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

Percentage Accurate: 68.9% → 87.9%

Time: 23.4s

Alternatives: 20

Speedup: 0.8×

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: 68.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+99}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+99)
   (+ y (* (/ x t) (- z a)))
   (if (<= t 3.6e+170)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+99) {
		tmp = y + ((x / t) * (z - a));
	} else if (t <= 3.6e+170) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+99)) then
        tmp = y + ((x / t) * (z - a))
    else if (t <= 3.6d+170) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+99) {
		tmp = y + ((x / t) * (z - a));
	} else if (t <= 3.6e+170) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+99:
		tmp = y + ((x / t) * (z - a))
	elif t <= 3.6e+170:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+99)
		tmp = Float64(y + Float64(Float64(x / t) * Float64(z - a)));
	elseif (t <= 3.6e+170)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+99)
		tmp = y + ((x / t) * (z - a));
	elseif (t <= 3.6e+170)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+99], N[(y + N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+170], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4500000000000001e99

   1. Initial program 30.9%

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

      1. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in t around inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate-*r/ 69.8%

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

      3. associate-*r/ 69.8%

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

      4. div-sub 69.8%

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

      5. distribute-lft-out-- 69.8%

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

      6. associate-*r/ 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. distribute-rgt-out-- 69.8%

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

      10. associate-/l* 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. associate-/l* 84.2%

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

      3. associate-/r/ 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

   9. Simplified 88.4%

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

   if -1.4500000000000001e99 < t < 3.6e170

   1. Initial program 76.5%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   if 3.6e170 < t

   1. Initial program 25.2%

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

      1. associate-/l* 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r/ 68.2%

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

      3. associate-*r/ 68.2%

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

      4. div-sub 68.2%

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

      5. distribute-lft-out-- 68.2%

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

      6. associate-*r/ 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. distribute-rgt-out-- 68.4%

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

      10. associate-/l* 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+99}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 2: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := \frac{z}{t} \cdot \left(x - y\right)\\ t_3 := y - z \cdot \frac{y}{t}\\ t_4 := \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-278}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a))))
        (t_2 (* (/ z t) (- x y)))
        (t_3 (- y (* z (/ y t))))
        (t_4 (/ y (/ a (- z t)))))
   (if (<= t -1.36e-8)
     t_3
     (if (<= t -2.8e-228)
       t_1
       (if (<= t 2.2e-278)
         t_4
         (if (<= t 6.3e-65)
           t_1
           (if (<= t 1.35e+23)
             t_2
             (if (<= t 1.4e+60)
               t_4
               (if (<= t 1.45e+128) t_2 (if (<= t 1.8e+169) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = (z / t) * (x - y);
	double t_3 = y - (z * (y / t));
	double t_4 = y / (a / (z - t));
	double tmp;
	if (t <= -1.36e-8) {
		tmp = t_3;
	} else if (t <= -2.8e-228) {
		tmp = t_1;
	} else if (t <= 2.2e-278) {
		tmp = t_4;
	} else if (t <= 6.3e-65) {
		tmp = t_1;
	} else if (t <= 1.35e+23) {
		tmp = t_2;
	} else if (t <= 1.4e+60) {
		tmp = t_4;
	} else if (t <= 1.45e+128) {
		tmp = t_2;
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = (z / t) * (x - y)
    t_3 = y - (z * (y / t))
    t_4 = y / (a / (z - t))
    if (t <= (-1.36d-8)) then
        tmp = t_3
    else if (t <= (-2.8d-228)) then
        tmp = t_1
    else if (t <= 2.2d-278) then
        tmp = t_4
    else if (t <= 6.3d-65) then
        tmp = t_1
    else if (t <= 1.35d+23) then
        tmp = t_2
    else if (t <= 1.4d+60) then
        tmp = t_4
    else if (t <= 1.45d+128) then
        tmp = t_2
    else if (t <= 1.8d+169) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = (z / t) * (x - y);
	double t_3 = y - (z * (y / t));
	double t_4 = y / (a / (z - t));
	double tmp;
	if (t <= -1.36e-8) {
		tmp = t_3;
	} else if (t <= -2.8e-228) {
		tmp = t_1;
	} else if (t <= 2.2e-278) {
		tmp = t_4;
	} else if (t <= 6.3e-65) {
		tmp = t_1;
	} else if (t <= 1.35e+23) {
		tmp = t_2;
	} else if (t <= 1.4e+60) {
		tmp = t_4;
	} else if (t <= 1.45e+128) {
		tmp = t_2;
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = (z / t) * (x - y)
	t_3 = y - (z * (y / t))
	t_4 = y / (a / (z - t))
	tmp = 0
	if t <= -1.36e-8:
		tmp = t_3
	elif t <= -2.8e-228:
		tmp = t_1
	elif t <= 2.2e-278:
		tmp = t_4
	elif t <= 6.3e-65:
		tmp = t_1
	elif t <= 1.35e+23:
		tmp = t_2
	elif t <= 1.4e+60:
		tmp = t_4
	elif t <= 1.45e+128:
		tmp = t_2
	elif t <= 1.8e+169:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(Float64(z / t) * Float64(x - y))
	t_3 = Float64(y - Float64(z * Float64(y / t)))
	t_4 = Float64(y / Float64(a / Float64(z - t)))
	tmp = 0.0
	if (t <= -1.36e-8)
		tmp = t_3;
	elseif (t <= -2.8e-228)
		tmp = t_1;
	elseif (t <= 2.2e-278)
		tmp = t_4;
	elseif (t <= 6.3e-65)
		tmp = t_1;
	elseif (t <= 1.35e+23)
		tmp = t_2;
	elseif (t <= 1.4e+60)
		tmp = t_4;
	elseif (t <= 1.45e+128)
		tmp = t_2;
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = (z / t) * (x - y);
	t_3 = y - (z * (y / t));
	t_4 = y / (a / (z - t));
	tmp = 0.0;
	if (t <= -1.36e-8)
		tmp = t_3;
	elseif (t <= -2.8e-228)
		tmp = t_1;
	elseif (t <= 2.2e-278)
		tmp = t_4;
	elseif (t <= 6.3e-65)
		tmp = t_1;
	elseif (t <= 1.35e+23)
		tmp = t_2;
	elseif (t <= 1.4e+60)
		tmp = t_4;
	elseif (t <= 1.45e+128)
		tmp = t_2;
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e-8], t$95$3, If[LessEqual[t, -2.8e-228], t$95$1, If[LessEqual[t, 2.2e-278], t$95$4, If[LessEqual[t, 6.3e-65], t$95$1, If[LessEqual[t, 1.35e+23], t$95$2, If[LessEqual[t, 1.4e+60], t$95$4, If[LessEqual[t, 1.45e+128], t$95$2, If[LessEqual[t, 1.8e+169], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3599999999999999e-8 or 1.80000000000000005e169 < t

