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

Percentage Accurate: 68.3% → 90.9%

Time: 18.6s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-271} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-271) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (* x (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-271) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-1d-271)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((x * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-271) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-271) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((x * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-271) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-271) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((x * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-271], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999963e-272 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.5%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   if -9.99999999999999963e-272 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 99.7%

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

      3. associate-/r/ 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

   9. Simplified 91.8%

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

   10. Taylor expanded in x around 0 99.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-271} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 2: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-296}:\\ \;\;\;\;y - \frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (+ x (/ y (/ a z))))
        (t_3 (* (- y x) (/ z (- a t)))))
   (if (<= a -3.3e+103)
     t_2
     (if (<= a -1.45e+78)
       (- y (* a (/ x t)))
       (if (<= a -1.3e+46)
         t_3
         (if (<= a -1e-24)
           t_1
           (if (<= a -2.65e-133)
             t_3
             (if (<= a -4.2e-171)
               t_1
               (if (<= a 1.65e-296)
                 (- y (/ x (/ (- t) z)))
                 (if (<= a 2.35e-116)
                   t_1
                   (if (<= a 2.3e+112) t_3 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double t_3 = (y - x) * (z / (a - t));
	double tmp;
	if (a <= -3.3e+103) {
		tmp = t_2;
	} else if (a <= -1.45e+78) {
		tmp = y - (a * (x / t));
	} else if (a <= -1.3e+46) {
		tmp = t_3;
	} else if (a <= -1e-24) {
		tmp = t_1;
	} else if (a <= -2.65e-133) {
		tmp = t_3;
	} else if (a <= -4.2e-171) {
		tmp = t_1;
	} else if (a <= 1.65e-296) {
		tmp = y - (x / (-t / z));
	} else if (a <= 2.35e-116) {
		tmp = t_1;
	} else if (a <= 2.3e+112) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    t_3 = (y - x) * (z / (a - t))
    if (a <= (-3.3d+103)) then
        tmp = t_2
    else if (a <= (-1.45d+78)) then
        tmp = y - (a * (x / t))
    else if (a <= (-1.3d+46)) then
        tmp = t_3
    else if (a <= (-1d-24)) then
        tmp = t_1
    else if (a <= (-2.65d-133)) then
        tmp = t_3
    else if (a <= (-4.2d-171)) then
        tmp = t_1
    else if (a <= 1.65d-296) then
        tmp = y - (x / (-t / z))
    else if (a <= 2.35d-116) then
        tmp = t_1
    else if (a <= 2.3d+112) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double t_3 = (y - x) * (z / (a - t));
	double tmp;
	if (a <= -3.3e+103) {
		tmp = t_2;
	} else if (a <= -1.45e+78) {
		tmp = y - (a * (x / t));
	} else if (a <= -1.3e+46) {
		tmp = t_3;
	} else if (a <= -1e-24) {
		tmp = t_1;
	} else if (a <= -2.65e-133) {
		tmp = t_3;
	} else if (a <= -4.2e-171) {
		tmp = t_1;
	} else if (a <= 1.65e-296) {
		tmp = y - (x / (-t / z));
	} else if (a <= 2.35e-116) {
		tmp = t_1;
	} else if (a <= 2.3e+112) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	t_3 = (y - x) * (z / (a - t))
	tmp = 0
	if a <= -3.3e+103:
		tmp = t_2
	elif a <= -1.45e+78:
		tmp = y - (a * (x / t))
	elif a <= -1.3e+46:
		tmp = t_3
	elif a <= -1e-24:
		tmp = t_1
	elif a <= -2.65e-133:
		tmp = t_3
	elif a <= -4.2e-171:
		tmp = t_1
	elif a <= 1.65e-296:
		tmp = y - (x / (-t / z))
	elif a <= 2.35e-116:
		tmp = t_1
	elif a <= 2.3e+112:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	t_3 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.3e+103)
		tmp = t_2;
	elseif (a <= -1.45e+78)
		tmp = Float64(y - Float64(a * Float64(x / t)));
	elseif (a <= -1.3e+46)
		tmp = t_3;
	elseif (a <= -1e-24)
		tmp = t_1;
	elseif (a <= -2.65e-133)
		tmp = t_3;
	elseif (a <= -4.2e-171)
		tmp = t_1;
	elseif (a <= 1.65e-296)
		tmp = Float64(y - Float64(x / Float64(Float64(-t) / z)));
	elseif (a <= 2.35e-116)
		tmp = t_1;
	elseif (a <= 2.3e+112)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	t_3 = (y - x) * (z / (a - t));
	tmp = 0.0;
	if (a <= -3.3e+103)
		tmp = t_2;
	elseif (a <= -1.45e+78)
		tmp = y - (a * (x / t));
	elseif (a <= -1.3e+46)
		tmp = t_3;
	elseif (a <= -1e-24)
		tmp = t_1;
	elseif (a <= -2.65e-133)
		tmp = t_3;
	elseif (a <= -4.2e-171)
		tmp = t_1;
	elseif (a <= 1.65e-296)
		tmp = y - (x / (-t / z));
	elseif (a <= 2.35e-116)
		tmp = t_1;
	elseif (a <= 2.3e+112)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+103], t$95$2, If[LessEqual[a, -1.45e+78], N[(y - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e+46], t$95$3, If[LessEqual[a, -1e-24], t$95$1, If[LessEqual[a, -2.65e-133], t$95$3, If[LessEqual[a, -4.2e-171], t$95$1, If[LessEqual[a, 1.65e-296], N[(y - N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e-116], t$95$1, If[LessEqual[a, 2.3e+112], t$95$3, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.30000000000000009e103 or 2.3e112 < a

   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/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 87.3%

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

   5. Taylor expanded in t around 0 68.1%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   if -3.30000000000000009e103 < a < -1.45000000000000008e78

   1. Initial program 17.7%

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

      1. associate-/l* 58.0%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in t around inf 30.0%

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

      1. associate--l+ 30.0%

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

      2. associate-*r/ 30.0%

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

      3. associate-*r/ 30.0%

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

      4. div-sub 30.0%

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

      5. distribute-lft-out-- 30.0%

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

      6. associate-*r/ 30.0%

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

      7. mul-1-neg 30.0%

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

      8. unsub-neg 30.0%

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

      9. distribute-rgt-out-- 31.0%

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

      10. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-/l* 77.7%

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

      3. associate-/r/ 77.7%

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

      4. distribute-rgt-neg-in 77.7%

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

   9. Simplified 77.7%

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

   10. Taylor expanded in z around 0 63.2%

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

       1. associate-*r/ 63.5%

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

   12. Simplified 63.5%

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

   if -1.45000000000000008e78 < a < -1.30000000000000007e46 or -9.99999999999999924e-25 < a < -2.64999999999999992e-133 or 2.34999999999999997e-116 < a < 2.3e112

   1. Initial program 63.4%

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

      1. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 64.9%

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

      1. div-sub 65.7%

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

      2. associate-*r/ 57.1%

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

      3. associate-/l* 66.3%

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

   6. Simplified 66.3%

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

      1. associate-/r/ 67.1%

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

   8. Applied egg-rr 67.1%

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

   if -1.30000000000000007e46 < a < -9.99999999999999924e-25 or -2.64999999999999992e-133 < a < -4.2e-171 or 1.65e-296 < a < 2.34999999999999997e-116

