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

Percentage Accurate: 68.2% → 89.1%

Time: 27.0s

Alternatives: 23

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: 68.2% 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: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+123} \lor \neg \left(t \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e+123) (not (<= t 1.85e+92)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+123) || !(t <= 1.85e+92)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.25d+123)) .or. (.not. (t <= 1.85d+92))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+123) || !(t <= 1.85e+92)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e+123) or not (t <= 1.85e+92):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e+123) || !(t <= 1.85e+92))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e+123) || ~((t <= 1.85e+92)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e+123], N[Not[LessEqual[t, 1.85e+92]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999994e123 or 1.84999999999999999e92 < t

   1. Initial program 39.3%

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

      1. associate-/l* 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. div-sub 74.2%

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

      5. distribute-lft-out-- 74.2%

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

      6. associate-*r/ 74.2%

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

      7. mul-1-neg 74.2%

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

      8. unsub-neg 74.2%

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

      9. distribute-rgt-out-- 74.4%

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

      10. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if -1.24999999999999994e123 < t < 1.84999999999999999e92

   1. Initial program 88.0%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+123} \lor \neg \left(t \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 2: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ t_2 := x - \frac{t \cdot y}{a}\\ \mathbf{if}\;a \leq -1.24 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -16000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))) (t_2 (- x (/ (* t y) a))))
   (if (<= a -1.24e+107)
     t_2
     (if (<= a -1.55e+47)
       t_1
       (if (<= a -16000000000.0)
         t_2
         (if (<= a 4e-192)
           t_1
           (if (<= a 2.9e-177)
             (/ z (/ t x))
             (if (<= a 6.3e-111)
               t_1
               (if (<= a 1.56e+97) (* z (/ (- y x) a)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x - ((t * y) / a);
	double tmp;
	if (a <= -1.24e+107) {
		tmp = t_2;
	} else if (a <= -1.55e+47) {
		tmp = t_1;
	} else if (a <= -16000000000.0) {
		tmp = t_2;
	} else if (a <= 4e-192) {
		tmp = t_1;
	} else if (a <= 2.9e-177) {
		tmp = z / (t / x);
	} else if (a <= 6.3e-111) {
		tmp = t_1;
	} else if (a <= 1.56e+97) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (y * (z / t))
    t_2 = x - ((t * y) / a)
    if (a <= (-1.24d+107)) then
        tmp = t_2
    else if (a <= (-1.55d+47)) then
        tmp = t_1
    else if (a <= (-16000000000.0d0)) then
        tmp = t_2
    else if (a <= 4d-192) then
        tmp = t_1
    else if (a <= 2.9d-177) then
        tmp = z / (t / x)
    else if (a <= 6.3d-111) then
        tmp = t_1
    else if (a <= 1.56d+97) then
        tmp = z * ((y - x) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x - ((t * y) / a);
	double tmp;
	if (a <= -1.24e+107) {
		tmp = t_2;
	} else if (a <= -1.55e+47) {
		tmp = t_1;
	} else if (a <= -16000000000.0) {
		tmp = t_2;
	} else if (a <= 4e-192) {
		tmp = t_1;
	} else if (a <= 2.9e-177) {
		tmp = z / (t / x);
	} else if (a <= 6.3e-111) {
		tmp = t_1;
	} else if (a <= 1.56e+97) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	t_2 = x - ((t * y) / a)
	tmp = 0
	if a <= -1.24e+107:
		tmp = t_2
	elif a <= -1.55e+47:
		tmp = t_1
	elif a <= -16000000000.0:
		tmp = t_2
	elif a <= 4e-192:
		tmp = t_1
	elif a <= 2.9e-177:
		tmp = z / (t / x)
	elif a <= 6.3e-111:
		tmp = t_1
	elif a <= 1.56e+97:
		tmp = z * ((y - x) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	t_2 = Float64(x - Float64(Float64(t * y) / a))
	tmp = 0.0
	if (a <= -1.24e+107)
		tmp = t_2;
	elseif (a <= -1.55e+47)
		tmp = t_1;
	elseif (a <= -16000000000.0)
		tmp = t_2;
	elseif (a <= 4e-192)
		tmp = t_1;
	elseif (a <= 2.9e-177)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 6.3e-111)
		tmp = t_1;
	elseif (a <= 1.56e+97)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	t_2 = x - ((t * y) / a);
	tmp = 0.0;
	if (a <= -1.24e+107)
		tmp = t_2;
	elseif (a <= -1.55e+47)
		tmp = t_1;
	elseif (a <= -16000000000.0)
		tmp = t_2;
	elseif (a <= 4e-192)
		tmp = t_1;
	elseif (a <= 2.9e-177)
		tmp = z / (t / x);
	elseif (a <= 6.3e-111)
		tmp = t_1;
	elseif (a <= 1.56e+97)
		tmp = z * ((y - x) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.24e+107], t$95$2, If[LessEqual[a, -1.55e+47], t$95$1, If[LessEqual[a, -16000000000.0], t$95$2, If[LessEqual[a, 4e-192], t$95$1, If[LessEqual[a, 2.9e-177], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.3e-111], t$95$1, If[LessEqual[a, 1.56e+97], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.24e107 or -1.55e47 < a < -1.6e10 or 1.56e97 < a

   1. Initial program 79.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 73.0%

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

      1. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in z around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. *-commutative 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in y around inf 59.3%

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

   if -1.24e107 < a < -1.55e47 or -1.6e10 < a < 4.0000000000000004e-192 or 2.89999999999999997e-177 < a < 6.3000000000000004e-111

   1. Initial program 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 67.5%

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

      4. associate-/r/ 74.1%

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

      5. fma-def 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in t around -inf 77.7%

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

   5. Taylor expanded in a around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in y around inf 57.9%

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

      1. associate-*r/ 62.6%

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

   10. Simplified 62.6%

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

   if 4.0000000000000004e-192 < a < 2.89999999999999997e-177

   1. Initial program 61.6%

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

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-/l* 71.5%

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

      4. associate-/r/ 61.0%

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

      5. fma-def 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in t around -inf 61.3%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. div-sub 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-/r/ 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 6.3000000000000004e-111 < a < 1.56e97