   1. Initial program 34.8%

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

      1. associate-/l* 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. associate-*r/ 65.2%

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

      3. associate-*r/ 65.2%

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

      4. div-sub 65.2%

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

      5. distribute-lft-out-- 65.2%

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

      6. associate-*r/ 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. distribute-rgt-out-- 65.4%

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

      10. associate-/l* 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in z around inf 71.3%

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

   8. Taylor expanded in y around inf 51.0%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -1.3599999999999999e-8 < t < -2.8000000000000003e-228 or 2.2000000000000001e-278 < t < 6.2999999999999997e-65 or 1.45e128 < t < 1.80000000000000005e169

   1. Initial program 80.6%

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

      1. +-commutative 80.6%

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

      2. associate-*l/ 88.8%

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

      3. fma-def 88.8%

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

   3. Simplified 88.8%

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

      1. fma-udef 88.8%

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

      2. associate-*l/ 80.6%

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

      3. associate-*r/ 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in t around 0 76.3%

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

   7. Taylor expanded in x around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

   9. Simplified 55.6%

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

   if -2.8000000000000003e-228 < t < 2.2000000000000001e-278 or 1.3499999999999999e23 < t < 1.4e60

   1. Initial program 77.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 65.0%

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

   5. Taylor expanded in a around inf 59.3%

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

      1. associate-/l* 71.8%

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

   7. Simplified 71.8%

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

   if 6.2999999999999997e-65 < t < 1.3499999999999999e23 or 1.4e60 < t < 1.45e128

   1. Initial program 75.6%

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

      1. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in t around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. associate-*r/ 79.3%

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

      3. associate-*r/ 79.3%

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

      4. div-sub 79.3%

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

      5. distribute-lft-out-- 79.3%

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

      6. associate-*r/ 79.3%

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

      7. mul-1-neg 79.3%

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

      8. unsub-neg 79.3%

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

      9. distribute-rgt-out-- 79.3%

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

      10. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in z around -inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. associate-*l/ 59.8%