   1. Initial program 58.8%

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

      1. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around 0 61.2%

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

      1. associate-*r/ 76.1%

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

   6. Simplified 76.1%

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

   if -4.2e-171 < a < 1.65e-296

   1. Initial program 61.0%

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

      1. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in t around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. associate-*r/ 91.4%

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

      3. associate-*r/ 91.4%

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

      4. div-sub 91.4%

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

      5. distribute-lft-out-- 91.4%

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

      6. associate-*r/ 91.4%

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

      7. mul-1-neg 91.4%

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

      8. unsub-neg 91.4%

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

      9. distribute-rgt-out-- 91.4%

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

      10. associate-/l* 94.0%

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

   6. Simplified 94.0%

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

   7. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 80.1%

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

      3. associate-/r/ 77.2%

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

      4. distribute-rgt-neg-in 77.2%

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

   9. Simplified 77.2%

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

   10. Taylor expanded in x around 0 74.5%

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

       1. associate-/l* 80.1%

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

   12. Simplified 80.1%

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

   13. Taylor expanded in a around 0 77.3%

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

       1. associate-*r/ 77.3%

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

       2. neg-mul-1 77.3%

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

   15. Simplified 77.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-133}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-296}:\\ \;\;\;\;y - \frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-116}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+112}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 3: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ t_3 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 12.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t))))
        (t_2 (+ x (/ (- y x) (/ a z))))
        (t_3 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -3.3e+103)
     t_2
     (if (<= a -2.25e+19)
       t_1
       (if (<= a -2.7e-45)
         t_3
         (if (<= a 9e-38)
           t_1
           (if (<= a 12.5) t_2 (if (<= a 4.7e+108) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.3e+103) {
		tmp = t_2;
	} else if (a <= -2.25e+19) {
		tmp = t_1;
	} else if (a <= -2.7e-45) {
		tmp = t_3;
	} else if (a <= 9e-38) {
		tmp = t_1;
	} else if (a <= 12.5) {
		tmp = t_2;
	} else if (a <= 4.7e+108) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + ((y - x) * ((a - z) / t))
    t_2 = x + ((y - x) / (a / z))
    t_3 = x - ((y / (a - t)) * (t - z))
    if (a <= (-3.3d+103)) then
        tmp = t_2
    else if (a <= (-2.25d+19)) then
        tmp = t_1
    else if (a <= (-2.7d-45)) then
        tmp = t_3
    else if (a <= 9d-38) then
        tmp = t_1
    else if (a <= 12.5d0) then
        tmp = t_2
    else if (a <= 4.7d+108) then
        tmp = t_1
    else
        tmp = t_3
    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 + ((y - x) * ((a - z) / t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.3e+103) {
		tmp = t_2;
	} else if (a <= -2.25e+19) {
		tmp = t_1;
	} else if (a <= -2.7e-45) {
		tmp = t_3;
	} else if (a <= 9e-38) {
		tmp = t_1;
	} else if (a <= 12.5) {
		tmp = t_2;
	} else if (a <= 4.7e+108) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	t_2 = x + ((y - x) / (a / z))
	t_3 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -3.3e+103:
		tmp = t_2
	elif a <= -2.25e+19:
		tmp = t_1
	elif a <= -2.7e-45:
		tmp = t_3
	elif a <= 9e-38:
		tmp = t_1
	elif a <= 12.5:
		tmp = t_2
	elif a <= 4.7e+108:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_3 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -3.3e+103)
		tmp = t_2;
	elseif (a <= -2.25e+19)
		tmp = t_1;
	elseif (a <= -2.7e-45)
		tmp = t_3;
	elseif (a <= 9e-38)
		tmp = t_1;
	elseif (a <= 12.5)
		tmp = t_2;
	elseif (a <= 4.7e+108)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	t_2 = x + ((y - x) / (a / z));
	t_3 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -3.3e+103)
		tmp = t_2;
	elseif (a <= -2.25e+19)
		tmp = t_1;
	elseif (a <= -2.7e-45)
		tmp = t_3;
	elseif (a <= 9e-38)
		tmp = t_1;
	elseif (a <= 12.5)
		tmp = t_2;
	elseif (a <= 4.7e+108)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+103], t$95$2, If[LessEqual[a, -2.25e+19], t$95$1, If[LessEqual[a, -2.7e-45], t$95$3, If[LessEqual[a, 9e-38], t$95$1, If[LessEqual[a, 12.5], t$95$2, If[LessEqual[a, 4.7e+108], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.30000000000000009e103 or 9.00000000000000018e-38 < a < 12.5

   1. Initial program 73.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 82.6%

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

   if -3.30000000000000009e103 < a < -2.25e19 or -2.69999999999999985e-45 < a < 9.00000000000000018e-38 or 12.5 < a < 4.6999999999999996e108

   1. Initial program 55.5%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in t around inf 72.8%

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

      1. associate--l+ 72.8%

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

      2. associate-*r/ 72.8%

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

      3. associate-*r/ 72.8%

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

      4. div-sub 72.8%

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

      5. distribute-lft-out-- 72.8%

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

      6. associate-*r/ 72.8%

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

      7. mul-1-neg 72.8%

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

      8. unsub-neg 72.8%

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

      9. distribute-rgt-out-- 72.9%

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

      10. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

      1. clear-num 83.6%

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

      2. inv-pow 83.6%

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

   8. Applied egg-rr 83.6%

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

      1. unpow-1 83.6%

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

   10. Simplified 83.6%

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

       1. associate-/r/ 83.6%

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

       2. /-rgt-identity 83.6%

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

       3. *-commutative 83.6%

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

   12. Applied egg-rr 83.6%

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

   if -2.25e19 < a < -2.69999999999999985e-45 or 4.6999999999999996e108 < a

   1. Initial program 72.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 86.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+19}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-38}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq 12.5:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+108}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 4: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ t_2 := x + \frac{y - x}{\frac{a}{z}}\\ t_3 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 49:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t))))
        (t_2 (+ x (/ (- y x) (/ a z))))
        (t_3 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -3.3e+105)
     t_2
     (if (<= a -2.1e+19)
       t_1
       (if (<= a -1.12e-43)
         t_3
         (if (<= a 6.2e-38)
           (+ y (/ (- x y) (/ t (- z a))))
           (if (<= a 49.0) t_2 (if (<= a 1.05e+108) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.3e+105) {
		tmp = t_2;
	} else if (a <= -2.1e+19) {
		tmp = t_1;
	} else if (a <= -1.12e-43) {
		tmp = t_3;
	} else if (a <= 6.2e-38) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (a <= 49.0) {
		tmp = t_2;
	} else if (a <= 1.05e+108) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + ((y - x) * ((a - z) / t))
    t_2 = x + ((y - x) / (a / z))
    t_3 = x - ((y / (a - t)) * (t - z))
    if (a <= (-3.3d+105)) then
        tmp = t_2
    else if (a <= (-2.1d+19)) then
        tmp = t_1
    else if (a <= (-1.12d-43)) then
        tmp = t_3
    else if (a <= 6.2d-38) then
        tmp = y + ((x - y) / (t / (z - a)))
    else if (a <= 49.0d0) then
        tmp = t_2
    else if (a <= 1.05d+108) then
        tmp = t_1
    else
        tmp = t_3
    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 + ((y - x) * ((a - z) / t));
	double t_2 = x + ((y - x) / (a / z));
	double t_3 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.3e+105) {
		tmp = t_2;
	} else if (a <= -2.1e+19) {
		tmp = t_1;
	} else if (a <= -1.12e-43) {
		tmp = t_3;
	} else if (a <= 6.2e-38) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (a <= 49.0) {
		tmp = t_2;
	} else if (a <= 1.05e+108) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	t_2 = x + ((y - x) / (a / z))
	t_3 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -3.3e+105:
		tmp = t_2
	elif a <= -2.1e+19:
		tmp = t_1
	elif a <= -1.12e-43:
		tmp = t_3
	elif a <= 6.2e-38:
		tmp = y + ((x - y) / (t / (z - a)))
	elif a <= 49.0:
		tmp = t_2
	elif a <= 1.05e+108:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_3 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -3.3e+105)
		tmp = t_2;
	elseif (a <= -2.1e+19)
		tmp = t_1;
	elseif (a <= -1.12e-43)
		tmp = t_3;
	elseif (a <= 6.2e-38)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	elseif (a <= 49.0)
		tmp = t_2;
	elseif (a <= 1.05e+108)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	t_2 = x + ((y - x) / (a / z));
	t_3 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -3.3e+105)
		tmp = t_2;
	elseif (a <= -2.1e+19)
		tmp = t_1;
	elseif (a <= -1.12e-43)
		tmp = t_3;
	elseif (a <= 6.2e-38)
		tmp = y + ((x - y) / (t / (z - a)));
	elseif (a <= 49.0)
		tmp = t_2;
	elseif (a <= 1.05e+108)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+105], t$95$2, If[LessEqual[a, -2.1e+19], t$95$1, If[LessEqual[a, -1.12e-43], t$95$3, If[LessEqual[a, 6.2e-38], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 49.0], t$95$2, If[LessEqual[a, 1.05e+108], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.29999999999999997e105 or 6.19999999999999966e-38 < a < 49

