tmp = t_1;
	elseif (y <= 8.8e+51)
		tmp = y * ((z - t) / (a - t));
	elseif (y <= 4.1e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-52], t$95$2, If[LessEqual[y, -6.2e-252], t$95$1, If[LessEqual[y, -1.65e-300], x, If[LessEqual[y, 1.95e-106], t$95$1, If[LessEqual[y, 8.8e+51], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+163], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5999999999999999e-52 or 4.0999999999999999e163 < y

   1. Initial program 64.3%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around 0 52.3%

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

      1. associate-/l* 71.9%

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

      2. associate-/r/ 73.2%

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

   7. Simplified 73.2%

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

   if -2.5999999999999999e-52 < y < -6.1999999999999997e-252 or -1.6500000000000001e-300 < y < 1.95000000000000005e-106 or 8.79999999999999967e51 < y < 4.0999999999999999e163

   1. Initial program 74.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 56.7%

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

      1. div-sub 56.7%

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

   7. Simplified 56.7%

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

   if -6.1999999999999997e-252 < y < -1.6500000000000001e-300

   1. Initial program 82.2%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in a around inf 58.7%

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

   if 1.95000000000000005e-106 < y < 8.79999999999999967e51

   1. Initial program 72.6%

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

      1. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around 0 61.3%

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

      1. associate-/l* 65.2%

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

      2. div-inv 65.1%

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

      3. clear-num 65.1%

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

   7. Applied egg-rr 65.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+163}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 195000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (+ x (/ z (/ a (- y x))))))
   (if (<= t -8.2e+74)
     t_1
     (if (<= t -6.2e-31)
       (* y (/ (- z t) (- a t)))
       (if (<= t -9.2e-55)
         t_1
         (if (<= t 3.6e-92)
           t_2
           (if (<= t 1.1e-27)
             t_1
             (if (<= t 195000000.0) t_2 (+ y (* z (/ (- x y) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -8.2e+74) {
		tmp = t_1;
	} else if (t <= -6.2e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -9.2e-55) {
		tmp = t_1;
	} else if (t <= 3.6e-92) {
		tmp = t_2;
	} else if (t <= 1.1e-27) {
		tmp = t_1;
	} else if (t <= 195000000.0) {
		tmp = t_2;
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / z))
    t_2 = x + (z / (a / (y - x)))
    if (t <= (-8.2d+74)) then
        tmp = t_1
    else if (t <= (-6.2d-31)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-9.2d-55)) then
        tmp = t_1
    else if (t <= 3.6d-92) then
        tmp = t_2
    else if (t <= 1.1d-27) then
        tmp = t_1
    else if (t <= 195000000.0d0) then
        tmp = t_2
    else
        tmp = y + (z * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -8.2e+74) {
		tmp = t_1;
	} else if (t <= -6.2e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -9.2e-55) {
		tmp = t_1;
	} else if (t <= 3.6e-92) {
		tmp = t_2;
	} else if (t <= 1.1e-27) {
		tmp = t_1;
	} else if (t <= 195000000.0) {
		tmp = t_2;
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = x + (z / (a / (y - x)))
	tmp = 0
	if t <= -8.2e+74:
		tmp = t_1
	elif t <= -6.2e-31:
		tmp = y * ((z - t) / (a - t))
	elif t <= -9.2e-55:
		tmp = t_1
	elif t <= 3.6e-92:
		tmp = t_2
	elif t <= 1.1e-27:
		tmp = t_1
	elif t <= 195000000.0:
		tmp = t_2
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (t <= -8.2e+74)
		tmp = t_1;
	elseif (t <= -6.2e-31)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -9.2e-55)
		tmp = t_1;
	elseif (t <= 3.6e-92)
		tmp = t_2;
	elseif (t <= 1.1e-27)
		tmp = t_1;
	elseif (t <= 195000000.0)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (t <= -8.2e+74)
		tmp = t_1;
	elseif (t <= -6.2e-31)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -9.2e-55)
		tmp = t_1;
	elseif (t <= 3.6e-92)
		tmp = t_2;
	elseif (t <= 1.1e-27)
		tmp = t_1;
	elseif (t <= 195000000.0)
		tmp = t_2;
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+74], t$95$1, If[LessEqual[t, -6.2e-31], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-55], t$95$1, If[LessEqual[t, 3.6e-92], t$95$2, If[LessEqual[t, 1.1e-27], t$95$1, If[LessEqual[t, 195000000.0], t$95$2, N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.2000000000000001e74 or -6.19999999999999999e-31 < t < -9.20000000000000046e-55 or 3.60000000000000016e-92 < t < 1.09999999999999993e-27

   1. Initial program 54.9%

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

      1. associate-*l/ 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in t around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. associate-*r/ 73.5%

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

      3. associate-*r/ 73.5%

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

      4. div-sub 73.5%

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

      5. distribute-lft-out-- 73.5%

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

      6. associate-*r/ 73.5%

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

      7. mul-1-neg 73.5%

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

      8. unsub-neg 73.5%

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

      9. distribute-rgt-out-- 73.5%

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

      10. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in z around inf 81.3%

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

   if -8.2000000000000001e74 < t < -6.19999999999999999e-31

   1. Initial program 70.2%

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

      1. associate-*l/ 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around 0 63.2%

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

      1. associate-/l* 66.6%

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

      2. div-inv 66.6%

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

      3. clear-num 66.7%

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

   7. Applied egg-rr 66.7%

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

   if -9.20000000000000046e-55 < t < 3.60000000000000016e-92 or 1.09999999999999993e-27 < t < 1.95e8

   1. Initial program 90.8%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 74.7%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if 1.95e8 < t

   1. Initial program 43.7%

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

      1. associate-*l/ 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. associate-*r/ 67.0%