   1. Initial program 86.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around inf 64.4%

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

      1. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in z around inf 46.6%

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

      1. div-sub 46.6%

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

   9. Simplified 46.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.24 \cdot 10^{+107}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -16000000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-192}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-111}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 3: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ t_2 := x - \frac{t \cdot y}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))) (t_2 (- x (/ (* t y) a))))
   (if (<= a -2.4e+106)
     t_2
     (if (<= a -1.7e+47)
       t_1
       (if (<= a -8e+14)
         t_2
         (if (<= a 4.2e-192)
           t_1
           (if (<= a 2.9e-177)
             (/ z (/ t x))
             (if (<= a 4.8e-111)
               t_1
               (if (<= a 1.55e+97) (/ z (/ a (- y x))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double t_2 = x - ((t * y) / a);
	double tmp;
	if (a <= -2.4e+106) {
		tmp = t_2;
	} else if (a <= -1.7e+47) {
		tmp = t_1;
	} else if (a <= -8e+14) {
		tmp = t_2;
	} else if (a <= 4.2e-192) {
		tmp = t_1;
	} else if (a <= 2.9e-177) {
		tmp = z / (t / x);
	} else if (a <= 4.8e-111) {
		tmp = t_1;
	} else if (a <= 1.55e+97) {
		tmp = z / (a / (y - x));
	} 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 * (z / t))
    t_2 = x - ((t * y) / a)
    if (a <= (-2.4d+106)) then
        tmp = t_2
    else if (a <= (-1.7d+47)) then
        tmp = t_1
    else if (a <= (-8d+14)) then
        tmp = t_2
    else if (a <= 4.2d-192) then
        tmp = t_1
    else if (a <= 2.9d-177) then
        tmp = z / (t / x)
    else if (a <= 4.8d-111) then
        tmp = t_1
    else if (a <= 1.55d+97) then
        tmp = z / (a / (y - x))
    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 * (z / t));
	double t_2 = x - ((t * y) / a);
	double tmp;
	if (a <= -2.4e+106) {
		tmp = t_2;
	} else if (a <= -1.7e+47) {
		tmp = t_1;
	} else if (a <= -8e+14) {
		tmp = t_2;
	} else if (a <= 4.2e-192) {
		tmp = t_1;
	} else if (a <= 2.9e-177) {
		tmp = z / (t / x);
	} else if (a <= 4.8e-111) {
		tmp = t_1;
	} else if (a <= 1.55e+97) {
		tmp = z / (a / (y - x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	t_2 = x - ((t * y) / a)
	tmp = 0
	if a <= -2.4e+106:
		tmp = t_2
	elif a <= -1.7e+47:
		tmp = t_1
	elif a <= -8e+14:
		tmp = t_2
	elif a <= 4.2e-192:
		tmp = t_1
	elif a <= 2.9e-177:
		tmp = z / (t / x)
	elif a <= 4.8e-111:
		tmp = t_1
	elif a <= 1.55e+97:
		tmp = z / (a / (y - x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	t_2 = Float64(x - Float64(Float64(t * y) / a))
	tmp = 0.0
	if (a <= -2.4e+106)
		tmp = t_2;
	elseif (a <= -1.7e+47)
		tmp = t_1;
	elseif (a <= -8e+14)
		tmp = t_2;
	elseif (a <= 4.2e-192)
		tmp = t_1;
	elseif (a <= 2.9e-177)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 4.8e-111)
		tmp = t_1;
	elseif (a <= 1.55e+97)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	t_2 = x - ((t * y) / a);
	tmp = 0.0;
	if (a <= -2.4e+106)
		tmp = t_2;
	elseif (a <= -1.7e+47)
		tmp = t_1;
	elseif (a <= -8e+14)
		tmp = t_2;
	elseif (a <= 4.2e-192)
		tmp = t_1;
	elseif (a <= 2.9e-177)
		tmp = z / (t / x);
	elseif (a <= 4.8e-111)
		tmp = t_1;
	elseif (a <= 1.55e+97)
		tmp = z / (a / (y - x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+106], t$95$2, If[LessEqual[a, -1.7e+47], t$95$1, If[LessEqual[a, -8e+14], t$95$2, If[LessEqual[a, 4.2e-192], t$95$1, If[LessEqual[a, 2.9e-177], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-111], t$95$1, If[LessEqual[a, 1.55e+97], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4000000000000001e106 or -1.6999999999999999e47 < a < -8e14 or 1.54999999999999991e97 < a

   1. Initial program 79.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 73.0%

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

      1. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in z around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. *-commutative 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in y around inf 59.3%

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

   if -2.4000000000000001e106 < a < -1.6999999999999999e47 or -8e14 < a < 4.19999999999999986e-192 or 2.89999999999999997e-177 < a < 4.8000000000000001e-111

   1. Initial program 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 67.5%

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

      4. associate-/r/ 74.1%

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

      5. fma-def 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in t around -inf 77.7%

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

   5. Taylor expanded in a around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in y around inf 57.9%

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

      1. associate-*r/ 62.6%

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

   10. Simplified 62.6%

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

   if 4.19999999999999986e-192 < a < 2.89999999999999997e-177

   1. Initial program 61.6%

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

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-/l* 71.5%

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

      4. associate-/r/ 61.0%

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

      5. fma-def 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in t around -inf 61.3%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. div-sub 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-/r/ 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 4.8000000000000001e-111 < a < 1.54999999999999991e97

   1. Initial program 86.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around inf 57.2%

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

      1. div-sub 57.2%

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

      2. associate-*r/ 53.2%

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

      3. associate-/l* 57.2%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in a around inf 46.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+106}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-192}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-111}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 4: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -120 \lor \neg \left(a \leq 1.6 \cdot 10^{-64}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- x y) (/ a (- z t))))))
   (if (<= a -1.85e+89)
     t_1
     (if (<= a -1.75e+47)
       (* y (/ (- z t) (- a t)))
       (if (or (<= a -120.0) (not (<= a 1.6e-64)))
         t_1
         (+ y (* (/ z t) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -1.85e+89) {
		tmp = t_1;
	} else if (a <= -1.75e+47) {
		tmp = y * ((z - t) / (a - t));
	} else if ((a <= -120.0) || !(a <= 1.6e-64)) {
		tmp = t_1;
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((x - y) / (a / (z - t)))
    if (a <= (-1.85d+89)) then
        tmp = t_1
    else if (a <= (-1.75d+47)) then
        tmp = y * ((z - t) / (a - t))
    else if ((a <= (-120.0d0)) .or. (.not. (a <= 1.6d-64))) then
        tmp = t_1
    else
        tmp = y + ((z / t) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -1.85e+89) {
		tmp = t_1;
	} else if (a <= -1.75e+47) {
		tmp = y * ((z - t) / (a - t));
	} else if ((a <= -120.0) || !(a <= 1.6e-64)) {
		tmp = t_1;
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((x - y) / (a / (z - t)))
	tmp = 0
	if a <= -1.85e+89:
		tmp = t_1
	elif a <= -1.75e+47:
		tmp = y * ((z - t) / (a - t))
	elif (a <= -120.0) or not (a <= 1.6e-64):
		tmp = t_1
	else:
		tmp = y + ((z / t) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -1.85e+89)
		tmp = t_1;
	elseif (a <= -1.75e+47)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif ((a <= -120.0) || !(a <= 1.6e-64))
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((x - y) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -1.85e+89)
		tmp = t_1;
	elseif (a <= -1.75e+47)
		tmp = y * ((z - t) / (a - t));
	elseif ((a <= -120.0) || ~((a <= 1.6e-64)))
		tmp = t_1;
	else
		tmp = y + ((z / t) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e+89], t$95$1, If[LessEqual[a, -1.75e+47], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -120.0], N[Not[LessEqual[a, 1.6e-64]], $MachinePrecision]], t$95$1, N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8499999999999999e89 or -1.75000000000000008e47 < a < -120 or 1.59999999999999988e-64 < a

   1. Initial program 79.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around inf 70.2%

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

      1. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   if -1.8499999999999999e89 < a < -1.75000000000000008e47

   1. Initial program 63.0%

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

      1. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around 0 63.6%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

   if -120 < a < 1.59999999999999988e-64

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-/l* 70.4%

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

      4. associate-/r/ 73.5%

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

      5. fma-def 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around -inf 81.3%