   1. Initial program 73.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 82.6%

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

   if -3.29999999999999997e105 < a < -2.1e19 or 49 < a < 1.05000000000000005e108

   1. Initial program 52.2%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around inf 58.3%

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

      1. associate--l+ 58.3%

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

      2. associate-*r/ 58.3%

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

      3. associate-*r/ 58.3%

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

      4. div-sub 58.3%

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

      5. distribute-lft-out-- 58.3%

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

      6. associate-*r/ 58.3%

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

      7. mul-1-neg 58.3%

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

      8. unsub-neg 58.3%

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

      9. distribute-rgt-out-- 58.9%

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

      10. associate-/l* 79.1%

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

   6. Simplified 79.1%

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

      1. clear-num 79.1%

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

      2. inv-pow 79.1%

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

   8. Applied egg-rr 79.1%

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

      1. unpow-1 79.1%

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

   10. Simplified 79.1%

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

       1. associate-/r/ 79.1%

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

       2. /-rgt-identity 79.1%

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

       3. *-commutative 79.1%

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

   12. Applied egg-rr 79.1%

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

   if -2.1e19 < a < -1.12e-43 or 1.05000000000000005e108 < a

   1. Initial program 72.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 86.0%

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

   if -1.12e-43 < a < 6.19999999999999966e-38

   1. Initial program 56.2%

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

      1. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 76.2%

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

      5. distribute-lft-out-- 76.2%

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

      6. associate-*r/ 76.2%

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

      7. mul-1-neg 76.2%

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

      8. unsub-neg 76.2%

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

      9. distribute-rgt-out-- 76.2%

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

      10. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-43}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 49:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-296}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= a -2.8e+119)
     t_1
     (if (<= a 3.4e-296)
       (+ y (* x (/ z t)))
       (if (<= a 1.35e-113)
         t_2
         (if (<= a 4.3e-10)
           (/ (- x) (/ (- a t) z))
           (if (<= a 1.12e+129) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -2.8e+119) {
		tmp = t_1;
	} else if (a <= 3.4e-296) {
		tmp = y + (x * (z / t));
	} else if (a <= 1.35e-113) {
		tmp = t_2;
	} else if (a <= 4.3e-10) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 1.12e+129) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    t_2 = y * ((z - t) / (a - t))
    if (a <= (-2.8d+119)) then
        tmp = t_1
    else if (a <= 3.4d-296) then
        tmp = y + (x * (z / t))
    else if (a <= 1.35d-113) then
        tmp = t_2
    else if (a <= 4.3d-10) then
        tmp = -x / ((a - t) / z)
    else if (a <= 1.12d+129) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -2.8e+119) {
		tmp = t_1;
	} else if (a <= 3.4e-296) {
		tmp = y + (x * (z / t));
	} else if (a <= 1.35e-113) {
		tmp = t_2;
	} else if (a <= 4.3e-10) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 1.12e+129) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -2.8e+119:
		tmp = t_1
	elif a <= 3.4e-296:
		tmp = y + (x * (z / t))
	elif a <= 1.35e-113:
		tmp = t_2
	elif a <= 4.3e-10:
		tmp = -x / ((a - t) / z)
	elif a <= 1.12e+129:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -2.8e+119)
		tmp = t_1;
	elseif (a <= 3.4e-296)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 1.35e-113)
		tmp = t_2;
	elseif (a <= 4.3e-10)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (a <= 1.12e+129)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -2.8e+119)
		tmp = t_1;
	elseif (a <= 3.4e-296)
		tmp = y + (x * (z / t));
	elseif (a <= 1.35e-113)
		tmp = t_2;
	elseif (a <= 4.3e-10)
		tmp = -x / ((a - t) / z);
	elseif (a <= 1.12e+129)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+119], t$95$1, If[LessEqual[a, 3.4e-296], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-113], t$95$2, If[LessEqual[a, 4.3e-10], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+129], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.80000000000000013e119 or 1.11999999999999993e129 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 87.9%

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

   5. Taylor expanded in t around 0 70.3%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -2.80000000000000013e119 < a < 3.39999999999999997e-296

   1. Initial program 60.5%

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

      1. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-*r/ 66.4%

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

      3. associate-*r/ 66.4%

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

      4. div-sub 66.5%

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

      5. distribute-lft-out-- 66.5%

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

      6. associate-*r/ 66.5%

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

      7. mul-1-neg 66.5%

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

      8. unsub-neg 66.5%

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

      9. distribute-rgt-out-- 66.6%

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

      10. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. associate-/l* 64.1%

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

      3. associate-/r/ 64.0%

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

      4. distribute-rgt-neg-in 64.0%

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

   9. Simplified 64.0%

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

   10. Taylor expanded in z around inf 57.1%

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

       1. associate-*r/ 57.1%

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

       2. mul-1-neg 57.1%

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

       3. distribute-lft-neg-out 57.1%

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

       4. *-commutative 57.1%

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

   12. Simplified 57.1%

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

   13. Taylor expanded in z around 0 57.1%

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

       1. mul-1-neg 57.1%

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

       2. associate-*r/ 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   15. Simplified 62.3%

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

   if 3.39999999999999997e-296 < a < 1.34999999999999998e-113 or 4.30000000000000014e-10 < a < 1.11999999999999993e129

   1. Initial program 56.4%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in x around 0 57.7%

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

      1. associate-*r/ 75.4%

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

   6. Simplified 75.4%

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

   if 1.34999999999999998e-113 < a < 4.30000000000000014e-10

   1. Initial program 57.7%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 62.1%

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

      1. div-sub 64.7%

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

      2. associate-*r/ 50.6%

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

      3. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in y around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. associate-/l* 57.5%