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

      7. mul-1-neg 67.0%

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

      8. unsub-neg 67.0%

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

      9. distribute-rgt-out-- 68.9%

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

      10. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around inf 62.0%

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

      1. associate-*r/ 69.1%

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

   10. Simplified 69.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-55}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 195000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+132}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 120000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (+ y (/ (- x y) (/ t z)))))
   (if (<= t -5.4e+132)
     (+ y (* (- z a) (/ x t)))
     (if (<= t -3.8e-31)
       (* y (/ (- z t) (- a t)))
       (if (<= t -1.3e-57)
         t_2
         (if (<= t 1.15e-91)
           t_1
           (if (<= t 8e-28)
             t_2
             (if (<= t 120000000.0) t_1 (+ y (* z (/ (- x y) t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -5.4e+132) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -3.8e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.3e-57) {
		tmp = t_2;
	} else if (t <= 1.15e-91) {
		tmp = t_1;
	} else if (t <= 8e-28) {
		tmp = t_2;
	} else if (t <= 120000000.0) {
		tmp = t_1;
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y + ((x - y) / (t / z))
    if (t <= (-5.4d+132)) then
        tmp = y + ((z - a) * (x / t))
    else if (t <= (-3.8d-31)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-1.3d-57)) then
        tmp = t_2
    else if (t <= 1.15d-91) then
        tmp = t_1
    else if (t <= 8d-28) then
        tmp = t_2
    else if (t <= 120000000.0d0) then
        tmp = t_1
    else
        tmp = y + (z * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -5.4e+132) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -3.8e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.3e-57) {
		tmp = t_2;
	} else if (t <= 1.15e-91) {
		tmp = t_1;
	} else if (t <= 8e-28) {
		tmp = t_2;
	} else if (t <= 120000000.0) {
		tmp = t_1;
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y + ((x - y) / (t / z))
	tmp = 0
	if t <= -5.4e+132:
		tmp = y + ((z - a) * (x / t))
	elif t <= -3.8e-31:
		tmp = y * ((z - t) / (a - t))
	elif t <= -1.3e-57:
		tmp = t_2
	elif t <= 1.15e-91:
		tmp = t_1
	elif t <= 8e-28:
		tmp = t_2
	elif t <= 120000000.0:
		tmp = t_1
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (t <= -5.4e+132)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	elseif (t <= -3.8e-31)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -1.3e-57)
		tmp = t_2;
	elseif (t <= 1.15e-91)
		tmp = t_1;
	elseif (t <= 8e-28)
		tmp = t_2;
	elseif (t <= 120000000.0)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y + ((x - y) / (t / z));
	tmp = 0.0;
	if (t <= -5.4e+132)
		tmp = y + ((z - a) * (x / t));
	elseif (t <= -3.8e-31)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -1.3e-57)
		tmp = t_2;
	elseif (t <= 1.15e-91)
		tmp = t_1;
	elseif (t <= 8e-28)
		tmp = t_2;
	elseif (t <= 120000000.0)
		tmp = t_1;
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+132], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-31], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e-57], t$95$2, If[LessEqual[t, 1.15e-91], t$95$1, If[LessEqual[t, 8e-28], t$95$2, If[LessEqual[t, 120000000.0], t$95$1, N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.3999999999999999e132

   1. Initial program 34.5%

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

      1. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in t around inf 59.2%

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

      1. associate--l+ 59.2%

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

      2. associate-*r/ 59.2%

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

      3. associate-*r/ 59.2%

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

      4. div-sub 59.2%

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

      5. distribute-lft-out-- 59.2%

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

      6. associate-*r/ 59.2%

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

      7. mul-1-neg 59.2%

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

      8. unsub-neg 59.2%

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

      9. distribute-rgt-out-- 59.2%

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

      10. associate-/l* 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-*l/ 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

   10. Simplified 80.3%

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

   if -5.3999999999999999e132 < t < -3.8e-31

   1. Initial program 60.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in x around 0 63.8%

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

      1. associate-/l* 71.4%

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

      2. div-inv 71.4%

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

      3. clear-num 71.5%

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

   7. Applied egg-rr 71.5%

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

   if -3.8e-31 < t < -1.29999999999999993e-57 or 1.14999999999999998e-91 < t < 7.99999999999999977e-28

   1. Initial program 83.7%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in t around inf 85.0%

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

      1. associate--l+ 85.0%

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

      2. associate-*r/ 85.0%

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

      3. associate-*r/ 85.0%

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

      4. div-sub 85.0%

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

      5. distribute-lft-out-- 85.0%

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

      6. associate-*r/ 85.0%

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

      7. mul-1-neg 85.0%

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

      8. unsub-neg 85.0%

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

      9. distribute-rgt-out-- 85.0%

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

      10. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in z around inf 84.1%

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

   if -1.29999999999999993e-57 < t < 1.14999999999999998e-91 or 7.99999999999999977e-28 < t < 1.2e8

   1. Initial program 90.8%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 74.7%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if 1.2e8 < t

   1. Initial program 43.7%

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

      1. associate-*l/ 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. associate-*r/ 67.0%