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

   5. Taylor expanded in a around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

      3. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

      1. associate-/r/ 83.8%

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

   9. Applied egg-rr 83.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -120 \lor \neg \left(a \leq 1.6 \cdot 10^{-64}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 5: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -750 \lor \neg \left(a \leq 2.4 \cdot 10^{-64}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- x y) (/ a (- z t))))))
   (if (<= a -1.7e+88)
     t_1
     (if (<= a -3.1e+47)
       (* y (/ (- z t) (- a t)))
       (if (or (<= a -750.0) (not (<= a 2.4e-64)))
         t_1
         (+ y (/ (- x y) (/ t (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -1.7e+88) {
		tmp = t_1;
	} else if (a <= -3.1e+47) {
		tmp = y * ((z - t) / (a - t));
	} else if ((a <= -750.0) || !(a <= 2.4e-64)) {
		tmp = t_1;
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((x - y) / (a / (z - t)))
    if (a <= (-1.7d+88)) then
        tmp = t_1
    else if (a <= (-3.1d+47)) then
        tmp = y * ((z - t) / (a - t))
    else if ((a <= (-750.0d0)) .or. (.not. (a <= 2.4d-64))) then
        tmp = t_1
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -1.7e+88) {
		tmp = t_1;
	} else if (a <= -3.1e+47) {
		tmp = y * ((z - t) / (a - t));
	} else if ((a <= -750.0) || !(a <= 2.4e-64)) {
		tmp = t_1;
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((x - y) / (a / (z - t)))
	tmp = 0
	if a <= -1.7e+88:
		tmp = t_1
	elif a <= -3.1e+47:
		tmp = y * ((z - t) / (a - t))
	elif (a <= -750.0) or not (a <= 2.4e-64):
		tmp = t_1
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -1.7e+88)
		tmp = t_1;
	elseif (a <= -3.1e+47)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif ((a <= -750.0) || !(a <= 2.4e-64))
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((x - y) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -1.7e+88)
		tmp = t_1;
	elseif (a <= -3.1e+47)
		tmp = y * ((z - t) / (a - t));
	elseif ((a <= -750.0) || ~((a <= 2.4e-64)))
		tmp = t_1;
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+88], t$95$1, If[LessEqual[a, -3.1e+47], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -750.0], N[Not[LessEqual[a, 2.4e-64]], $MachinePrecision]], t$95$1, N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000002e88 or -3.1000000000000001e47 < a < -750 or 2.39999999999999998e-64 < a

   1. Initial program 79.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around inf 70.2%

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

      1. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   if -1.70000000000000002e88 < a < -3.1000000000000001e47

   1. Initial program 63.0%

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

      1. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around 0 63.6%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

   if -750 < a < 2.39999999999999998e-64

   1. Initial program 66.9%

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

      1. associate-/l* 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. associate-*r/ 78.5%

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

      4. div-sub 81.3%

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

      5. distribute-lft-out-- 81.3%

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

      6. associate-*r/ 81.3%

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

      7. mul-1-neg 81.3%

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

      8. unsub-neg 81.3%

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

      9. distribute-rgt-out-- 81.3%

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

      10. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -750 \lor \neg \left(a \leq 2.4 \cdot 10^{-64}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 6: 32.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-219}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+167)
   (* y (/ z a))
   (if (<= z -9.6e+78)
     y
     (if (<= z -4.6e-10)
       x
       (if (<= z 2.85e-219) y (if (<= z 5.2e+38) x (* x (/ (- z a) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+167) {
		tmp = y * (z / a);
	} else if (z <= -9.6e+78) {
		tmp = y;
	} else if (z <= -4.6e-10) {
		tmp = x;
	} else if (z <= 2.85e-219) {
		tmp = y;
	} else if (z <= 5.2e+38) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-4.3d+167)) then
        tmp = y * (z / a)
    else if (z <= (-9.6d+78)) then
        tmp = y
    else if (z <= (-4.6d-10)) then
        tmp = x
    else if (z <= 2.85d-219) then
        tmp = y
    else if (z <= 5.2d+38) then
        tmp = x
    else
        tmp = 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 (z <= -4.3e+167) {
		tmp = y * (z / a);
	} else if (z <= -9.6e+78) {
		tmp = y;
	} else if (z <= -4.6e-10) {
		tmp = x;
	} else if (z <= 2.85e-219) {
		tmp = y;
	} else if (z <= 5.2e+38) {
		tmp = x;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+167:
		tmp = y * (z / a)
	elif z <= -9.6e+78:
		tmp = y
	elif z <= -4.6e-10:
		tmp = x
	elif z <= 2.85e-219:
		tmp = y
	elif z <= 5.2e+38:
		tmp = x
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+167)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= -9.6e+78)
		tmp = y;
	elseif (z <= -4.6e-10)
		tmp = x;
	elseif (z <= 2.85e-219)
		tmp = y;
	elseif (z <= 5.2e+38)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+167)
		tmp = y * (z / a);
	elseif (z <= -9.6e+78)
		tmp = y;
	elseif (z <= -4.6e-10)
		tmp = x;
	elseif (z <= 2.85e-219)
		tmp = y;
	elseif (z <= 5.2e+38)
		tmp = x;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+167], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.6e+78], y, If[LessEqual[z, -4.6e-10], x, If[LessEqual[z, 2.85e-219], y, If[LessEqual[z, 5.2e+38], x, N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3000000000000002e167

   1. Initial program 78.2%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in y around inf 58.3%

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

      1. div-sub 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in z around inf 58.3%

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

   if -4.3000000000000002e167 < z < -9.5999999999999994e78 or -4.60000000000000014e-10 < z < 2.85000000000000003e-219

   1. Initial program 64.4%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around inf 46.3%

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

   if -9.5999999999999994e78 < z < -4.60000000000000014e-10 or 2.85000000000000003e-219 < z < 5.1999999999999998e38

   1. Initial program 84.0%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around inf 47.3%

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

   if 5.1999999999999998e38 < z

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. *-commutative 76.2%

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

      3. associate-/l* 80.8%

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

      4. associate-/r/ 87.4%

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

      5. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in t around -inf 46.2%

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

   5. Taylor expanded in x around inf 42.2%

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

      1. div-sub 42.5%

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

   7. Simplified 42.5%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-219}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]

Alternative 7: 41.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t \cdot y}{a}\\ t_2 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-245}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 15500000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* t y) a))) (t_2 (* z (/ (- y x) a))))
   (if (<= z -2.1e-27)
     t_2
     (if (<= z -1.9e-143)
       y
       (if (<= z -6.5e-273)
         t_1
         (if (<= z 9.2e-245) y (if (<= z 15500000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t * y) / a);
	double t_2 = z * ((y - x) / a);
	double tmp;
	if (z <= -2.1e-27) {
		tmp = t_2;
	} else if (z <= -1.9e-143) {
		tmp = y;
	} else if (z <= -6.5e-273) {
		tmp = t_1;
	} else if (z <= 9.2e-245) {
		tmp = y;
	} else if (z <= 15500000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t * y) / a)
    t_2 = z * ((y - x) / a)
    if (z <= (-2.1d-27)) then
        tmp = t_2
    else if (z <= (-1.9d-143)) then
        tmp = y
    else if (z <= (-6.5d-273)) then
        tmp = t_1
    else if (z <= 9.2d-245) then
        tmp = y
    else if (z <= 15500000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t * y) / a);
	double t_2 = z * ((y - x) / a);
	double tmp;
	if (z <= -2.1e-27) {
		tmp = t_2;
	} else if (z <= -1.9e-143) {
		tmp = y;
	} else if (z <= -6.5e-273) {
		tmp = t_1;
	} else if (z <= 9.2e-245) {
		tmp = y;
	} else if (z <= 15500000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t * y) / a)
	t_2 = z * ((y - x) / a)
	tmp = 0
	if z <= -2.1e-27:
		tmp = t_2
	elif z <= -1.9e-143:
		tmp = y
	elif z <= -6.5e-273:
		tmp = t_1
	elif z <= 9.2e-245:
		tmp = y
	elif z <= 15500000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t * y) / a))
	t_2 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (z <= -2.1e-27)
		tmp = t_2;
	elseif (z <= -1.9e-143)
		tmp = y;
	elseif (z <= -6.5e-273)
		tmp = t_1;
	elseif (z <= 9.2e-245)
		tmp = y;
	elseif (z <= 15500000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t * y) / a);
	t_2 = z * ((y - x) / a);
	tmp = 0.0;
	if (z <= -2.1e-27)
		tmp = t_2;
	elseif (z <= -1.9e-143)
		tmp = y;
	elseif (z <= -6.5e-273)
		tmp = t_1;
	elseif (z <= 9.2e-245)
		tmp = y;
	elseif (z <= 15500000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e-27], t$95$2, If[LessEqual[z, -1.9e-143], y, If[LessEqual[z, -6.5e-273], t$95$1, If[LessEqual[z, 9.2e-245], y, If[LessEqual[z, 15500000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000015e-27 or 1.55e7 < z