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

      3. distribute-neg-frac 57.5%

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

   9. Simplified 57.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-296}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{y - x}{\frac{t}{z}}\\ t_2 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ (- y x) (/ t z)))) (t_2 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -6.4e-46)
     t_2
     (if (<= a 3.5e-41)
       t_1
       (if (<= a 7.2)
         (+ x (/ (- y x) (/ a z)))
         (if (<= a 1.05e+108) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((y - x) / (t / z));
	double t_2 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -6.4e-46) {
		tmp = t_2;
	} else if (a <= 3.5e-41) {
		tmp = t_1;
	} else if (a <= 7.2) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 1.05e+108) {
		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 - ((y - x) / (t / z))
    t_2 = x - ((y / (a - t)) * (t - z))
    if (a <= (-6.4d-46)) then
        tmp = t_2
    else if (a <= 3.5d-41) then
        tmp = t_1
    else if (a <= 7.2d0) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 1.05d+108) 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 - ((y - x) / (t / z));
	double t_2 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -6.4e-46) {
		tmp = t_2;
	} else if (a <= 3.5e-41) {
		tmp = t_1;
	} else if (a <= 7.2) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 1.05e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((y - x) / (t / z))
	t_2 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -6.4e-46:
		tmp = t_2
	elif a <= 3.5e-41:
		tmp = t_1
	elif a <= 7.2:
		tmp = x + ((y - x) / (a / z))
	elif a <= 1.05e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(y - x) / Float64(t / z)))
	t_2 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -6.4e-46)
		tmp = t_2;
	elseif (a <= 3.5e-41)
		tmp = t_1;
	elseif (a <= 7.2)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 1.05e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((y - x) / (t / z));
	t_2 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -6.4e-46)
		tmp = t_2;
	elseif (a <= 3.5e-41)
		tmp = t_1;
	elseif (a <= 7.2)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 1.05e+108)
		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[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.4e-46], t$95$2, If[LessEqual[a, 3.5e-41], t$95$1, If[LessEqual[a, 7.2], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.3999999999999998e-46 or 1.05000000000000005e108 < a

   1. Initial program 69.7%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 81.1%

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

   if -6.3999999999999998e-46 < a < 3.5e-41 or 7.20000000000000018 < a < 1.05000000000000005e108

   1. Initial program 55.8%

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

      1. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in t around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. associate-*r/ 75.5%

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

      3. associate-*r/ 75.5%

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

      4. div-sub 75.5%

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

      5. distribute-lft-out-- 75.5%

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

      6. associate-*r/ 75.5%

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

      7. mul-1-neg 75.5%

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

      8. unsub-neg 75.5%

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

      9. distribute-rgt-out-- 75.5%

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

      10. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around inf 80.3%

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

   if 3.5e-41 < a < 7.20000000000000018

   1. Initial program 77.5%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around 0 70.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 7.2:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 7: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -22:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-296}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+110}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -22.0)
     t_1
     (if (<= a 2.3e-296)
       (+ y (* x (/ z t)))
       (if (<= a 2.55e-113)
         (* y (/ (- z t) (- a t)))
         (if (<= a 4.9e+110) (* (- y x) (/ z (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -22.0) {
		tmp = t_1;
	} else if (a <= 2.3e-296) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.55e-113) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 4.9e+110) {
		tmp = (y - 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 = x + ((y - x) / (a / z))
    if (a <= (-22.0d0)) then
        tmp = t_1
    else if (a <= 2.3d-296) then
        tmp = y + (x * (z / t))
    else if (a <= 2.55d-113) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 4.9d+110) then
        tmp = (y - 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 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -22.0) {
		tmp = t_1;
	} else if (a <= 2.3e-296) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.55e-113) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 4.9e+110) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -22.0:
		tmp = t_1
	elif a <= 2.3e-296:
		tmp = y + (x * (z / t))
	elif a <= 2.55e-113:
		tmp = y * ((z - t) / (a - t))
	elif a <= 4.9e+110:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -22.0)
		tmp = t_1;
	elseif (a <= 2.3e-296)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 2.55e-113)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 4.9e+110)
		tmp = Float64(Float64(y - 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 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -22.0)
		tmp = t_1;
	elseif (a <= 2.3e-296)
		tmp = y + (x * (z / t));
	elseif (a <= 2.55e-113)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 4.9e+110)
		tmp = (y - 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[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -22.0], t$95$1, If[LessEqual[a, 2.3e-296], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e-113], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+110], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -22 or 4.90000000000000002e110 < a

   1. Initial program 68.8%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around 0 75.6%

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

   if -22 < a < 2.30000000000000004e-296

   1. Initial program 61.0%

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

      1. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in t around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. associate-*r/ 72.5%

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

      3. associate-*r/ 72.5%

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

      4. div-sub 72.5%

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

      5. distribute-lft-out-- 72.5%

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

      6. associate-*r/ 72.5%

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

      7. mul-1-neg 72.5%

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

      8. unsub-neg 72.5%

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

      9. distribute-rgt-out-- 72.5%

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

      10. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 67.7%

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

      3. associate-/r/ 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in z around inf 62.9%

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

       1. associate-*r/ 62.9%

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

       2. mul-1-neg 62.9%

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

       3. distribute-lft-neg-out 62.9%

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

       4. *-commutative 62.9%

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

   12. Simplified 62.9%

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

   13. Taylor expanded in z around 0 62.9%

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

       1. mul-1-neg 62.9%

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

       2. associate-*r/ 67.9%

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

       3. distribute-rgt-neg-in 67.9%

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

   15. Simplified 67.9%

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

   if 2.30000000000000004e-296 < a < 2.54999999999999989e-113

   1. Initial program 57.6%

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

      1. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in x around 0 63.5%

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

      1. associate-*r/ 80.6%

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

   6. Simplified 80.6%

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

   if 2.54999999999999989e-113 < a < 4.90000000000000002e110

   1. Initial program 57.2%

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

      1. associate-/l* 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 59.4%

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

      1. div-sub 60.6%

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

      2. associate-*r/ 47.4%

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

      3. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

      1. associate-/r/ 60.6%

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

   8. Applied egg-rr 60.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -22:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-296}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+110}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+199}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+59)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 4e+199)
     (- x (* (- z t) (/ (- x y) (- a t))))
     (+ y (* (- z a) (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+59) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 4e+199) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((z - a) * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+59)) then
        tmp = y + ((y - x) * ((a - z) / t))
    else if (t <= 4d+199) then
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    else
        tmp = y + ((z - a) * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+59) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 4e+199) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((z - a) * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+59:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t <= 4e+199:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	else:
		tmp = y + ((z - a) * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+59)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 4e+199)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+59)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t <= 4e+199)
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	else
		tmp = y + ((z - a) * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+59], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+199], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999995e59

   1. Initial program 28.0%

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

      1. associate-/l* 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in t around inf 59.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   5. 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-- 59.4%

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

      10. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

      1. clear-num 87.2%

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

      2. inv-pow 87.2%

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

   8. Applied egg-rr 87.2%

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

      1. unpow-1 87.2%

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

   10. Simplified 87.2%

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

       1. associate-/r/ 87.3%

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

       2. /-rgt-identity 87.3%

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

       3. *-commutative 87.3%

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

   12. Applied egg-rr 87.3%

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

   if -1.44999999999999995e59 < t < 4.00000000000000039e199

   1. Initial program 80.2%

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

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

   if 4.00000000000000039e199 < t

   1. Initial program 25.9%

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

      1. associate-/l* 54.1%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in t around inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. associate-*r/ 67.2%