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

      7. mul-1-neg 67.0%

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

      8. unsub-neg 67.0%

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

      9. distribute-rgt-out-- 68.9%

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

      10. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around inf 62.0%

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

      1. associate-*r/ 69.1%

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

   10. Simplified 69.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+132}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-57}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-28}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 120000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{z}}{y}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -7.5e-54)
       (* y (+ (/ a t) 1.0))
       (if (<= t -8.2e-237)
         x
         (if (<= t -9.5e-280)
           (/ 1.0 (/ (/ a z) y))
           (if (<= t 9.5e-93) x (if (<= t 3e+193) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -7.5e-54) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -8.2e-237) {
		tmp = x;
	} else if (t <= -9.5e-280) {
		tmp = 1.0 / ((a / z) / y);
	} else if (t <= 9.5e-93) {
		tmp = x;
	} else if (t <= 3e+193) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-7.5d-54)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-8.2d-237)) then
        tmp = x
    else if (t <= (-9.5d-280)) then
        tmp = 1.0d0 / ((a / z) / y)
    else if (t <= 9.5d-93) then
        tmp = x
    else if (t <= 3d+193) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -7.5e-54) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -8.2e-237) {
		tmp = x;
	} else if (t <= -9.5e-280) {
		tmp = 1.0 / ((a / z) / y);
	} else if (t <= 9.5e-93) {
		tmp = x;
	} else if (t <= 3e+193) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -7.5e-54:
		tmp = y * ((a / t) + 1.0)
	elif t <= -8.2e-237:
		tmp = x
	elif t <= -9.5e-280:
		tmp = 1.0 / ((a / z) / y)
	elif t <= 9.5e-93:
		tmp = x
	elif t <= 3e+193:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -7.5e-54)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -8.2e-237)
		tmp = x;
	elseif (t <= -9.5e-280)
		tmp = Float64(1.0 / Float64(Float64(a / z) / y));
	elseif (t <= 9.5e-93)
		tmp = x;
	elseif (t <= 3e+193)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -7.5e-54)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -8.2e-237)
		tmp = x;
	elseif (t <= -9.5e-280)
		tmp = 1.0 / ((a / z) / y);
	elseif (t <= 9.5e-93)
		tmp = x;
	elseif (t <= 3e+193)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -7.5e-54], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.2e-237], x, If[LessEqual[t, -9.5e-280], N[(1.0 / N[(N[(a / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-93], x, If[LessEqual[t, 3e+193], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.7999999999999995e279 or 9.5000000000000001e-93 < t < 3e193

   1. Initial program 63.3%

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

      1. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in x around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. associate--r+ 36.9%

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

      5. sub-neg 36.9%

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

      6. metadata-eval 36.9%

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

   7. Simplified 36.9%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in t around -inf 34.4%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 43.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   10. Simplified 43.5%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   if -5.7999999999999995e279 < t < -7.5000000000000005e-54

   1. Initial program 59.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.3%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.3%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 76.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around 0 45.5%

      \[\leadsto y - \frac{y - x}{\color{blue}{-1 \cdot \frac{t}{a}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 45.5%

         \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-1 \cdot t}{a}}} \]

      2. neg-mul-1 45.5%

         \[\leadsto y - \frac{y - x}{\frac{\color{blue}{-t}}{a}} \]

   10. Simplified 45.5%

       \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-t}{a}}} \]

   11. Taylor expanded in y around inf 39.8%

       \[\leadsto \color{blue}{y \cdot \left(1 - -1 \cdot \frac{a}{t}\right)} \]
   12. Step-by-step derivation

       1. sub-neg 39.8%

          \[\leadsto y \cdot \color{blue}{\left(1 + \left(--1 \cdot \frac{a}{t}\right)\right)} \]

       2. mul-1-neg 39.8%

          \[\leadsto y \cdot \left(1 + \left(-\color{blue}{\left(-\frac{a}{t}\right)}\right)\right) \]

       3. remove-double-neg 39.8%

          \[\leadsto y \cdot \left(1 + \color{blue}{\frac{a}{t}}\right) \]

   13. Simplified 39.8%

       \[\leadsto \color{blue}{y \cdot \left(1 + \frac{a}{t}\right)} \]

   if -7.5000000000000005e-54 < t < -8.2000000000000002e-237 or -9.50000000000000082e-280 < t < 9.5000000000000001e-93

   1. Initial program 90.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{x} \]

   if -8.2000000000000002e-237 < t < -9.50000000000000082e-280

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
   9. Step-by-step derivation

      1. clear-num 56.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y}}} \]

      2. inv-pow 56.6%

         \[\leadsto \color{blue}{{\left(\frac{\frac{a}{z}}{y}\right)}^{-1}} \]

   10. Applied egg-rr 56.6%

       \[\leadsto \color{blue}{{\left(\frac{\frac{a}{z}}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 56.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y}}} \]

   12. Simplified 56.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y}}} \]

   if 3e193 < t

   1. Initial program 22.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{z}}{y}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))))
   (if (<= t -5.8e+279)
     t_1
     (if (<= t -1.15e-53)
       (* y (+ (/ a t) 1.0))
       (if (<= t 4.5e-92)
         x
         (if (<= t 2e-26)
           (* x (/ z t))
           (if (<= t 3e+46) (/ y (/ a (- z t))) (if (<= t 6e+192) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -1.15e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= 4.5e-92) {
		tmp = x;
	} else if (t <= 2e-26) {
		tmp = x * (z / t);
	} else if (t <= 3e+46) {
		tmp = y / (a / (z - t));
	} else if (t <= 6e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    if (t <= (-5.8d+279)) then
        tmp = t_1
    else if (t <= (-1.15d-53)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= 4.5d-92) then
        tmp = x
    else if (t <= 2d-26) then
        tmp = x * (z / t)
    else if (t <= 3d+46) then
        tmp = y / (a / (z - t))
    else if (t <= 6d+192) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = t_1;
	} else if (t <= -1.15e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= 4.5e-92) {
		tmp = x;
	} else if (t <= 2e-26) {
		tmp = x * (z / t);
	} else if (t <= 3e+46) {
		tmp = y / (a / (z - t));
	} else if (t <= 6e+192) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	tmp = 0
	if t <= -5.8e+279:
		tmp = t_1
	elif t <= -1.15e-53:
		tmp = y * ((a / t) + 1.0)
	elif t <= 4.5e-92:
		tmp = x
	elif t <= 2e-26:
		tmp = x * (z / t)
	elif t <= 3e+46:
		tmp = y / (a / (z - t))
	elif t <= 6e+192:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -1.15e-53)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= 4.5e-92)
		tmp = x;
	elseif (t <= 2e-26)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 3e+46)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 6e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = t_1;
	elseif (t <= -1.15e-53)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= 4.5e-92)
		tmp = x;
	elseif (t <= 2e-26)
		tmp = x * (z / t);
	elseif (t <= 3e+46)
		tmp = y / (a / (z - t));
	elseif (t <= 6e+192)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], t$95$1, If[LessEqual[t, -1.15e-53], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-92], x, If[LessEqual[t, 2e-26], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+46], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+192], t$95$1, y]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.7999999999999995e279 or 3.00000000000000023e46 < t < 6e192

   1. Initial program 38.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 48.6%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 21.0%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 21.0%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 21.0%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 21.0%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in t around -inf 33.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 52.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   10. Simplified 52.5%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   if -5.7999999999999995e279 < t < -1.1500000000000001e-53