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

      3. *-commutative 59.8%

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

      4. distribute-rgt-neg-in 59.8%

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

      5. distribute-frac-neg 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-8}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+23}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+128}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - z \cdot \frac{y}{t}\\ t_3 := \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-279}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a))))
        (t_2 (- y (* z (/ y t))))
        (t_3 (/ y (/ a (- z t)))))
   (if (<= t -2.3e-9)
     t_2
     (if (<= t -2.2e-236)
       t_1
       (if (<= t 6.3e-279)
         t_3
         (if (<= t 6e-65)
           t_1
           (if (<= t 9.4e+38) t_3 (if (<= t 1.8e+169) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y - (z * (y / t));
	double t_3 = y / (a / (z - t));
	double tmp;
	if (t <= -2.3e-9) {
		tmp = t_2;
	} else if (t <= -2.2e-236) {
		tmp = t_1;
	} else if (t <= 6.3e-279) {
		tmp = t_3;
	} else if (t <= 6e-65) {
		tmp = t_1;
	} else if (t <= 9.4e+38) {
		tmp = t_3;
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y - (z * (y / t))
    t_3 = y / (a / (z - t))
    if (t <= (-2.3d-9)) then
        tmp = t_2
    else if (t <= (-2.2d-236)) then
        tmp = t_1
    else if (t <= 6.3d-279) then
        tmp = t_3
    else if (t <= 6d-65) then
        tmp = t_1
    else if (t <= 9.4d+38) then
        tmp = t_3
    else if (t <= 1.8d+169) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y - (z * (y / t));
	double t_3 = y / (a / (z - t));
	double tmp;
	if (t <= -2.3e-9) {
		tmp = t_2;
	} else if (t <= -2.2e-236) {
		tmp = t_1;
	} else if (t <= 6.3e-279) {
		tmp = t_3;
	} else if (t <= 6e-65) {
		tmp = t_1;
	} else if (t <= 9.4e+38) {
		tmp = t_3;
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y - (z * (y / t))
	t_3 = y / (a / (z - t))
	tmp = 0
	if t <= -2.3e-9:
		tmp = t_2
	elif t <= -2.2e-236:
		tmp = t_1
	elif t <= 6.3e-279:
		tmp = t_3
	elif t <= 6e-65:
		tmp = t_1
	elif t <= 9.4e+38:
		tmp = t_3
	elif t <= 1.8e+169:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y - Float64(z * Float64(y / t)))
	t_3 = Float64(y / Float64(a / Float64(z - t)))
	tmp = 0.0
	if (t <= -2.3e-9)
		tmp = t_2;
	elseif (t <= -2.2e-236)
		tmp = t_1;
	elseif (t <= 6.3e-279)
		tmp = t_3;
	elseif (t <= 6e-65)
		tmp = t_1;
	elseif (t <= 9.4e+38)
		tmp = t_3;
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y - (z * (y / t));
	t_3 = y / (a / (z - t));
	tmp = 0.0;
	if (t <= -2.3e-9)
		tmp = t_2;
	elseif (t <= -2.2e-236)
		tmp = t_1;
	elseif (t <= 6.3e-279)
		tmp = t_3;
	elseif (t <= 6e-65)
		tmp = t_1;
	elseif (t <= 9.4e+38)
		tmp = t_3;
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-9], t$95$2, If[LessEqual[t, -2.2e-236], t$95$1, If[LessEqual[t, 6.3e-279], t$95$3, If[LessEqual[t, 6e-65], t$95$1, If[LessEqual[t, 9.4e+38], t$95$3, If[LessEqual[t, 1.8e+169], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999999e-9 or 1.80000000000000005e169 < t

   1. Initial program 34.8%

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

      1. associate-/l* 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. associate-*r/ 65.2%

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

      3. associate-*r/ 65.2%

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

      4. div-sub 65.2%

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

      5. distribute-lft-out-- 65.2%

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

      6. associate-*r/ 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. distribute-rgt-out-- 65.4%

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

      10. associate-/l* 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in z around inf 71.3%

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

   8. Taylor expanded in y around inf 51.0%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -2.2999999999999999e-9 < t < -2.19999999999999992e-236 or 6.2999999999999998e-279 < t < 5.99999999999999996e-65 or 9.3999999999999998e38 < t < 1.80000000000000005e169