   1. Initial program 75.8%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in a around inf 54.5%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in z around inf 48.9%

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

      1. div-sub 49.0%

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

   9. Simplified 49.0%

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

   if -2.10000000000000015e-27 < z < -1.89999999999999991e-143 or -6.49999999999999979e-273 < z < 9.2000000000000007e-245

   1. Initial program 53.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 58.4%

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

   if -1.89999999999999991e-143 < z < -6.49999999999999979e-273 or 9.2000000000000007e-245 < z < 1.55e7

   1. Initial program 82.1%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in a around inf 58.2%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in z around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

      3. *-commutative 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in y around inf 55.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-245}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 15500000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \end{array} \]

Alternative 8: 42.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-128}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 54000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+165}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+169)
   (* z (/ (- y x) a))
   (if (<= z -8e-128)
     (- y (* y (/ z t)))
     (if (<= z 3.5e-236)
       (* y (/ (- t) (- a t)))
       (if (<= z 54000000.0)
         (- x (/ (* t y) a))
         (if (<= z 7.5e+165) (/ z (/ a (- y x))) (* z (/ (- x y) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+169) {
		tmp = z * ((y - x) / a);
	} else if (z <= -8e-128) {
		tmp = y - (y * (z / t));
	} else if (z <= 3.5e-236) {
		tmp = y * (-t / (a - t));
	} else if (z <= 54000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 7.5e+165) {
		tmp = z / (a / (y - x));
	} else {
		tmp = z * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+169)) then
        tmp = z * ((y - x) / a)
    else if (z <= (-8d-128)) then
        tmp = y - (y * (z / t))
    else if (z <= 3.5d-236) then
        tmp = y * (-t / (a - t))
    else if (z <= 54000000.0d0) then
        tmp = x - ((t * y) / a)
    else if (z <= 7.5d+165) then
        tmp = z / (a / (y - x))
    else
        tmp = z * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+169) {
		tmp = z * ((y - x) / a);
	} else if (z <= -8e-128) {
		tmp = y - (y * (z / t));
	} else if (z <= 3.5e-236) {
		tmp = y * (-t / (a - t));
	} else if (z <= 54000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 7.5e+165) {
		tmp = z / (a / (y - x));
	} else {
		tmp = z * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+169:
		tmp = z * ((y - x) / a)
	elif z <= -8e-128:
		tmp = y - (y * (z / t))
	elif z <= 3.5e-236:
		tmp = y * (-t / (a - t))
	elif z <= 54000000.0:
		tmp = x - ((t * y) / a)
	elif z <= 7.5e+165:
		tmp = z / (a / (y - x))
	else:
		tmp = z * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+169)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= -8e-128)
		tmp = Float64(y - Float64(y * Float64(z / t)));
	elseif (z <= 3.5e-236)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (z <= 54000000.0)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (z <= 7.5e+165)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = Float64(z * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+169)
		tmp = z * ((y - x) / a);
	elseif (z <= -8e-128)
		tmp = y - (y * (z / t));
	elseif (z <= 3.5e-236)
		tmp = y * (-t / (a - t));
	elseif (z <= 54000000.0)
		tmp = x - ((t * y) / a);
	elseif (z <= 7.5e+165)
		tmp = z / (a / (y - x));
	else
		tmp = z * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+169], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-128], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-236], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 54000000.0], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+165], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.25000000000000004e169

   1. Initial program 78.2%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in z around inf 77.1%

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

      1. div-sub 77.2%

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

   9. Simplified 77.2%

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

   if -1.25000000000000004e169 < z < -8.00000000000000043e-128

   1. Initial program 66.1%

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

      1. +-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-/l* 74.8%

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

      4. associate-/r/ 77.6%

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

      5. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around -inf 57.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in y around inf 45.8%

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

      1. associate-*r/ 47.8%

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

   10. Simplified 47.8%

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

   if -8.00000000000000043e-128 < z < 3.49999999999999994e-236

   1. Initial program 69.2%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. associate-*r/ 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in z around 0 63.7%

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

      1. neg-mul-1 63.7%

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

      2. distribute-neg-frac 63.7%

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

   9. Simplified 63.7%

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

   if 3.49999999999999994e-236 < z < 5.4e7

   1. Initial program 82.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around inf 58.3%

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

   if 5.4e7 < z < 7.49999999999999996e165

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 57.4%

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

      1. div-sub 57.4%

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

      2. associate-*r/ 54.1%

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

      3. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in a around inf 46.6%

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

   if 7.49999999999999996e165 < z

   1. Initial program 83.3%

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

      1. +-commutative 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-/l* 86.7%

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

      4. associate-/r/ 93.4%

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

      5. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around -inf 51.5%

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

   5. Taylor expanded in z around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. distribute-rgt-neg-in 59.4%

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

      3. div-sub 59.4%

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

   7. Simplified 59.4%

      \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-128}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 54000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+165}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 9: 42.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-127}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 75000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+167)
   (* z (/ (- y x) a))
   (if (<= z -1.8e-127)
     (- y (* y (/ z t)))
     (if (<= z 2e-244)
       (* y (/ (- t) (- a t)))
       (if (<= z 75000000.0)
         (- x (/ (* t y) a))
         (if (<= z 8.5e+160) (/ z (/ a (- y x))) (* (/ z t) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+167) {
		tmp = z * ((y - x) / a);
	} else if (z <= -1.8e-127) {
		tmp = y - (y * (z / t));
	} else if (z <= 2e-244) {
		tmp = y * (-t / (a - t));
	} else if (z <= 75000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 8.5e+160) {
		tmp = z / (a / (y - x));
	} else {
		tmp = (z / t) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d+167)) then
        tmp = z * ((y - x) / a)
    else if (z <= (-1.8d-127)) then
        tmp = y - (y * (z / t))
    else if (z <= 2d-244) then
        tmp = y * (-t / (a - t))
    else if (z <= 75000000.0d0) then
        tmp = x - ((t * y) / a)
    else if (z <= 8.5d+160) then
        tmp = z / (a / (y - x))
    else
        tmp = (z / t) * (x - 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 (z <= -4.3e+167) {
		tmp = z * ((y - x) / a);
	} else if (z <= -1.8e-127) {
		tmp = y - (y * (z / t));
	} else if (z <= 2e-244) {
		tmp = y * (-t / (a - t));
	} else if (z <= 75000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 8.5e+160) {
		tmp = z / (a / (y - x));
	} else {
		tmp = (z / t) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+167:
		tmp = z * ((y - x) / a)
	elif z <= -1.8e-127:
		tmp = y - (y * (z / t))
	elif z <= 2e-244:
		tmp = y * (-t / (a - t))
	elif z <= 75000000.0:
		tmp = x - ((t * y) / a)
	elif z <= 8.5e+160:
		tmp = z / (a / (y - x))
	else:
		tmp = (z / t) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+167)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= -1.8e-127)
		tmp = Float64(y - Float64(y * Float64(z / t)));
	elseif (z <= 2e-244)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (z <= 75000000.0)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (z <= 8.5e+160)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = Float64(Float64(z / t) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+167)
		tmp = z * ((y - x) / a);
	elseif (z <= -1.8e-127)
		tmp = y - (y * (z / t));
	elseif (z <= 2e-244)
		tmp = y * (-t / (a - t));
	elseif (z <= 75000000.0)
		tmp = x - ((t * y) / a);
	elseif (z <= 8.5e+160)
		tmp = z / (a / (y - x));
	else
		tmp = (z / t) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+167], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-127], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-244], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 75000000.0], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+160], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.3000000000000002e167