   1. Initial program 59.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.3%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.3%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 76.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around 0 45.5%

      \[\leadsto y - \frac{y - x}{\color{blue}{-1 \cdot \frac{t}{a}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 45.5%

         \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-1 \cdot t}{a}}} \]

      2. neg-mul-1 45.5%

         \[\leadsto y - \frac{y - x}{\frac{\color{blue}{-t}}{a}} \]

   10. Simplified 45.5%

       \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-t}{a}}} \]

   11. Taylor expanded in y around inf 39.8%

       \[\leadsto \color{blue}{y \cdot \left(1 - -1 \cdot \frac{a}{t}\right)} \]
   12. Step-by-step derivation

       1. sub-neg 39.8%

          \[\leadsto y \cdot \color{blue}{\left(1 + \left(--1 \cdot \frac{a}{t}\right)\right)} \]

       2. mul-1-neg 39.8%

          \[\leadsto y \cdot \left(1 + \left(-\color{blue}{\left(-\frac{a}{t}\right)}\right)\right) \]

       3. remove-double-neg 39.8%

          \[\leadsto y \cdot \left(1 + \color{blue}{\frac{a}{t}}\right) \]

   13. Simplified 39.8%

       \[\leadsto \color{blue}{y \cdot \left(1 + \frac{a}{t}\right)} \]

   if -1.1500000000000001e-53 < t < 4.5e-92

   1. Initial program 90.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{x} \]

   if 4.5e-92 < t < 2.0000000000000001e-26

   1. Initial program 80.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 70.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 70.7%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 70.7%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 70.7%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 60.8%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 60.8%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 60.8%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 60.8%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in a around 0 51.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \cdot \left(-x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 51.3%

         \[\leadsto \color{blue}{\frac{-1 \cdot z}{t}} \cdot \left(-x\right) \]

      2. mul-1-neg 51.3%

         \[\leadsto \frac{\color{blue}{-z}}{t} \cdot \left(-x\right) \]

   10. Simplified 51.3%

       \[\leadsto \color{blue}{\frac{-z}{t}} \cdot \left(-x\right) \]

   if 2.0000000000000001e-26 < t < 3.00000000000000023e46

   1. Initial program 93.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 60.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 54.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   8. Simplified 54.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   if 6e192 < t

   1. Initial program 22.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 130000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ z (/ a (- y x))))))
   (if (<= t -5.8e+279)
     (/ x (/ t (- z a)))
     (if (<= t -4.2e-54)
       t_1
       (if (<= t 1.25e-92)
         t_2
         (if (<= t 1.75e-31)
           (* z (/ (- y x) (- a t)))
           (if (<= t 130000000.0) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = x / (t / (z - a));
	} else if (t <= -4.2e-54) {
		tmp = t_1;
	} else if (t <= 1.25e-92) {
		tmp = t_2;
	} else if (t <= 1.75e-31) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 130000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (z / (a / (y - x)))
    if (t <= (-5.8d+279)) then
        tmp = x / (t / (z - a))
    else if (t <= (-4.2d-54)) then
        tmp = t_1
    else if (t <= 1.25d-92) then
        tmp = t_2
    else if (t <= 1.75d-31) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 130000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -5.8e+279) {
		tmp = x / (t / (z - a));
	} else if (t <= -4.2e-54) {
		tmp = t_1;
	} else if (t <= 1.25e-92) {
		tmp = t_2;
	} else if (t <= 1.75e-31) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 130000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (z / (a / (y - x)))
	tmp = 0
	if t <= -5.8e+279:
		tmp = x / (t / (z - a))
	elif t <= -4.2e-54:
		tmp = t_1
	elif t <= 1.25e-92:
		tmp = t_2
	elif t <= 1.75e-31:
		tmp = z * ((y - x) / (a - t))
	elif t <= 130000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (t <= -5.8e+279)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (t <= -4.2e-54)
		tmp = t_1;
	elseif (t <= 1.25e-92)
		tmp = t_2;
	elseif (t <= 1.75e-31)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 130000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (t <= -5.8e+279)
		tmp = x / (t / (z - a));
	elseif (t <= -4.2e-54)
		tmp = t_1;
	elseif (t <= 1.25e-92)
		tmp = t_2;
	elseif (t <= 1.75e-31)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 130000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+279], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-54], t$95$1, If[LessEqual[t, 1.25e-92], t$95$2, If[LessEqual[t, 1.75e-31], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 130000000.0], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.7999999999999995e279

   1. Initial program 1.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 17.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 17.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 77.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.5%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 77.5%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 77.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 17.3%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 17.3%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 17.3%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 17.3%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in t around -inf 45.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 96.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   10. Simplified 96.0%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   if -5.7999999999999995e279 < t < -4.2e-54 or 1.3e8 < t

   1. Initial program 52.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 45.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

      2. div-inv 64.8%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{a - t}{z - t}}} \]

      3. clear-num 64.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   7. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -4.2e-54 < t < 1.25000000000000003e-92 or 1.74999999999999993e-31 < t < 1.3e8

   1. Initial program 90.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.1%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.4%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 79.4%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   if 1.25000000000000003e-92 < t < 1.74999999999999993e-31