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

      3. associate-*r/ 67.2%

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

      4. div-sub 67.2%

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

      5. distribute-lft-out-- 67.2%

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

      6. associate-*r/ 67.2%

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

      7. mul-1-neg 67.2%

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

      8. unsub-neg 67.2%

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

      9. distribute-rgt-out-- 67.2%

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

      10. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-/l* 84.3%

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

      3. associate-/r/ 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

   9. Simplified 88.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+199}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 9: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -2.8e+119)
     t_2
     (if (<= a 7.6e-248)
       t_1
       (if (<= a 2.5e-213)
         (/ z (/ (- a t) y))
         (if (<= a 1.12e+129) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.8e+119) {
		tmp = t_2;
	} else if (a <= 7.6e-248) {
		tmp = t_1;
	} else if (a <= 2.5e-213) {
		tmp = z / ((a - t) / y);
	} else if (a <= 1.12e+129) {
		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 * (z / t))
    t_2 = x + (y / (a / z))
    if (a <= (-2.8d+119)) then
        tmp = t_2
    else if (a <= 7.6d-248) then
        tmp = t_1
    else if (a <= 2.5d-213) then
        tmp = z / ((a - t) / y)
    else if (a <= 1.12d+129) 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 * (z / t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -2.8e+119) {
		tmp = t_2;
	} else if (a <= 7.6e-248) {
		tmp = t_1;
	} else if (a <= 2.5e-213) {
		tmp = z / ((a - t) / y);
	} else if (a <= 1.12e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * (z / t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -2.8e+119:
		tmp = t_2
	elif a <= 7.6e-248:
		tmp = t_1
	elif a <= 2.5e-213:
		tmp = z / ((a - t) / y)
	elif a <= 1.12e+129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(z / t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.8e+119)
		tmp = t_2;
	elseif (a <= 7.6e-248)
		tmp = t_1;
	elseif (a <= 2.5e-213)
		tmp = Float64(z / Float64(Float64(a - t) / y));
	elseif (a <= 1.12e+129)
		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 * (z / t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2.8e+119)
		tmp = t_2;
	elseif (a <= 7.6e-248)
		tmp = t_1;
	elseif (a <= 2.5e-213)
		tmp = z / ((a - t) / y);
	elseif (a <= 1.12e+129)
		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[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+119], t$95$2, If[LessEqual[a, 7.6e-248], t$95$1, If[LessEqual[a, 2.5e-213], N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+129], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.80000000000000013e119 or 1.11999999999999993e129 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 87.9%

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

   5. Taylor expanded in t around 0 70.3%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -2.80000000000000013e119 < a < 7.5999999999999998e-248 or 2.49999999999999989e-213 < a < 1.11999999999999993e129

   1. Initial program 58.0%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. associate-*r/ 67.2%

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

      3. associate-*r/ 67.2%

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

      4. div-sub 67.2%

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

      5. distribute-lft-out-- 67.2%

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

      6. associate-*r/ 67.2%

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

      7. mul-1-neg 67.2%

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

      8. unsub-neg 67.2%

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

      9. distribute-rgt-out-- 67.3%

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

      10. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around 0 59.4%

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

      1. mul-1-neg 59.4%

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

      2. associate-/l* 64.4%

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

      3. associate-/r/ 62.2%

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

      4. distribute-rgt-neg-in 62.2%

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

   9. Simplified 62.2%

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

   10. Taylor expanded in z around inf 53.8%

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

       1. associate-*r/ 53.8%

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

       2. mul-1-neg 53.8%

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

       3. distribute-lft-neg-out 53.8%

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

       4. *-commutative 53.8%

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

   12. Simplified 53.8%

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

   13. Taylor expanded in z around 0 53.8%

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

       1. mul-1-neg 53.8%

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

       2. associate-*r/ 59.9%

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

       3. distribute-rgt-neg-in 59.9%

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

   15. Simplified 59.9%

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

   if 7.5999999999999998e-248 < a < 2.49999999999999989e-213

   1. Initial program 71.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 59.5%

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

      3. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in y around inf 87.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-248}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+129}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -3.05 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-248}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -3.05e+119)
     t_1
     (if (<= a 7.6e-248)
       (+ y (* x (/ z t)))
       (if (<= a 2.5e-213)
         (/ z (/ (- a t) y))
         (if (<= a 1.25e+129) (+ y (* z (/ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -3.05e+119) {
		tmp = t_1;
	} else if (a <= 7.6e-248) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.5e-213) {
		tmp = z / ((a - t) / y);
	} else if (a <= 1.25e+129) {
		tmp = y + (z * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-3.05d+119)) then
        tmp = t_1
    else if (a <= 7.6d-248) then
        tmp = y + (x * (z / t))
    else if (a <= 2.5d-213) then
        tmp = z / ((a - t) / y)
    else if (a <= 1.25d+129) then
        tmp = y + (z * (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -3.05e+119) {
		tmp = t_1;
	} else if (a <= 7.6e-248) {
		tmp = y + (x * (z / t));
	} else if (a <= 2.5e-213) {
		tmp = z / ((a - t) / y);
	} else if (a <= 1.25e+129) {
		tmp = y + (z * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -3.05e+119:
		tmp = t_1
	elif a <= 7.6e-248:
		tmp = y + (x * (z / t))
	elif a <= 2.5e-213:
		tmp = z / ((a - t) / y)
	elif a <= 1.25e+129:
		tmp = y + (z * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -3.05e+119)
		tmp = t_1;
	elseif (a <= 7.6e-248)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 2.5e-213)
		tmp = Float64(z / Float64(Float64(a - t) / y));
	elseif (a <= 1.25e+129)
		tmp = Float64(y + Float64(z * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -3.05e+119)
		tmp = t_1;
	elseif (a <= 7.6e-248)
		tmp = y + (x * (z / t));
	elseif (a <= 2.5e-213)
		tmp = z / ((a - t) / y);
	elseif (a <= 1.25e+129)
		tmp = y + (z * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.05e+119], t$95$1, If[LessEqual[a, 7.6e-248], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-213], N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+129], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.05e119 or 1.2500000000000001e129 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 87.9%

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

   5. Taylor expanded in t around 0 70.3%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -3.05e119 < a < 7.5999999999999998e-248

   1. Initial program 60.6%

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

      1. associate-/l* 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in t around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. associate-*r/ 70.9%

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

      3. associate-*r/ 70.9%

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

      4. div-sub 71.0%

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

      5. distribute-lft-out-- 71.0%

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

      6. associate-*r/ 71.0%

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

      7. mul-1-neg 71.0%

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

      8. unsub-neg 71.0%

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

      9. distribute-rgt-out-- 71.0%

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

      10. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l* 65.2%

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

      3. associate-/r/ 63.4%

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

      4. distribute-rgt-neg-in 63.4%

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

   9. Simplified 63.4%

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

   10. Taylor expanded in z around inf 57.4%

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

       1. associate-*r/ 57.4%

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

       2. mul-1-neg 57.4%

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

       3. distribute-lft-neg-out 57.4%

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

       4. *-commutative 57.4%

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

   12. Simplified 57.4%

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

   13. Taylor expanded in z around 0 57.4%

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

       1. mul-1-neg 57.4%

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

       2. associate-*r/ 63.7%

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

       3. distribute-rgt-neg-in 63.7%

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

   15. Simplified 63.7%

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

   if 7.5999999999999998e-248 < a < 2.49999999999999989e-213

   1. Initial program 71.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 59.5%

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

      3. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in y around inf 87.4%

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

   if 2.49999999999999989e-213 < a < 1.2500000000000001e129

   1. Initial program 54.0%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in t around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. associate-*r/ 61.5%