   1. Initial program 78.2%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in z around inf 77.1%

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

      1. div-sub 77.2%

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

   9. Simplified 77.2%

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

   if -4.3000000000000002e167 < z < -1.8e-127

   1. Initial program 66.1%

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

      1. +-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-/l* 74.8%

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

      4. associate-/r/ 77.6%

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

      5. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around -inf 57.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in y around inf 45.8%

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

      1. associate-*r/ 47.8%

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

   10. Simplified 47.8%

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

   if -1.8e-127 < z < 1.9999999999999999e-244

   1. Initial program 69.2%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. associate-*r/ 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in z around 0 63.7%

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

      1. neg-mul-1 63.7%

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

      2. distribute-neg-frac 63.7%

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

   9. Simplified 63.7%

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

   if 1.9999999999999999e-244 < z < 7.5e7

   1. Initial program 82.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around inf 58.3%

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

   if 7.5e7 < z < 8.49999999999999982e160

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 57.4%

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

      1. div-sub 57.4%

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

      2. associate-*r/ 54.1%

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

      3. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in a around inf 46.6%

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

   if 8.49999999999999982e160 < z

   1. Initial program 83.3%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 51.2%

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

      1. associate--l+ 51.2%

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

      2. associate-*r/ 51.2%

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

      3. associate-*r/ 51.2%

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

      4. div-sub 51.5%

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

      5. distribute-lft-out-- 51.5%

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

      6. associate-*r/ 51.5%

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

      7. mul-1-neg 51.5%

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

      8. unsub-neg 51.5%

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

      9. distribute-rgt-out-- 51.5%

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

      10. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in z around -inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-*r/ 60.3%

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

      4. *-commutative 60.3%

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

      5. distribute-rgt-neg-in 60.3%

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

      6. neg-sub0 60.3%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      7. associate--r- 60.3%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      8. neg-sub0 60.3%

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

   9. Simplified 60.3%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(\left(-y\right) + x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-127}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 75000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 10: 43.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-137}:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 92000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+167}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.25e+165)
   (* z (/ (- y x) a))
   (if (<= z -9.2e-137)
     (+ y (/ (* x z) t))
     (if (<= z 1.1e-240)
       (* y (/ (- t) (- a t)))
       (if (<= z 92000000.0)
         (- x (/ (* t y) a))
         (if (<= z 1.3e+167) (/ z (/ a (- y x))) (* (/ z t) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.25e+165) {
		tmp = z * ((y - x) / a);
	} else if (z <= -9.2e-137) {
		tmp = y + ((x * z) / t);
	} else if (z <= 1.1e-240) {
		tmp = y * (-t / (a - t));
	} else if (z <= 92000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 1.3e+167) {
		tmp = z / (a / (y - x));
	} else {
		tmp = (z / t) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.25d+165)) then
        tmp = z * ((y - x) / a)
    else if (z <= (-9.2d-137)) then
        tmp = y + ((x * z) / t)
    else if (z <= 1.1d-240) then
        tmp = y * (-t / (a - t))
    else if (z <= 92000000.0d0) then
        tmp = x - ((t * y) / a)
    else if (z <= 1.3d+167) then
        tmp = z / (a / (y - x))
    else
        tmp = (z / t) * (x - 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 (z <= -3.25e+165) {
		tmp = z * ((y - x) / a);
	} else if (z <= -9.2e-137) {
		tmp = y + ((x * z) / t);
	} else if (z <= 1.1e-240) {
		tmp = y * (-t / (a - t));
	} else if (z <= 92000000.0) {
		tmp = x - ((t * y) / a);
	} else if (z <= 1.3e+167) {
		tmp = z / (a / (y - x));
	} else {
		tmp = (z / t) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.25e+165:
		tmp = z * ((y - x) / a)
	elif z <= -9.2e-137:
		tmp = y + ((x * z) / t)
	elif z <= 1.1e-240:
		tmp = y * (-t / (a - t))
	elif z <= 92000000.0:
		tmp = x - ((t * y) / a)
	elif z <= 1.3e+167:
		tmp = z / (a / (y - x))
	else:
		tmp = (z / t) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.25e+165)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= -9.2e-137)
		tmp = Float64(y + Float64(Float64(x * z) / t));
	elseif (z <= 1.1e-240)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (z <= 92000000.0)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (z <= 1.3e+167)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = Float64(Float64(z / t) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.25e+165)
		tmp = z * ((y - x) / a);
	elseif (z <= -9.2e-137)
		tmp = y + ((x * z) / t);
	elseif (z <= 1.1e-240)
		tmp = y * (-t / (a - t));
	elseif (z <= 92000000.0)
		tmp = x - ((t * y) / a);
	elseif (z <= 1.3e+167)
		tmp = z / (a / (y - x));
	else
		tmp = (z / t) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.25e+165], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-137], N[(y + N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-240], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 92000000.0], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+167], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.2499999999999999e165

   1. Initial program 75.7%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 59.5%

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

      1. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in z around inf 74.7%

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

      1. div-sub 74.7%

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

   9. Simplified 74.7%

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

   if -3.2499999999999999e165 < z < -9.20000000000000032e-137

   1. Initial program 66.2%

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

      1. +-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-/l* 74.5%

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

      4. associate-/r/ 77.2%

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

      5. fma-def 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in t around -inf 59.3%

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

   5. Taylor expanded in a around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

      3. associate-/l* 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in y around 0 49.9%

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

      1. associate-*r/ 49.9%

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

      2. *-commutative 49.9%

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

      3. neg-mul-1 49.9%

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

      4. distribute-lft-neg-in 49.9%

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

      5. *-commutative 49.9%

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

   10. Simplified 49.9%

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

   if -9.20000000000000032e-137 < z < 1.1e-240

   1. Initial program 70.6%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 57.0%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in z around 0 64.6%

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

      1. neg-mul-1 64.6%

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

      2. distribute-neg-frac 64.6%

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

   9. Simplified 64.6%

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

   if 1.1e-240 < z < 9.2e7

   1. Initial program 82.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around inf 58.3%

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

   if 9.2e7 < z < 1.3000000000000001e167

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 57.4%

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

      1. div-sub 57.4%

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

      2. associate-*r/ 54.1%

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

      3. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in a around inf 46.6%

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

   if 1.3000000000000001e167 < z

   1. Initial program 83.3%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 51.2%

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

      1. associate--l+ 51.2%

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

      2. associate-*r/ 51.2%

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

      3. associate-*r/ 51.2%

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

      4. div-sub 51.5%

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

      5. distribute-lft-out-- 51.5%

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

      6. associate-*r/ 51.5%

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

      7. mul-1-neg 51.5%

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

      8. unsub-neg 51.5%

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

      9. distribute-rgt-out-- 51.5%

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

      10. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in z around -inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-*r/ 60.3%

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

      4. *-commutative 60.3%

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

      5. distribute-rgt-neg-in 60.3%

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

      6. neg-sub0 60.3%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      7. associate--r- 60.3%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      8. neg-sub0 60.3%