   1. Initial program 78.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 78.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.1%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 62.1%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 62.1%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+279}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 130000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+136}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5e+136)
   (+ y (* (- z a) (/ x t)))
   (if (<= t -1.2e-31)
     (* y (/ (- z t) (- a t)))
     (if (<= t -1.15e-53)
       (+ y (/ (- x y) (/ t z)))
       (if (<= t 3.3e+74)
         (+ x (* (- y x) (/ z (- a t))))
         (+ y (* z (/ (- x y) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5e+136) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -1.2e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.15e-53) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 3.3e+74) {
		tmp = x + ((y - x) * (z / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5d+136)) then
        tmp = y + ((z - a) * (x / t))
    else if (t <= (-1.2d-31)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-1.15d-53)) then
        tmp = y + ((x - y) / (t / z))
    else if (t <= 3.3d+74) then
        tmp = x + ((y - x) * (z / (a - t)))
    else
        tmp = y + (z * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5e+136) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -1.2e-31) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.15e-53) {
		tmp = y + ((x - y) / (t / z));
	} else if (t <= 3.3e+74) {
		tmp = x + ((y - x) * (z / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5e+136:
		tmp = y + ((z - a) * (x / t))
	elif t <= -1.2e-31:
		tmp = y * ((z - t) / (a - t))
	elif t <= -1.15e-53:
		tmp = y + ((x - y) / (t / z))
	elif t <= 3.3e+74:
		tmp = x + ((y - x) * (z / (a - t)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5e+136)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	elseif (t <= -1.2e-31)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -1.15e-53)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (t <= 3.3e+74)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5e+136)
		tmp = y + ((z - a) * (x / t));
	elseif (t <= -1.2e-31)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -1.15e-53)
		tmp = y + ((x - y) / (t / z));
	elseif (t <= 3.3e+74)
		tmp = x + ((y - x) * (z / (a - t)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5e+136], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-31], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-53], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+74], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.0000000000000002e136

   1. Initial program 34.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 59.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 59.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 59.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 59.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 59.2%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 59.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 59.2%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 59.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 59.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 59.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 89.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 89.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in y around 0 63.9%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-*l/ 80.3%

         \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot \left(z - a\right)}\right) \]

      3. distribute-rgt-neg-in 80.3%

         \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   10. Simplified 80.3%

       \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   if -5.0000000000000002e136 < t < -1.2e-31

   1. Initial program 60.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.4%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

      2. div-inv 71.4%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{a - t}{z - t}}} \]

      3. clear-num 71.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   7. Applied egg-rr 71.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.2e-31 < t < -1.1500000000000001e-53

   1. Initial program 97.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 92.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 92.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 92.0%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 92.0%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 92.0%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 92.0%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 92.0%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 92.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 92.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 92.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 92.0%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 92.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 88.7%

      \[\leadsto y - \frac{y - x}{\color{blue}{\frac{t}{z}}} \]

   if -1.1500000000000001e-53 < t < 3.3000000000000002e74

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 92.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 92.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 92.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 92.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 92.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 92.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in z around inf 84.3%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{a - t}} + x \]

   if 3.3000000000000002e74 < t

   1. Initial program 31.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 72.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 72.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 72.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 72.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 72.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 72.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 72.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 72.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 75.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.2%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 68.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 77.7%

         \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]

   10. Simplified 77.7%

       \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+136}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-53)
   y
   (if (<= t -8.8e-238)
     x
     (if (<= t -2.1e-279)
       (/ y (/ a z))
       (if (<= t 5.8e-94) x (if (<= t 5e+67) (/ (* x z) t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y;
	} else if (t <= -8.8e-238) {
		tmp = x;
	} else if (t <= -2.1e-279) {
		tmp = y / (a / z);
	} else if (t <= 5.8e-94) {
		tmp = x;
	} else if (t <= 5e+67) {
		tmp = (x * z) / t;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-53)) then
        tmp = y
    else if (t <= (-8.8d-238)) then
        tmp = x
    else if (t <= (-2.1d-279)) then
        tmp = y / (a / z)
    else if (t <= 5.8d-94) then
        tmp = x
    else if (t <= 5d+67) then
        tmp = (x * z) / t
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y;
	} else if (t <= -8.8e-238) {
		tmp = x;
	} else if (t <= -2.1e-279) {
		tmp = y / (a / z);
	} else if (t <= 5.8e-94) {
		tmp = x;
	} else if (t <= 5e+67) {
		tmp = (x * z) / t;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-53:
		tmp = y
	elif t <= -8.8e-238:
		tmp = x
	elif t <= -2.1e-279:
		tmp = y / (a / z)
	elif t <= 5.8e-94:
		tmp = x
	elif t <= 5e+67:
		tmp = (x * z) / t
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-53)
		tmp = y;
	elseif (t <= -8.8e-238)
		tmp = x;
	elseif (t <= -2.1e-279)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.8e-94)
		tmp = x;
	elseif (t <= 5e+67)
		tmp = Float64(Float64(x * z) / t);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-53)
		tmp = y;
	elseif (t <= -8.8e-238)
		tmp = x;
	elseif (t <= -2.1e-279)
		tmp = y / (a / z);
	elseif (t <= 5.8e-94)
		tmp = x;
	elseif (t <= 5e+67)
		tmp = (x * z) / t;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-53], y, If[LessEqual[t, -8.8e-238], x, If[LessEqual[t, -2.1e-279], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-94], x, If[LessEqual[t, 5e+67], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1500000000000001e-53 or 4.99999999999999976e67 < t

   1. Initial program 45.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 40.6%

      \[\leadsto \color{blue}{y} \]

   if -1.1500000000000001e-53 < t < -8.79999999999999965e-238 or -2.10000000000000006e-279 < t < 5.79999999999999991e-94

   1. Initial program 90.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{x} \]

   if -8.79999999999999965e-238 < t < -2.10000000000000006e-279

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 5.79999999999999991e-94 < t < 4.99999999999999976e67