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

      3. associate-*r/ 61.5%

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

      4. div-sub 61.5%

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

      5. distribute-lft-out-- 61.5%

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

      6. associate-*r/ 61.5%

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

      7. mul-1-neg 61.5%

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

      8. unsub-neg 61.5%

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

      9. distribute-rgt-out-- 61.6%

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

      10. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in y around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 63.0%

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

      3. associate-/r/ 60.3%

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

      4. distribute-rgt-neg-in 60.3%

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

   9. Simplified 60.3%

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

   10. Taylor expanded in z around inf 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-*l/ 54.1%

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

       3. *-commutative 54.1%

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

       4. distribute-rgt-neg-in 54.1%

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

       5. distribute-frac-neg 54.1%

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

   12. Simplified 54.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-248}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-116}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+95)
   (- y (/ x (/ (- t) z)))
   (if (<= t -5e-116)
     (* (- y x) (/ z (- a t)))
     (if (<= t 4e+29) (+ x (/ z (/ a (- y x)))) (+ y (* z (/ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+95) {
		tmp = y - (x / (-t / z));
	} else if (t <= -5e-116) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 4e+29) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.5d+95)) then
        tmp = y - (x / (-t / z))
    else if (t <= (-5d-116)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 4d+29) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = y + (z * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+95) {
		tmp = y - (x / (-t / z));
	} else if (t <= -5e-116) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 4e+29) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+95:
		tmp = y - (x / (-t / z))
	elif t <= -5e-116:
		tmp = (y - x) * (z / (a - t))
	elif t <= 4e+29:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+95)
		tmp = Float64(y - Float64(x / Float64(Float64(-t) / z)));
	elseif (t <= -5e-116)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 4e+29)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+95)
		tmp = y - (x / (-t / z));
	elseif (t <= -5e-116)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 4e+29)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+95], N[(y - N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-116], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+29], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.49999999999999996e95

   1. Initial program 25.4%

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

      1. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in t around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. associate-*r/ 58.1%

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

      3. associate-*r/ 58.1%

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

      4. div-sub 58.1%

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

      5. distribute-lft-out-- 58.1%

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

      6. associate-*r/ 58.1%

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

      7. mul-1-neg 58.1%

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

      8. unsub-neg 58.1%

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

      9. distribute-rgt-out-- 58.4%

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

      10. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in y around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 77.1%

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

      4. distribute-rgt-neg-in 77.1%

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

   9. Simplified 77.1%

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

   10. Taylor expanded in x around 0 66.9%

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

       1. associate-/l* 77.2%

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

   12. Simplified 77.2%

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

   13. Taylor expanded in a around 0 66.5%

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

       1. associate-*r/ 66.5%

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

       2. neg-mul-1 66.5%

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

   15. Simplified 66.5%

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

   if -1.49999999999999996e95 < t < -5.0000000000000003e-116

   1. Initial program 77.9%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 61.2%

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

      1. div-sub 61.2%

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

      2. associate-*r/ 57.2%

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

      3. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

      1. associate-/r/ 65.0%

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

   8. Applied egg-rr 65.0%

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

   if -5.0000000000000003e-116 < t < 3.99999999999999966e29

   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* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   if 3.99999999999999966e29 < t

   1. Initial program 41.1%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around inf 67.7%

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

      1. associate--l+ 67.7%

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

      2. associate-*r/ 67.7%

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

      3. associate-*r/ 67.7%

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

      4. div-sub 67.7%

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

      5. distribute-lft-out-- 67.7%

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

      6. associate-*r/ 67.7%

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

      7. mul-1-neg 67.7%

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

      8. unsub-neg 67.7%

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

      9. distribute-rgt-out-- 67.7%

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

      10. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

   7. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 67.0%

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

      3. associate-/r/ 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

   9. Simplified 68.6%

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

   10. Taylor expanded in z around inf 62.5%

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

       1. mul-1-neg 62.5%

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

       2. associate-*l/ 64.5%

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

       3. *-commutative 64.5%

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

       4. distribute-rgt-neg-in 64.5%

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

       5. distribute-frac-neg 64.5%

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

   12. Simplified 64.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-116}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 12: 69.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ x (/ t (- a z))))))
   (if (<= t -8.6e+94)
     t_1
     (if (<= t -1.05e-115)
       (* (- y x) (/ z (- a t)))
       (if (<= t 9.2e+27) (+ x (/ z (/ a (- y x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x / (t / (a - z)));
	double tmp;
	if (t <= -8.6e+94) {
		tmp = t_1;
	} else if (t <= -1.05e-115) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 9.2e+27) {
		tmp = x + (z / (a / (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 = y - (x / (t / (a - z)))
    if (t <= (-8.6d+94)) then
        tmp = t_1
    else if (t <= (-1.05d-115)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 9.2d+27) then
        tmp = x + (z / (a / (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 = y - (x / (t / (a - z)));
	double tmp;
	if (t <= -8.6e+94) {
		tmp = t_1;
	} else if (t <= -1.05e-115) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 9.2e+27) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x / (t / (a - z)))
	tmp = 0
	if t <= -8.6e+94:
		tmp = t_1
	elif t <= -1.05e-115:
		tmp = (y - x) * (z / (a - t))
	elif t <= 9.2e+27:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -8.6e+94)
		tmp = t_1;
	elseif (t <= -1.05e-115)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 9.2e+27)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x / (t / (a - z)));
	tmp = 0.0;
	if (t <= -8.6e+94)
		tmp = t_1;
	elseif (t <= -1.05e-115)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 9.2e+27)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+94], t$95$1, If[LessEqual[t, -1.05e-115], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+27], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.6e94 or 9.2000000000000002e27 < t

   1. Initial program 33.4%

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

      1. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in t around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-*r/ 63.0%

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

      3. associate-*r/ 63.0%

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

      4. div-sub 63.0%

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

      5. distribute-lft-out-- 63.0%

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

      6. associate-*r/ 63.0%

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

      7. mul-1-neg 63.0%

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

      8. unsub-neg 63.0%

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

      9. distribute-rgt-out-- 63.2%

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

      10. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 71.9%

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

      3. associate-/r/ 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

   9. Simplified 72.8%

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

   10. Taylor expanded in x around 0 67.6%

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

       1. associate-/l* 71.9%

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

   12. Simplified 71.9%

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

   if -8.6e94 < t < -1.05000000000000001e-115

   1. Initial program 77.9%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 61.2%

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

      1. div-sub 61.2%

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

      2. associate-*r/ 57.2%

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

      3. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

      1. associate-/r/ 65.0%

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

   8. Applied egg-rr 65.0%

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

   if -1.05000000000000001e-115 < t < 9.2000000000000002e27

   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* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;y - \frac{x}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 13: 67.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{x}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+95)
   (- y (/ x (/ t (- a z))))
   (if (<= t -1.05e-115)
     (* (- y x) (/ z (- a t)))
     (if (<= t 5e+22) (+ x (/ z (/ a (- y x)))) (+ y (/ (* x (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+95) {
		tmp = y - (x / (t / (a - z)));
	} else if (t <= -1.05e-115) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 5e+22) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d+95)) then
        tmp = y - (x / (t / (a - z)))
    else if (t <= (-1.05d-115)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 5d+22) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = y + ((x * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+95) {
		tmp = y - (x / (t / (a - z)));
	} else if (t <= -1.05e-115) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 5e+22) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+95:
		tmp = y - (x / (t / (a - z)))
	elif t <= -1.05e-115:
		tmp = (y - x) * (z / (a - t))
	elif t <= 5e+22:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = y + ((x * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+95)
		tmp = Float64(y - Float64(x / Float64(t / Float64(a - z))));
	elseif (t <= -1.05e-115)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 5e+22)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+95)
		tmp = y - (x / (t / (a - z)));
	elseif (t <= -1.05e-115)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 5e+22)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = y + ((x * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+95], N[(y - N[(x / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-115], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+22], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1e95