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

   9. Simplified 60.3%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(\left(-y\right) + x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-137}:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 92000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+167}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 11: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot \left(x - y\right)}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-29}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* z (- x y)) a))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -8.5e+46)
     t_2
     (if (<= t 1.45e-173)
       t_1
       (if (<= t 1.46e-29)
         (* (- y x) (/ z (- a t)))
         (if (<= t 1.25e+54) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * (x - y)) / a);
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.5e+46) {
		tmp = t_2;
	} else if (t <= 1.45e-173) {
		tmp = t_1;
	} else if (t <= 1.46e-29) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((z * (x - y)) / a)
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-8.5d+46)) then
        tmp = t_2
    else if (t <= 1.45d-173) then
        tmp = t_1
    else if (t <= 1.46d-29) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 1.25d+54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * (x - y)) / a);
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.5e+46) {
		tmp = t_2;
	} else if (t <= 1.45e-173) {
		tmp = t_1;
	} else if (t <= 1.46e-29) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z * (x - y)) / a)
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -8.5e+46:
		tmp = t_2
	elif t <= 1.45e-173:
		tmp = t_1
	elif t <= 1.46e-29:
		tmp = (y - x) * (z / (a - t))
	elif t <= 1.25e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z * Float64(x - y)) / a))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -8.5e+46)
		tmp = t_2;
	elseif (t <= 1.45e-173)
		tmp = t_1;
	elseif (t <= 1.46e-29)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 1.25e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z * (x - y)) / a);
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -8.5e+46)
		tmp = t_2;
	elseif (t <= 1.45e-173)
		tmp = t_1;
	elseif (t <= 1.46e-29)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 1.25e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+46], t$95$2, If[LessEqual[t, 1.45e-173], t$95$1, If[LessEqual[t, 1.46e-29], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999996e46 or 1.25000000000000001e54 < t

   1. Initial program 47.9%

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

      1. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in x around 0 50.9%

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

      1. associate-*r/ 69.1%

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

   6. Simplified 69.1%

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

   if -8.4999999999999996e46 < t < 1.4499999999999999e-173 or 1.4600000000000001e-29 < t < 1.25000000000000001e54

   1. Initial program 92.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around 0 76.1%

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

   if 1.4499999999999999e-173 < t < 1.4600000000000001e-29

   1. Initial program 86.9%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around inf 65.4%

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

      1. div-sub 65.4%

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

      2. associate-*r/ 59.4%

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

      3. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

      1. associate-/r/ 65.4%

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

   8. Applied egg-rr 65.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-29}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 12: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+122} \lor \neg \left(t \leq 2.4 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e+122) (not (<= t 2.4e+90)))
   (+ y (/ (- x y) (/ t (- z a))))
   (- x (* (/ (- y x) (- a t)) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+122) || !(t <= 2.4e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - 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 <= (-9d+122)) .or. (.not. (t <= 2.4d+90))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x - (((y - x) / (a - t)) * (t - 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 <= -9e+122) || !(t <= 2.4e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e+122) or not (t <= 2.4e+90):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e+122) || !(t <= 2.4e+90))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e+122) || ~((t <= 2.4e+90)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e+122], N[Not[LessEqual[t, 2.4e+90]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999995e122 or 2.4000000000000001e90 < t

   1. Initial program 39.3%

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

      1. associate-/l* 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. div-sub 74.2%

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

      5. distribute-lft-out-- 74.2%

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

      6. associate-*r/ 74.2%

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

      7. mul-1-neg 74.2%

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

      8. unsub-neg 74.2%

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

      9. distribute-rgt-out-- 74.4%

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

      10. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if -8.99999999999999995e122 < t < 2.4000000000000001e90

   1. Initial program 88.0%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+122} \lor \neg \left(t \leq 2.4 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 13: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e+52)
   y
   (if (<= t -4.9e-107)
     x
     (if (<= t 1.9e-297)
       (* y (/ z a))
       (if (<= t 9e-170)
         x
         (if (<= t 3e-20) (* x (/ z t)) (if (<= t 1.3e+54) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+52) {
		tmp = y;
	} else if (t <= -4.9e-107) {
		tmp = x;
	} else if (t <= 1.9e-297) {
		tmp = y * (z / a);
	} else if (t <= 9e-170) {
		tmp = x;
	} else if (t <= 3e-20) {
		tmp = x * (z / t);
	} else if (t <= 1.3e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.5d+52)) then
        tmp = y
    else if (t <= (-4.9d-107)) then
        tmp = x
    else if (t <= 1.9d-297) then
        tmp = y * (z / a)
    else if (t <= 9d-170) then
        tmp = x
    else if (t <= 3d-20) then
        tmp = x * (z / t)
    else if (t <= 1.3d+54) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+52) {
		tmp = y;
	} else if (t <= -4.9e-107) {
		tmp = x;
	} else if (t <= 1.9e-297) {
		tmp = y * (z / a);
	} else if (t <= 9e-170) {
		tmp = x;
	} else if (t <= 3e-20) {
		tmp = x * (z / t);
	} else if (t <= 1.3e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e+52:
		tmp = y
	elif t <= -4.9e-107:
		tmp = x
	elif t <= 1.9e-297:
		tmp = y * (z / a)
	elif t <= 9e-170:
		tmp = x
	elif t <= 3e-20:
		tmp = x * (z / t)
	elif t <= 1.3e+54:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e+52)
		tmp = y;
	elseif (t <= -4.9e-107)
		tmp = x;
	elseif (t <= 1.9e-297)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 9e-170)
		tmp = x;
	elseif (t <= 3e-20)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.3e+54)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.5e+52)
		tmp = y;
	elseif (t <= -4.9e-107)
		tmp = x;
	elseif (t <= 1.9e-297)
		tmp = y * (z / a);
	elseif (t <= 9e-170)
		tmp = x;
	elseif (t <= 3e-20)
		tmp = x * (z / t);
	elseif (t <= 1.3e+54)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e+52], y, If[LessEqual[t, -4.9e-107], x, If[LessEqual[t, 1.9e-297], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-170], x, If[LessEqual[t, 3e-20], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+54], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.49999999999999995e52 or 1.30000000000000003e54 < t

   1. Initial program 47.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around inf 52.6%

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

   if -7.49999999999999995e52 < t < -4.8999999999999998e-107 or 1.90000000000000002e-297 < t < 9.00000000000000003e-170 or 3.00000000000000029e-20 < t < 1.30000000000000003e54

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 44.9%

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

   if -4.8999999999999998e-107 < t < 1.90000000000000002e-297

   1. Initial program 93.9%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around inf 84.7%

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

      1. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in y around inf 44.2%

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

      1. div-sub 44.2%

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

   9. Simplified 44.2%

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

   10. Taylor expanded in z around inf 41.7%

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

   if 9.00000000000000003e-170 < t < 3.00000000000000029e-20

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-/l* 91.0%

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

      4. associate-/r/ 93.4%

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

      5. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around -inf 50.4%

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

   5. Taylor expanded in x around inf 38.8%

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

      1. div-sub 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in z around inf 37.7%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 42.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 30000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) a))))
   (if (<= z -4.6e+167)
     t_1
     (if (<= z -1.12e-128)
       (- y (* y (/ z t)))
       (if (<= z 3.2e-236)
         (* y (/ (- t) (- a t)))
         (if (<= z 30000000.0) (- x (/ (* t y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -4.6e+167) {
		tmp = t_1;
	} else if (z <= -1.12e-128) {
		tmp = y - (y * (z / t));
	} else if (z <= 3.2e-236) {
		tmp = y * (-t / (a - t));
	} else if (z <= 30000000.0) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / a)
    if (z <= (-4.6d+167)) then
        tmp = t_1
    else if (z <= (-1.12d-128)) then
        tmp = y - (y * (z / t))
    else if (z <= 3.2d-236) then
        tmp = y * (-t / (a - t))
    else if (z <= 30000000.0d0) then
        tmp = x - ((t * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -4.6e+167) {
		tmp = t_1;
	} else if (z <= -1.12e-128) {
		tmp = y - (y * (z / t));
	} else if (z <= 3.2e-236) {
		tmp = y * (-t / (a - t));
	} else if (z <= 30000000.0) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / a)
	tmp = 0
	if z <= -4.6e+167:
		tmp = t_1
	elif z <= -1.12e-128:
		tmp = y - (y * (z / t))
	elif z <= 3.2e-236:
		tmp = y * (-t / (a - t))
	elif z <= 30000000.0:
		tmp = x - ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (z <= -4.6e+167)
		tmp = t_1;
	elseif (z <= -1.12e-128)
		tmp = Float64(y - Float64(y * Float64(z / t)));
	elseif (z <= 3.2e-236)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (z <= 30000000.0)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / a);
	tmp = 0.0;
	if (z <= -4.6e+167)
		tmp = t_1;
	elseif (z <= -1.12e-128)
		tmp = y - (y * (z / t));
	elseif (z <= 3.2e-236)
		tmp = y * (-t / (a - t));
	elseif (z <= 30000000.0)
		tmp = x - ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+167], t$95$1, If[LessEqual[z, -1.12e-128], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-236], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 30000000.0], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.59999999999999976e167 or 3e7 < z