   1. Initial program 84.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 57.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 57.4%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 57.4%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 57.4%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 50.5%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 50.5%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 50.5%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 50.5%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in a around 0 35.1%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-53)
   (* y (+ (/ a t) 1.0))
   (if (<= t -7.2e-240)
     x
     (if (<= t -1.45e-282)
       (/ y (/ a z))
       (if (<= t 2.95e-92) x (if (<= t 1.45e+66) (/ (* x z) t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -7.2e-240) {
		tmp = x;
	} else if (t <= -1.45e-282) {
		tmp = y / (a / z);
	} else if (t <= 2.95e-92) {
		tmp = x;
	} else if (t <= 1.45e+66) {
		tmp = (x * z) / t;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-53)) then
        tmp = y * ((a / t) + 1.0d0)
    else if (t <= (-7.2d-240)) then
        tmp = x
    else if (t <= (-1.45d-282)) then
        tmp = y / (a / z)
    else if (t <= 2.95d-92) then
        tmp = x
    else if (t <= 1.45d+66) then
        tmp = (x * z) / t
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y * ((a / t) + 1.0);
	} else if (t <= -7.2e-240) {
		tmp = x;
	} else if (t <= -1.45e-282) {
		tmp = y / (a / z);
	} else if (t <= 2.95e-92) {
		tmp = x;
	} else if (t <= 1.45e+66) {
		tmp = (x * z) / t;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-53:
		tmp = y * ((a / t) + 1.0)
	elif t <= -7.2e-240:
		tmp = x
	elif t <= -1.45e-282:
		tmp = y / (a / z)
	elif t <= 2.95e-92:
		tmp = x
	elif t <= 1.45e+66:
		tmp = (x * z) / t
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-53)
		tmp = Float64(y * Float64(Float64(a / t) + 1.0));
	elseif (t <= -7.2e-240)
		tmp = x;
	elseif (t <= -1.45e-282)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 2.95e-92)
		tmp = x;
	elseif (t <= 1.45e+66)
		tmp = Float64(Float64(x * z) / t);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-53)
		tmp = y * ((a / t) + 1.0);
	elseif (t <= -7.2e-240)
		tmp = x;
	elseif (t <= -1.45e-282)
		tmp = y / (a / z);
	elseif (t <= 2.95e-92)
		tmp = x;
	elseif (t <= 1.45e+66)
		tmp = (x * z) / t;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-53], N[(y * N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-240], x, If[LessEqual[t, -1.45e-282], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e-92], x, If[LessEqual[t, 1.45e+66], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.1500000000000001e-53

   1. Initial program 53.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 66.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 66.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 66.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 66.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 66.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 66.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 66.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 78.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around 0 43.7%

      \[\leadsto y - \frac{y - x}{\color{blue}{-1 \cdot \frac{t}{a}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 43.7%

         \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-1 \cdot t}{a}}} \]

      2. neg-mul-1 43.7%

         \[\leadsto y - \frac{y - x}{\frac{\color{blue}{-t}}{a}} \]

   10. Simplified 43.7%

       \[\leadsto y - \frac{y - x}{\color{blue}{\frac{-t}{a}}} \]

   11. Taylor expanded in y around inf 36.1%

       \[\leadsto \color{blue}{y \cdot \left(1 - -1 \cdot \frac{a}{t}\right)} \]
   12. Step-by-step derivation

       1. sub-neg 36.1%

          \[\leadsto y \cdot \color{blue}{\left(1 + \left(--1 \cdot \frac{a}{t}\right)\right)} \]

       2. mul-1-neg 36.1%

          \[\leadsto y \cdot \left(1 + \left(-\color{blue}{\left(-\frac{a}{t}\right)}\right)\right) \]

       3. remove-double-neg 36.1%

          \[\leadsto y \cdot \left(1 + \color{blue}{\frac{a}{t}}\right) \]

   13. Simplified 36.1%

       \[\leadsto \color{blue}{y \cdot \left(1 + \frac{a}{t}\right)} \]

   if -1.1500000000000001e-53 < t < -7.1999999999999998e-240 or -1.44999999999999999e-282 < t < 2.95e-92

   1. Initial program 90.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{x} \]

   if -7.1999999999999998e-240 < t < -1.44999999999999999e-282

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 2.95e-92 < t < 1.44999999999999993e66

   1. Initial program 84.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 57.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 57.4%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 57.4%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 57.4%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 50.5%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 50.5%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 50.5%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 50.5%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in a around 0 35.1%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]

   if 1.44999999999999993e66 < t

   1. Initial program 30.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 58.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\frac{a}{t} + 1\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 54.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -3.55 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -3.55e-50)
     t_1
     (if (<= y -6e-211)
       (/ x (/ t (- z a)))
       (if (<= y 8.2e-145) (/ (* x (- z)) (- a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.55e-50) {
		tmp = t_1;
	} else if (y <= -6e-211) {
		tmp = x / (t / (z - a));
	} else if (y <= 8.2e-145) {
		tmp = (x * -z) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-3.55d-50)) then
        tmp = t_1
    else if (y <= (-6d-211)) then
        tmp = x / (t / (z - a))
    else if (y <= 8.2d-145) then
        tmp = (x * -z) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.55e-50) {
		tmp = t_1;
	} else if (y <= -6e-211) {
		tmp = x / (t / (z - a));
	} else if (y <= 8.2e-145) {
		tmp = (x * -z) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -3.55e-50:
		tmp = t_1
	elif y <= -6e-211:
		tmp = x / (t / (z - a))
	elif y <= 8.2e-145:
		tmp = (x * -z) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -3.55e-50)
		tmp = t_1;
	elseif (y <= -6e-211)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (y <= 8.2e-145)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -3.55e-50)
		tmp = t_1;
	elseif (y <= -6e-211)
		tmp = x / (t / (z - a));
	elseif (y <= 8.2e-145)
		tmp = (x * -z) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.55e-50], t$95$1, If[LessEqual[y, -6e-211], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-145], N[(N[(x * (-z)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5499999999999999e-50 or 8.1999999999999995e-145 < y

   1. Initial program 67.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 51.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* 66.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

      2. div-inv 66.3%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{a - t}{z - t}}} \]

      3. clear-num 66.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   7. Applied egg-rr 66.4%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -3.5499999999999999e-50 < y < -6.00000000000000009e-211

   1. Initial program 63.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 61.2%

         \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. *-commutative 61.2%

         \[\leadsto -\color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot x} \]

      3. distribute-rgt-neg-in 61.2%

         \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \cdot \left(-x\right)} \]

      4. associate--r+ 47.5%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} - 1\right) - \frac{t}{a - t}\right)} \cdot \left(-x\right) \]

      5. sub-neg 47.5%

         \[\leadsto \left(\color{blue}{\left(\frac{z}{a - t} + \left(-1\right)\right)} - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

      6. metadata-eval 47.5%

         \[\leadsto \left(\left(\frac{z}{a - t} + \color{blue}{-1}\right) - \frac{t}{a - t}\right) \cdot \left(-x\right) \]