   1. Initial program 25.4%

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

      1. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in t around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. associate-*r/ 58.1%

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

      3. associate-*r/ 58.1%

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

      4. div-sub 58.1%

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

      5. distribute-lft-out-- 58.1%

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

      6. associate-*r/ 58.1%

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

      7. mul-1-neg 58.1%

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

      8. unsub-neg 58.1%

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

      9. distribute-rgt-out-- 58.4%

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

      10. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in y around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 77.1%

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

      4. distribute-rgt-neg-in 77.1%

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

   9. Simplified 77.1%

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

   10. Taylor expanded in x around 0 66.9%

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

       1. associate-/l* 77.2%

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

   12. Simplified 77.2%

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

   if -2.1e95 < t < -1.05000000000000001e-115

   1. Initial program 77.9%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 61.2%

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

      1. div-sub 61.2%

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

      2. associate-*r/ 57.2%

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

      3. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

      1. associate-/r/ 65.0%

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

   8. Applied egg-rr 65.0%

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

   if -1.05000000000000001e-115 < t < 4.9999999999999996e22

   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* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   if 4.9999999999999996e22 < t

   1. Initial program 41.1%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around inf 67.7%

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

      1. associate--l+ 67.7%

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

      2. associate-*r/ 67.7%

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

      3. associate-*r/ 67.7%

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

      4. div-sub 67.7%

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

      5. distribute-lft-out-- 67.7%

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

      6. associate-*r/ 67.7%

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

      7. mul-1-neg 67.7%

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

      8. unsub-neg 67.7%

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

      9. distribute-rgt-out-- 67.7%

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

      10. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

   7. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 67.0%

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

      3. associate-/r/ 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

   9. Simplified 68.6%

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

   10. Taylor expanded in x around 0 68.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{x}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 14: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-71} \lor \neg \left(t \leq 1.55 \cdot 10^{+23}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e-71) (not (<= t 1.55e+23)))
   (+ y (/ (- x y) (/ t z)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e-71) || !(t <= 1.55e+23)) {
		tmp = y + ((x - y) / (t / z));
	} 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) :: tmp
    if ((t <= (-2d-71)) .or. (.not. (t <= 1.55d+23))) then
        tmp = y + ((x - y) / (t / z))
    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 tmp;
	if ((t <= -2e-71) || !(t <= 1.55e+23)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e-71) or not (t <= 1.55e+23):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e-71) || !(t <= 1.55e+23))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	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)
	tmp = 0.0;
	if ((t <= -2e-71) || ~((t <= 1.55e+23)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e-71], N[Not[LessEqual[t, 1.55e+23]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999998e-71 or 1.54999999999999985e23 < t

   1. Initial program 44.3%

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

      1. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-*r/ 62.3%

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

      3. associate-*r/ 62.3%

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

      4. div-sub 62.3%

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

      5. distribute-lft-out-- 62.3%

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

      6. associate-*r/ 62.3%

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

      7. mul-1-neg 62.3%

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

      8. unsub-neg 62.3%

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

      9. distribute-rgt-out-- 62.5%

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

      10. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in z around inf 71.0%

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

   if -1.9999999999999998e-71 < t < 1.54999999999999985e23

   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* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-71} \lor \neg \left(t \leq 1.55 \cdot 10^{+23}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 15: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+93} \lor \neg \left(t \leq 1.2 \cdot 10^{+26}\right):\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+93) (not (<= t 1.2e+26)))
   (- y (* a (/ x t)))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+93) || !(t <= 1.2e+26)) {
		tmp = y - (a * (x / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d+93)) .or. (.not. (t <= 1.2d+26))) then
        tmp = y - (a * (x / t))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+93) || !(t <= 1.2e+26)) {
		tmp = y - (a * (x / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+93) or not (t <= 1.2e+26):
		tmp = y - (a * (x / t))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+93) || !(t <= 1.2e+26))
		tmp = Float64(y - Float64(a * Float64(x / t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+93) || ~((t <= 1.2e+26)))
		tmp = y - (a * (x / t));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+93], N[Not[LessEqual[t, 1.2e+26]], $MachinePrecision]], N[(y - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000035e93 or 1.20000000000000002e26 < t

   1. Initial program 34.0%

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

      1. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in t around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. associate-*r/ 63.4%

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

      3. associate-*r/ 63.4%

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

      4. div-sub 63.4%

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

      5. distribute-lft-out-- 63.4%

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

      6. associate-*r/ 63.4%

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

      7. mul-1-neg 63.4%

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

      8. unsub-neg 63.4%

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

      9. distribute-rgt-out-- 63.5%

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

      10. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in y around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. associate-/l* 71.3%

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

      3. associate-/r/ 72.1%

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

      4. distribute-rgt-neg-in 72.1%

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

   9. Simplified 72.1%

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

   10. Taylor expanded in z around 0 54.5%

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

       1. associate-*r/ 53.0%

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

   12. Simplified 53.0%

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

   if -8.00000000000000035e93 < t < 1.20000000000000002e26

   1. Initial program 85.7%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 69.3%

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

   5. Taylor expanded in t around 0 51.7%

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

      1. associate-/l* 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+93} \lor \neg \left(t \leq 1.2 \cdot 10^{+26}\right):\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 16: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+94) y (if (<= t 1.65e+111) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+94) {
		tmp = y;
	} else if (t <= 1.65e+111) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9d+94)) then
        tmp = y
    else if (t <= 1.65d+111) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+94) {
		tmp = y;
	} else if (t <= 1.65e+111) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+94:
		tmp = y
	elif t <= 1.65e+111:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+94)
		tmp = y;
	elseif (t <= 1.65e+111)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+94)
		tmp = y;
	elseif (t <= 1.65e+111)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+94], y, If[LessEqual[t, 1.65e+111], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999944e94 or 1.6500000000000001e111 < t

   1. Initial program 30.1%

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

      1. associate-/l* 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in t around inf 50.8%

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

   if -8.99999999999999944e94 < t < 1.6500000000000001e111

   1. Initial program 81.9%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in t around 0 62.5%

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

   5. Taylor expanded in x around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

   7. Simplified 46.9%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+94}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+93) y (if (<= t 1.4e+25) (+ x (/ y (/ a z))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+93) {
		tmp = y;
	} else if (t <= 1.4e+25) {
		tmp = x + (y / (a / z));
	} 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 <= (-2.7d+93)) then
        tmp = y
    else if (t <= 1.4d+25) then
        tmp = x + (y / (a / z))
    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 <= -2.7e+93) {
		tmp = y;
	} else if (t <= 1.4e+25) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+93:
		tmp = y
	elif t <= 1.4e+25:
		tmp = x + (y / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+93)
		tmp = y;
	elseif (t <= 1.4e+25)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+93)
		tmp = y;
	elseif (t <= 1.4e+25)
		tmp = x + (y / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+93], y, If[LessEqual[t, 1.4e+25], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6999999999999999e93 or 1.4000000000000001e25 < t