   1. Initial program 76.4%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in a around inf 58.5%

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

      1. associate-/l* 65.4%

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

   6. Simplified 65.4%

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

   7. Taylor expanded in z around inf 57.0%

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

      1. div-sub 57.0%

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

   9. Simplified 57.0%

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

   if -4.59999999999999976e167 < z < -1.12e-128

   1. Initial program 66.1%

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

      1. +-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-/l* 74.8%

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

      4. associate-/r/ 77.6%

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

      5. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around -inf 57.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in y around inf 45.8%

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

      1. associate-*r/ 47.8%

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

   10. Simplified 47.8%

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

   if -1.12e-128 < z < 3.2e-236

   1. Initial program 69.2%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. associate-*r/ 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in z around 0 63.7%

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

      1. neg-mul-1 63.7%

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

      2. distribute-neg-frac 63.7%

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

   9. Simplified 63.7%

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

   if 3.2e-236 < z < 3e7

   1. Initial program 82.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around inf 58.3%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;z \leq 30000000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \end{array} \]

Alternative 15: 56.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x + \frac{t \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -3.3e-155)
     t_1
     (if (<= y -2e-233)
       (+ x (/ (* t x) a))
       (if (<= y 3.4e-148) (/ (- x) (/ (- a t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.3e-155) {
		tmp = t_1;
	} else if (y <= -2e-233) {
		tmp = x + ((t * x) / a);
	} else if (y <= 3.4e-148) {
		tmp = -x / ((a - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-3.3d-155)) then
        tmp = t_1
    else if (y <= (-2d-233)) then
        tmp = x + ((t * x) / a)
    else if (y <= 3.4d-148) then
        tmp = -x / ((a - t) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.3e-155) {
		tmp = t_1;
	} else if (y <= -2e-233) {
		tmp = x + ((t * x) / a);
	} else if (y <= 3.4e-148) {
		tmp = -x / ((a - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -3.3e-155:
		tmp = t_1
	elif y <= -2e-233:
		tmp = x + ((t * x) / a)
	elif y <= 3.4e-148:
		tmp = -x / ((a - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -3.3e-155)
		tmp = t_1;
	elseif (y <= -2e-233)
		tmp = Float64(x + Float64(Float64(t * x) / a));
	elseif (y <= 3.4e-148)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -3.3e-155)
		tmp = t_1;
	elseif (y <= -2e-233)
		tmp = x + ((t * x) / a);
	elseif (y <= 3.4e-148)
		tmp = -x / ((a - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-155], t$95$1, If[LessEqual[y, -2e-233], N[(x + N[(N[(t * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-148], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999986e-155 or 3.4000000000000002e-148 < y

   1. Initial program 73.1%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in x around 0 52.9%

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

      1. associate-*r/ 63.6%

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

   6. Simplified 63.6%

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

   if -3.29999999999999986e-155 < y < -1.99999999999999992e-233

   1. Initial program 84.1%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in a around inf 64.0%

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

      1. associate-/l* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. *-commutative 67.2%

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

   9. Simplified 67.2%

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

   10. Taylor expanded in y around 0 67.2%

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

       1. associate-*r/ 67.2%

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

       2. associate-*r* 67.2%

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

       3. neg-mul-1 67.2%

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

   12. Simplified 67.2%

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

   if -1.99999999999999992e-233 < y < 3.4000000000000002e-148

   1. Initial program 71.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 49.9%

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

      1. div-sub 49.9%

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

      2. associate-*r/ 47.4%

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

      3. associate-/l* 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in y around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. associate-/l* 49.0%

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

      3. distribute-neg-frac 49.0%

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

   9. Simplified 49.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x + \frac{t \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 16: 56.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 7200000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z (- a t)))))
   (if (<= z -5.9e+196)
     t_1
     (if (<= z 1.75e-245)
       (* y (/ (- z t) (- a t)))
       (if (<= z 7200000.0) (- x (/ (* t y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double tmp;
	if (z <= -5.9e+196) {
		tmp = t_1;
	} else if (z <= 1.75e-245) {
		tmp = y * ((z - t) / (a - t));
	} else if (z <= 7200000.0) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / (a - t))
    if (z <= (-5.9d+196)) then
        tmp = t_1
    else if (z <= 1.75d-245) then
        tmp = y * ((z - t) / (a - t))
    else if (z <= 7200000.0d0) then
        tmp = x - ((t * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double tmp;
	if (z <= -5.9e+196) {
		tmp = t_1;
	} else if (z <= 1.75e-245) {
		tmp = y * ((z - t) / (a - t));
	} else if (z <= 7200000.0) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / (a - t))
	tmp = 0
	if z <= -5.9e+196:
		tmp = t_1
	elif z <= 1.75e-245:
		tmp = y * ((z - t) / (a - t))
	elif z <= 7200000.0:
		tmp = x - ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -5.9e+196)
		tmp = t_1;
	elseif (z <= 1.75e-245)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (z <= 7200000.0)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / (a - t));
	tmp = 0.0;
	if (z <= -5.9e+196)
		tmp = t_1;
	elseif (z <= 1.75e-245)
		tmp = y * ((z - t) / (a - t));
	elseif (z <= 7200000.0)
		tmp = x - ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.9e+196], t$95$1, If[LessEqual[z, 1.75e-245], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7200000.0], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8999999999999999e196 or 7.2e6 < z

   1. Initial program 76.6%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 79.4%

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

      1. div-sub 79.5%

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

      2. associate-*r/ 70.1%

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

      3. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

      1. associate-/r/ 80.4%

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

   8. Applied egg-rr 80.4%

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

   if -5.8999999999999999e196 < z < 1.75000000000000008e-245

   1. Initial program 67.6%

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

      1. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 52.0%

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

      1. associate-*r/ 63.3%

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

   6. Simplified 63.3%

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

   if 1.75000000000000008e-245 < z < 7.2e6

   1. Initial program 82.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around inf 58.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+196}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 7200000:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 17: 34.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e-26)
   (* y (/ z (- a t)))
   (if (<= z 1.56e-214) y (if (<= z 9.5e+38) x (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e-26) {
		tmp = y * (z / (a - t));
	} else if (z <= 1.56e-214) {
		tmp = y;
	} else if (z <= 9.5e+38) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-2.1d-26)) then
        tmp = y * (z / (a - t))
    else if (z <= 1.56d-214) then
        tmp = y
    else if (z <= 9.5d+38) then
        tmp = x
    else
        tmp = 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 (z <= -2.1e-26) {
		tmp = y * (z / (a - t));
	} else if (z <= 1.56e-214) {
		tmp = y;
	} else if (z <= 9.5e+38) {
		tmp = x;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e-26:
		tmp = y * (z / (a - t))
	elif z <= 1.56e-214:
		tmp = y
	elif z <= 9.5e+38:
		tmp = x
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e-26)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (z <= 1.56e-214)
		tmp = y;
	elseif (z <= 9.5e+38)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e-26)
		tmp = y * (z / (a - t));
	elseif (z <= 1.56e-214)
		tmp = y;
	elseif (z <= 9.5e+38)
		tmp = x;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e-26], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e-214], y, If[LessEqual[z, 9.5e+38], x, N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000008e-26