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-*l/ 89.2%

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

      3. fma-def 89.2%

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

   3. Simplified 89.2%

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

      1. fma-udef 89.2%

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

      2. associate-*l/ 80.3%

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

      3. associate-*r/ 91.6%

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

   5. Applied egg-rr 91.6%

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

   6. Taylor expanded in t around 0 75.7%

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

   7. Taylor expanded in x around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   9. Simplified 54.9%

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

   if -2.19999999999999992e-236 < t < 6.2999999999999998e-279 or 5.99999999999999996e-65 < t < 9.3999999999999998e38

   1. Initial program 76.5%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around 0 60.6%

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

   5. Taylor expanded in a around inf 44.6%

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

      1. associate-/l* 58.3%

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

   7. Simplified 58.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ x t) (- a z)))))
   (if (<= t -3.6e+110)
     t_1
     (if (<= t -8.4e-10)
       (* y (/ (- z t) (- a t)))
       (if (<= t 6.5e-65)
         (+ x (/ (- y x) (/ a z)))
         (if (<= t 2.45e+41)
           (* (- z t) (/ y (- a t)))
           (if (<= t 1.8e+169) (+ x (/ z (/ a (- y x)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -3.6e+110) {
		tmp = t_1;
	} else if (t <= -8.4e-10) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.45e+41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.8e+169) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - ((x / t) * (a - z))
    if (t <= (-3.6d+110)) then
        tmp = t_1
    else if (t <= (-8.4d-10)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.5d-65) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.45d+41) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 1.8d+169) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -3.6e+110) {
		tmp = t_1;
	} else if (t <= -8.4e-10) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.45e+41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.8e+169) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((x / t) * (a - z))
	tmp = 0
	if t <= -3.6e+110:
		tmp = t_1
	elif t <= -8.4e-10:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.5e-65:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.45e+41:
		tmp = (z - t) * (y / (a - t))
	elif t <= 1.8e+169:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(x / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -3.6e+110)
		tmp = t_1;
	elseif (t <= -8.4e-10)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.5e-65)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.45e+41)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 1.8e+169)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((x / t) * (a - z));
	tmp = 0.0;
	if (t <= -3.6e+110)
		tmp = t_1;
	elseif (t <= -8.4e-10)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.5e-65)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.45e+41)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 1.8e+169)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+110], t$95$1, If[LessEqual[t, -8.4e-10], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-65], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+41], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.5999999999999997e110 or 1.80000000000000005e169 < t

   1. Initial program 27.6%

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

      1. associate-/l* 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in t around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. associate-*r/ 68.7%

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

      3. associate-*r/ 68.7%

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

      4. div-sub 68.7%

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

      5. distribute-lft-out-- 68.7%

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

      6. associate-*r/ 68.7%

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

      7. mul-1-neg 68.7%

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

      8. unsub-neg 68.7%

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

      9. distribute-rgt-out-- 68.8%

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

      10. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in y around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. associate-/l* 83.5%

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

      3. associate-/r/ 84.9%

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

      4. distribute-rgt-neg-in 84.9%

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

   9. Simplified 84.9%

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

   if -3.5999999999999997e110 < t < -8.3999999999999999e-10

   1. Initial program 58.9%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in x around 0 49.0%

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

      1. associate-*r/ 68.0%

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

   6. Simplified 68.0%

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

   if -8.3999999999999999e-10 < t < 6.5e-65

   1. Initial program 84.4%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around 0 79.7%

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

   if 6.5e-65 < t < 2.4499999999999999e41

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-*l/ 86.5%

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

      3. fma-def 86.3%

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

   3. Simplified 86.3%

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

      1. fma-udef 86.5%

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

      2. associate-*l/ 77.7%

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

      3. associate-*r/ 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in y around -inf 55.6%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.4%

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

   8. Simplified 64.4%

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

   if 2.4499999999999999e41 < t < 1.80000000000000005e169

   1. Initial program 54.2%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around 0 51.0%

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

      1. associate-/l* 68.8%

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

   6. Simplified 68.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+110}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \end{array} \]