   7. Simplified 47.5%

      \[\leadsto \color{blue}{\left(\left(\frac{z}{a - t} + -1\right) - \frac{t}{a - t}\right) \cdot \left(-x\right)} \]

   8. Taylor expanded in t around -inf 43.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 47.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   10. Simplified 47.1%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z - a}}} \]

   if -6.00000000000000009e-211 < y < 8.1999999999999995e-145

   1. Initial program 80.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 76.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 76.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 79.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 79.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 79.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]
   7. Step-by-step derivation

      1. clear-num 79.6%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} + x \]

      2. un-div-inv 79.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

   8. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

   9. Taylor expanded in z around -inf 50.3%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 45.9%

          \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   11. Simplified 45.9%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   12. Taylor expanded in y around 0 48.9%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a - t}} \]
   13. Step-by-step derivation

       1. associate-*r/ 48.9%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{a - t}} \]

       2. mul-1-neg 48.9%

          \[\leadsto \frac{\color{blue}{-x \cdot z}}{a - t} \]

   14. Simplified 48.9%

       \[\leadsto \color{blue}{\frac{-x \cdot z}{a - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+71} \lor \neg \left(t \leq 8.5 \cdot 10^{+91}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.55e+71) (not (<= t 8.5e+91)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e+71) || !(t <= 8.5e+91)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.55d+71)) .or. (.not. (t <= 8.5d+91))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e+71) || !(t <= 8.5e+91)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.55e+71) or not (t <= 8.5e+91):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.55e+71) || !(t <= 8.5e+91))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.55e+71) || ~((t <= 8.5e+91)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.55e+71], N[Not[LessEqual[t, 8.5e+91]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000009e71 or 8.4999999999999995e91 < t

   1. Initial program 33.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 58.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 71.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.6%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -1.55000000000000009e71 < t < 8.4999999999999995e91

   1. Initial program 86.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+71} \lor \neg \left(t \leq 8.5 \cdot 10^{+91}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+71} \lor \neg \left(t \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+71) (not (<= t 1.75e+86)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+71) || !(t <= 1.75e+86)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d+71)) .or. (.not. (t <= 1.75d+86))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+71) || !(t <= 1.75e+86)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+71) or not (t <= 1.75e+86):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+71) || !(t <= 1.75e+86))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+71) || ~((t <= 1.75e+86)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+71], N[Not[LessEqual[t, 1.75e+86]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.09999999999999989e71 or 1.75000000000000009e86 < t

   1. Initial program 33.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 58.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 71.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.6%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -2.09999999999999989e71 < t < 1.75000000000000009e86

   1. Initial program 86.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/r/ 91.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   6. Applied egg-rr 91.4%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+71} \lor \neg \left(t \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+73} \lor \neg \left(t \leq 6.5 \cdot 10^{+93}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.6e+73) (not (<= t 6.5e+93)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- y x) (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+73) || !(t <= 6.5e+93)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.6d+73)) .or. (.not. (t <= 6.5d+93))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+73) || !(t <= 6.5e+93)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.6e+73) or not (t <= 6.5e+93):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.6e+73) || !(t <= 6.5e+93))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.6e+73) || ~((t <= 6.5e+93)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.6e+73], N[Not[LessEqual[t, 6.5e+93]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.60000000000000026e73 or 6.4999999999999998e93 < t

   1. Initial program 33.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 58.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 71.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.6%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -8.60000000000000026e73 < t < 6.4999999999999998e93

   1. Initial program 86.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 91.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 91.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 91.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 91.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 91.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 91.4%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+73} \lor \neg \left(t \leq 6.5 \cdot 10^{+93}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-56)
   y
   (if (<= t -4.8e-239)
     x
     (if (<= t -2.2e-277) (* z (/ y a)) (if (<= t 5.4e+45) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-56) {
		tmp = y;
	} else if (t <= -4.8e-239) {
		tmp = x;
	} else if (t <= -2.2e-277) {
		tmp = z * (y / a);
	} else if (t <= 5.4e+45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.5d-56)) then
        tmp = y
    else if (t <= (-4.8d-239)) then
        tmp = x
    else if (t <= (-2.2d-277)) then
        tmp = z * (y / a)
    else if (t <= 5.4d+45) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-56) {
		tmp = y;
	} else if (t <= -4.8e-239) {
		tmp = x;
	} else if (t <= -2.2e-277) {
		tmp = z * (y / a);
	} else if (t <= 5.4e+45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-56:
		tmp = y
	elif t <= -4.8e-239:
		tmp = x
	elif t <= -2.2e-277:
		tmp = z * (y / a)
	elif t <= 5.4e+45:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-56)
		tmp = y;
	elseif (t <= -4.8e-239)
		tmp = x;
	elseif (t <= -2.2e-277)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 5.4e+45)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-56)
		tmp = y;
	elseif (t <= -4.8e-239)
		tmp = x;
	elseif (t <= -2.2e-277)
		tmp = z * (y / a);
	elseif (t <= 5.4e+45)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-56], y, If[LessEqual[t, -4.8e-239], x, If[LessEqual[t, -2.2e-277], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+45], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999991e-56 or 5.39999999999999968e45 < t

   1. Initial program 46.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 39.2%

      \[\leadsto \color{blue}{y} \]

   if -9.4999999999999991e-56 < t < -4.79999999999999985e-239 or -2.19999999999999996e-277 < t < 5.39999999999999968e45