   1. Initial program 76.1%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around 0 46.2%

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

      1. associate-*r/ 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in z around inf 45.9%

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

   if -2.10000000000000008e-26 < z < 1.56e-214

   1. Initial program 65.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 49.9%

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

   if 1.56e-214 < z < 9.4999999999999995e38

   1. Initial program 80.3%

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

      1. associate-/l* 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around inf 48.4%

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

   if 9.4999999999999995e38 < z

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. *-commutative 76.2%

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

      3. associate-/l* 80.8%

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

      4. associate-/r/ 87.4%

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

      5. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in t around -inf 46.2%

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

   5. Taylor expanded in x around inf 42.2%

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

      1. div-sub 42.5%

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

   7. Simplified 42.5%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]

Alternative 18: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) a))))
   (if (<= z -9.5e-27)
     t_1
     (if (<= z 1.02e-216) y (if (<= z 50000000.0) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -9.5e-27) {
		tmp = t_1;
	} else if (z <= 1.02e-216) {
		tmp = y;
	} else if (z <= 50000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / a)
    if (z <= (-9.5d-27)) then
        tmp = t_1
    else if (z <= 1.02d-216) then
        tmp = y
    else if (z <= 50000000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -9.5e-27) {
		tmp = t_1;
	} else if (z <= 1.02e-216) {
		tmp = y;
	} else if (z <= 50000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / a)
	tmp = 0
	if z <= -9.5e-27:
		tmp = t_1
	elif z <= 1.02e-216:
		tmp = y
	elif z <= 50000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (z <= -9.5e-27)
		tmp = t_1;
	elseif (z <= 1.02e-216)
		tmp = y;
	elseif (z <= 50000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / a);
	tmp = 0.0;
	if (z <= -9.5e-27)
		tmp = t_1;
	elseif (z <= 1.02e-216)
		tmp = y;
	elseif (z <= 50000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-27], t$95$1, If[LessEqual[z, 1.02e-216], y, If[LessEqual[z, 50000000.0], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000037e-27 or 5e7 < z

   1. Initial program 75.8%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in a around inf 54.5%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in z around inf 48.9%

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

      1. div-sub 49.0%

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

   9. Simplified 49.0%

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

   if -9.50000000000000037e-27 < z < 1.0199999999999999e-216

   1. Initial program 65.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 49.9%

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

   if 1.0199999999999999e-216 < z < 5e7

   1. Initial program 81.8%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in a around inf 51.9%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \end{array} \]

Alternative 19: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+43} \lor \neg \left(t \leq 8.2 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+43) (not (<= t 8.2e+53)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+43) || !(t <= 8.2e+53)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (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 <= (-4.2d+43)) .or. (.not. (t <= 8.2d+53))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (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 <= -4.2e+43) || !(t <= 8.2e+53)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+43) or not (t <= 8.2e+53):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+43) || !(t <= 8.2e+53))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e+43) || ~((t <= 8.2e+53)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+43], N[Not[LessEqual[t, 8.2e+53]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000003e43 or 8.20000000000000037e53 < t

   1. Initial program 47.9%

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

      1. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in x around 0 50.9%

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

      1. associate-*r/ 69.1%

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

   6. Simplified 69.1%

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

   if -4.20000000000000003e43 < t < 8.20000000000000037e53

   1. Initial program 91.3%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around 0 74.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+43} \lor \neg \left(t \leq 8.2 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 20: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+51} \lor \neg \left(t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+51) (not (<= t 5e+52)))
   (+ y (* (/ z t) (- x y)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+51) || !(t <= 5e+52)) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = x + ((y - x) / (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 <= (-2.8d+51)) .or. (.not. (t <= 5d+52))) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = x + ((y - x) / (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 <= -2.8e+51) || !(t <= 5e+52)) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+51) or not (t <= 5e+52):
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+51) || !(t <= 5e+52))
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+51) || ~((t <= 5e+52)))
		tmp = y + ((z / t) * (x - y));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+51], N[Not[LessEqual[t, 5e+52]], $MachinePrecision]], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000005e51 or 5e52 < t

   1. Initial program 48.3%

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

      1. +-commutative 48.3%

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

      2. *-commutative 48.3%

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

      3. associate-/l* 59.0%

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

      4. associate-/r/ 66.1%

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

      5. fma-def 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in t around -inf 71.1%

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

   5. Taylor expanded in a around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

      3. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

      1. associate-/r/ 74.6%

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

   9. Applied egg-rr 74.6%

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

   if -2.80000000000000005e51 < t < 5e52

   1. Initial program 90.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around 0 73.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+51} \lor \neg \left(t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 21: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.4e+52)
   y
   (if (<= t 9e-170)
     x
     (if (<= t 2.9e-20) (* x (/ z t)) (if (<= t 1.95e+55) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.4e+52) {
		tmp = y;
	} else if (t <= 9e-170) {
		tmp = x;
	} else if (t <= 2.9e-20) {
		tmp = x * (z / t);
	} else if (t <= 1.95e+55) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.4d+52)) then
        tmp = y
    else if (t <= 9d-170) then
        tmp = x
    else if (t <= 2.9d-20) then
        tmp = x * (z / t)
    else if (t <= 1.95d+55) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.4e+52) {
		tmp = y;
	} else if (t <= 9e-170) {
		tmp = x;
	} else if (t <= 2.9e-20) {
		tmp = x * (z / t);
	} else if (t <= 1.95e+55) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.4e+52:
		tmp = y
	elif t <= 9e-170:
		tmp = x
	elif t <= 2.9e-20:
		tmp = x * (z / t)
	elif t <= 1.95e+55:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.4e+52)
		tmp = y;
	elseif (t <= 9e-170)
		tmp = x;
	elseif (t <= 2.9e-20)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.95e+55)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.4e+52)
		tmp = y;
	elseif (t <= 9e-170)
		tmp = x;
	elseif (t <= 2.9e-20)
		tmp = x * (z / t);
	elseif (t <= 1.95e+55)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.4e+52], y, If[LessEqual[t, 9e-170], x, If[LessEqual[t, 2.9e-20], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+55], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.3999999999999999e52 or 1.95000000000000014e55 < t

   1. Initial program 47.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around inf 52.6%

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

   if -7.3999999999999999e52 < t < 9.00000000000000003e-170 or 2.9e-20 < t < 1.95000000000000014e55

   1. Initial program 91.7%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 39.8%

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

   if 9.00000000000000003e-170 < t < 2.9e-20

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-/l* 91.0%

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

      4. associate-/r/ 93.4%

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

      5. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around -inf 50.4%

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

   5. Taylor expanded in x around inf 38.8%

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

      1. div-sub 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in z around inf 37.7%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+51) y (if (<= t 2.5e+56) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+51) {
		tmp = y;
	} else if (t <= 2.5e+56) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d+51)) then
        tmp = y
    else if (t <= 2.5d+56) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+51) {
		tmp = y;
	} else if (t <= 2.5e+56) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+51:
		tmp = y
	elif t <= 2.5e+56:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+51)
		tmp = y;
	elseif (t <= 2.5e+56)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+51)
		tmp = y;
	elseif (t <= 2.5e+56)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+51], y, If[LessEqual[t, 2.5e+56], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5e51 or 2.50000000000000012e56 < t

   1. Initial program 47.3%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around inf 52.6%

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

   if -5.5e51 < t < 2.50000000000000012e56

   1. Initial program 90.9%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around inf 35.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 24.7% 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 73.5%

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

   1. associate-/l* 84.0%

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

3. Simplified 84.0%

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

4. Taylor expanded in a around inf 24.4%

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

5. Final simplification 24.4%

   \[\leadsto x \]

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 2023308 
(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))))