   1. Initial program 34.0%

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

      1. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in t around inf 46.2%

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

   if -2.6999999999999999e93 < t < 1.4000000000000001e25

   1. Initial program 85.7%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 69.3%

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

   5. Taylor expanded in t around 0 51.7%

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

      1. associate-/l* 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+94)
   (- y (* a (/ x t)))
   (if (<= t 4e+25) (+ x (/ y (/ a z))) (- y (* x (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+94) {
		tmp = y - (a * (x / t));
	} else if (t <= 4e+25) {
		tmp = x + (y / (a / z));
	} else {
		tmp = 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 <= (-2.4d+94)) then
        tmp = y - (a * (x / t))
    else if (t <= 4d+25) then
        tmp = x + (y / (a / z))
    else
        tmp = 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 <= -2.4e+94) {
		tmp = y - (a * (x / t));
	} else if (t <= 4e+25) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+94:
		tmp = y - (a * (x / t))
	elif t <= 4e+25:
		tmp = x + (y / (a / z))
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+94)
		tmp = Float64(y - Float64(a * Float64(x / t)));
	elseif (t <= 4e+25)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+94)
		tmp = y - (a * (x / t));
	elseif (t <= 4e+25)
		tmp = x + (y / (a / z));
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+94], N[(y - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+25], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999983e94

   1. Initial program 26.7%

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

      1. associate-/l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in t around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. associate-*r/ 58.9%

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

      3. associate-*r/ 58.9%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 59.2%

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

      10. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in y around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-/l* 75.8%

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

      3. associate-/r/ 75.8%

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

      4. distribute-rgt-neg-in 75.8%

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

   9. Simplified 75.8%

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

   10. Taylor expanded in z around 0 58.8%

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

       1. associate-*r/ 58.9%

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

   12. Simplified 58.9%

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

   if -2.39999999999999983e94 < t < 4.00000000000000036e25

   1. Initial program 85.7%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 69.3%

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

   5. Taylor expanded in t around 0 51.7%

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

      1. associate-/l* 54.6%

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

   7. Simplified 54.6%

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

   if 4.00000000000000036e25 < t

   1. Initial program 41.1%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around inf 67.7%

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

      1. associate--l+ 67.7%

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

      2. associate-*r/ 67.7%

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

      3. associate-*r/ 67.7%

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

      4. div-sub 67.7%

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

      5. distribute-lft-out-- 67.7%

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

      6. associate-*r/ 67.7%

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

      7. mul-1-neg 67.7%

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

      8. unsub-neg 67.7%

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

      9. distribute-rgt-out-- 67.7%

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

      10. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

   7. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 67.0%

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

      3. associate-/r/ 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

   9. Simplified 68.6%

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

   10. Taylor expanded in x around 0 68.1%

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

       1. associate-/l* 67.0%

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

   12. Simplified 67.0%

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

   13. Taylor expanded in a around inf 50.3%

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

       1. associate-/l* 47.3%

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

       2. associate-/r/ 48.4%

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

   15. Simplified 48.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]

Alternative 19: 55.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+92}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+92)
   (- y (* a (/ x t)))
   (if (<= t 2.5e+29) (+ x (/ y (/ a z))) (- y (/ (* x a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+92) {
		tmp = y - (a * (x / t));
	} else if (t <= 2.5e+29) {
		tmp = x + (y / (a / z));
	} else {
		tmp = 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 <= (-1.9d+92)) then
        tmp = y - (a * (x / t))
    else if (t <= 2.5d+29) then
        tmp = x + (y / (a / z))
    else
        tmp = 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 <= -1.9e+92) {
		tmp = y - (a * (x / t));
	} else if (t <= 2.5e+29) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - ((x * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+92:
		tmp = y - (a * (x / t))
	elif t <= 2.5e+29:
		tmp = x + (y / (a / z))
	else:
		tmp = y - ((x * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+92)
		tmp = Float64(y - Float64(a * Float64(x / t)));
	elseif (t <= 2.5e+29)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y - Float64(Float64(x * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+92)
		tmp = y - (a * (x / t));
	elseif (t <= 2.5e+29)
		tmp = x + (y / (a / z));
	else
		tmp = y - ((x * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+92], N[(y - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+29], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(x * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e92

   1. Initial program 26.7%

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

      1. associate-/l* 70.4%

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

   3. Simplified 70.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 58.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. associate--l+ 58.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 58.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 58.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 58.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 58.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 58.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 58.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 58.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 59.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.8%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   6. Simplified 87.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in y around 0 65.8%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 65.8%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 75.8%

         \[\leadsto y - \left(-\color{blue}{\frac{x}{\frac{t}{z - a}}}\right) \]

      3. associate-/r/ 75.8%

         \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot \left(z - a\right)}\right) \]

      4. distribute-rgt-neg-in 75.8%

         \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   9. Simplified 75.8%

      \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   10. Taylor expanded in z around 0 58.8%

       \[\leadsto y - \color{blue}{\frac{a \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-*r/ 58.9%

          \[\leadsto y - \color{blue}{a \cdot \frac{x}{t}} \]

   12. Simplified 58.9%

       \[\leadsto y - \color{blue}{a \cdot \frac{x}{t}} \]

   if -1.9e92 < t < 2.5e29

   1. Initial program 85.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 69.3%

      \[\leadsto x + \color{blue}{\frac{y}{a - t}} \cdot \left(z - t\right) \]

   5. Taylor expanded in t around 0 51.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   7. Simplified 54.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 2.5e29 < t

   1. Initial program 41.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 64.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 64.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 67.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. associate--l+ 67.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 67.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 67.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 67.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 67.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 67.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 67.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 67.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 67.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 74.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   6. Simplified 74.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in y around 0 68.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 67.0%

         \[\leadsto y - \left(-\color{blue}{\frac{x}{\frac{t}{z - a}}}\right) \]

      3. associate-/r/ 68.6%

         \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot \left(z - a\right)}\right) \]

      4. distribute-rgt-neg-in 68.6%

         \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   9. Simplified 68.6%

      \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-\left(z - a\right)\right)} \]

   10. Taylor expanded in z around 0 50.3%

       \[\leadsto y - \color{blue}{\frac{a \cdot x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+92}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot a}{t}\\ \end{array} \]

Alternative 20: 37.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+129}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.85e+119) x (if (<= a 1.22e+129) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+119) {
		tmp = x;
	} else if (a <= 1.22e+129) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.85d+119)) then
        tmp = x
    else if (a <= 1.22d+129) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+119) {
		tmp = x;
	} else if (a <= 1.22e+129) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.85e+119:
		tmp = x
	elif a <= 1.22e+129:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.85e+119)
		tmp = x;
	elseif (a <= 1.22e+129)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.85e+119)
		tmp = x;
	elseif (a <= 1.22e+129)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.85e+119], x, If[LessEqual[a, 1.22e+129], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8500000000000001e119 or 1.2200000000000001e129 < a

   1. Initial program 72.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in a around inf 62.0%

      \[\leadsto \color{blue}{x} \]

   if -2.8500000000000001e119 < a < 1.2200000000000001e129

   1. Initial program 58.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 74.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in t around inf 32.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+129}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.1% 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 62.7%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 81.0%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

4. Taylor expanded in a around inf 24.0%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 24.0%

   \[\leadsto x \]

Developer target: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023318 
(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))))