   1. Initial program 89.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{x} \]

   if -4.79999999999999985e-239 < t < -2.19999999999999996e-277

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 55.9%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   10. Applied egg-rr 55.9%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e-54)
   y
   (if (<= t -1.7e-237)
     x
     (if (<= t -4.5e-278) (/ y (/ a z)) (if (<= t 5.5e+45) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e-54) {
		tmp = y;
	} else if (t <= -1.7e-237) {
		tmp = x;
	} else if (t <= -4.5e-278) {
		tmp = y / (a / z);
	} else if (t <= 5.5e+45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9d-54)) then
        tmp = y
    else if (t <= (-1.7d-237)) then
        tmp = x
    else if (t <= (-4.5d-278)) then
        tmp = y / (a / z)
    else if (t <= 5.5d+45) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e-54) {
		tmp = y;
	} else if (t <= -1.7e-237) {
		tmp = x;
	} else if (t <= -4.5e-278) {
		tmp = y / (a / z);
	} else if (t <= 5.5e+45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e-54:
		tmp = y
	elif t <= -1.7e-237:
		tmp = x
	elif t <= -4.5e-278:
		tmp = y / (a / z)
	elif t <= 5.5e+45:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e-54)
		tmp = y;
	elseif (t <= -1.7e-237)
		tmp = x;
	elseif (t <= -4.5e-278)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.5e+45)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e-54)
		tmp = y;
	elseif (t <= -1.7e-237)
		tmp = x;
	elseif (t <= -4.5e-278)
		tmp = y / (a / z);
	elseif (t <= 5.5e+45)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e-54], y, If[LessEqual[t, -1.7e-237], x, If[LessEqual[t, -4.5e-278], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+45], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999997e-54 or 5.5000000000000001e45 < t

   1. Initial program 46.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 39.2%

      \[\leadsto \color{blue}{y} \]

   if -8.9999999999999997e-54 < t < -1.7000000000000001e-237 or -4.4999999999999998e-278 < t < 5.5000000000000001e45

   1. Initial program 89.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{x} \]

   if -1.7000000000000001e-237 < t < -4.4999999999999998e-278

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   6. Taylor expanded in t around 0 48.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53} \lor \neg \left(t \leq 9.2 \cdot 10^{+45}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e-53) (not (<= t 9.2e+45)))
   (+ y (* (- y x) (/ (- a z) t)))
   (+ x (* (- y x) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e-53) || !(t <= 9.2e+45)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + ((y - x) * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d-53)) .or. (.not. (t <= 9.2d+45))) then
        tmp = y + ((y - x) * ((a - z) / t))
    else
        tmp = x + ((y - x) * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e-53) || !(t <= 9.2e+45)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + ((y - x) * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e-53) or not (t <= 9.2e+45):
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = x + ((y - x) * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e-53) || !(t <= 9.2e+45))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e-53) || ~((t <= 9.2e+45)))
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = x + ((y - x) * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e-53], N[Not[LessEqual[t, 9.2e+45]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1500000000000001e-53 or 9.20000000000000049e45 < t

   1. Initial program 46.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 68.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 68.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 68.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 68.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 68.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 68.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 68.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 68.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 80.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 80.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
   8. Step-by-step derivation

      1. clear-num 80.6%

         \[\leadsto y - \color{blue}{\frac{1}{\frac{\frac{t}{z - a}}{y - x}}} \]

      2. associate-/r/ 80.6%

         \[\leadsto y - \color{blue}{\frac{1}{\frac{t}{z - a}} \cdot \left(y - x\right)} \]

      3. clear-num 80.6%

         \[\leadsto y - \color{blue}{\frac{z - a}{t}} \cdot \left(y - x\right) \]

   9. Applied egg-rr 80.6%

      \[\leadsto y - \color{blue}{\frac{z - a}{t} \cdot \left(y - x\right)} \]

   if -1.1500000000000001e-53 < t < 9.20000000000000049e45

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 89.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 93.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 93.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 93.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 93.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 93.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 93.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in z around inf 85.5%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{a - t}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53} \lor \neg \left(t \leq 9.2 \cdot 10^{+45}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+45}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-53)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 5.6e+45)
     (+ x (* (- y x) (/ z (- a t))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 5.6e+45) {
		tmp = x + ((y - x) * (z / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-53)) then
        tmp = y + ((y - x) * ((a - z) / t))
    else if (t <= 5.6d+45) then
        tmp = x + ((y - x) * (z / (a - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 5.6e+45) {
		tmp = x + ((y - x) * (z / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-53:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t <= 5.6e+45:
		tmp = x + ((y - x) * (z / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-53)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 5.6e+45)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-53)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t <= 5.6e+45)
		tmp = x + ((y - x) * (z / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-53], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+45], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e-53

   1. Initial program 53.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 66.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 66.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 66.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 66.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 66.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 66.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 66.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 78.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
   8. Step-by-step derivation

      1. clear-num 78.8%

         \[\leadsto y - \color{blue}{\frac{1}{\frac{\frac{t}{z - a}}{y - x}}} \]

      2. associate-/r/ 78.7%

         \[\leadsto y - \color{blue}{\frac{1}{\frac{t}{z - a}} \cdot \left(y - x\right)} \]

      3. clear-num 78.9%

         \[\leadsto y - \color{blue}{\frac{z - a}{t}} \cdot \left(y - x\right) \]

   9. Applied egg-rr 78.9%

      \[\leadsto y - \color{blue}{\frac{z - a}{t} \cdot \left(y - x\right)} \]

   if -1.1500000000000001e-53 < t < 5.5999999999999999e45

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 89.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 93.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 93.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 93.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 93.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 93.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 93.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in z around inf 85.5%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z}{a - t}} + x \]

   if 5.5999999999999999e45 < t

   1. Initial program 36.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 60.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 71.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 71.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 71.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 71.2%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 71.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 71.2%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 71.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 71.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 73.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 83.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+45}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-53) y (if (<= t 1.5e+46) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y;
	} else if (t <= 1.5e+46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-53)) then
        tmp = y
    else if (t <= 1.5d+46) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y;
	} else if (t <= 1.5e+46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-53:
		tmp = y
	elif t <= 1.5e+46:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-53)
		tmp = y;
	elseif (t <= 1.5e+46)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-53)
		tmp = y;
	elseif (t <= 1.5e+46)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-53], y, If[LessEqual[t, 1.5e+46], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1500000000000001e-53 or 1.50000000000000012e46 < t

   1. Initial program 46.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 39.2%

      \[\leadsto \color{blue}{y} \]

   if -1.1500000000000001e-53 < t < 1.50000000000000012e46

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 25.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 70.2%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 81.4%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 81.4%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 24.9%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 24.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))