Alternative 5: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-18} \lor \neg \left(t \leq 1.22 \cdot 10^{-67} \lor \neg \left(t \leq 2.6 \cdot 10^{+16}\right) \land t \leq 2.8 \cdot 10^{+169}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e-18)
         (not (or (<= t 1.22e-67) (and (not (<= t 2.6e+16)) (<= t 2.8e+169)))))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-18) || !((t <= 1.22e-67) || (!(t <= 2.6e+16) && (t <= 2.8e+169)))) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d-18)) .or. (.not. (t <= 1.22d-67) .or. (.not. (t <= 2.6d+16)) .and. (t <= 2.8d+169))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-18) || !((t <= 1.22e-67) || (!(t <= 2.6e+16) && (t <= 2.8e+169)))) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e-18) or not ((t <= 1.22e-67) or (not (t <= 2.6e+16) and (t <= 2.8e+169))):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e-18) || !((t <= 1.22e-67) || (!(t <= 2.6e+16) && (t <= 2.8e+169))))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e-18) || ~(((t <= 1.22e-67) || (~((t <= 2.6e+16)) && (t <= 2.8e+169)))))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e-18], N[Not[Or[LessEqual[t, 1.22e-67], And[N[Not[LessEqual[t, 2.6e+16]], $MachinePrecision], LessEqual[t, 2.8e+169]]]], $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[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e-18 or 1.22e-67 < t < 2.6e16 or 2.8000000000000002e169 < t

   1. Initial program 40.6%

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

      1. associate-/l* 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in t around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.7%

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

      5. distribute-lft-out-- 67.7%

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

      6. associate-*r/ 67.7%

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

      7. mul-1-neg 67.7%

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

      8. unsub-neg 67.7%

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

      9. distribute-rgt-out-- 67.8%

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

      10. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   if -2.1e-18 < t < 1.22e-67 or 2.6e16 < t < 2.8000000000000002e169

   1. Initial program 80.5%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around inf 69.6%

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

      1. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-18} \lor \neg \left(t \leq 1.22 \cdot 10^{-67} \lor \neg \left(t \leq 2.6 \cdot 10^{+16}\right) \land t \leq 2.8 \cdot 10^{+169}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 6: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{x - y}{a}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ (- x y) a)))))
   (if (<= a -3.6e+51)
     t_1
     (if (<= a -1.9e-132)
       (+ y (* (/ x t) (- z a)))
       (if (<= a 1.15e-215)
         (+ y (/ (- x y) (/ t z)))
         (if (<= a 2.4e+125) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / a));
	double tmp;
	if (a <= -3.6e+51) {
		tmp = t_1;
	} else if (a <= -1.9e-132) {
		tmp = y + ((x / t) * (z - a));
	} else if (a <= 1.15e-215) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2.4e+125) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((z - t) * ((x - y) / a))
    if (a <= (-3.6d+51)) then
        tmp = t_1
    else if (a <= (-1.9d-132)) then
        tmp = y + ((x / t) * (z - a))
    else if (a <= 1.15d-215) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 2.4d+125) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / a));
	double tmp;
	if (a <= -3.6e+51) {
		tmp = t_1;
	} else if (a <= -1.9e-132) {
		tmp = y + ((x / t) * (z - a));
	} else if (a <= 1.15e-215) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 2.4e+125) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * ((x - y) / a))
	tmp = 0
	if a <= -3.6e+51:
		tmp = t_1
	elif a <= -1.9e-132:
		tmp = y + ((x / t) * (z - a))
	elif a <= 1.15e-215:
		tmp = y + ((x - y) / (t / z))
	elif a <= 2.4e+125:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / a)))
	tmp = 0.0
	if (a <= -3.6e+51)
		tmp = t_1;
	elseif (a <= -1.9e-132)
		tmp = Float64(y + Float64(Float64(x / t) * Float64(z - a)));
	elseif (a <= 1.15e-215)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 2.4e+125)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - t) * ((x - y) / a));
	tmp = 0.0;
	if (a <= -3.6e+51)
		tmp = t_1;
	elseif (a <= -1.9e-132)
		tmp = y + ((x / t) * (z - a));
	elseif (a <= 1.15e-215)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 2.4e+125)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+51], t$95$1, If[LessEqual[a, -1.9e-132], N[(y + N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-215], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+125], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.60000000000000011e51 or 2.4e125 < a

   1. Initial program 61.6%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in a around inf 79.0%

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

   if -3.60000000000000011e51 < a < -1.8999999999999998e-132

   1. Initial program 57.5%

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

      1. associate-/l* 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in t around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. associate-*r/ 77.8%

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

      3. associate-*r/ 77.8%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

      6. associate-*r/ 77.9%

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

      7. mul-1-neg 77.9%

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

      8. unsub-neg 77.9%

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

      9. distribute-rgt-out-- 77.9%

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

      10. associate-/l* 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in y around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. associate-/l* 77.9%

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

      3. associate-/r/ 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

   9. Simplified 77.8%

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

   if -1.8999999999999998e-132 < a < 1.15e-215

   1. Initial program 67.9%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around inf 85.6%

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

      1. associate--l+ 85.6%

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

      2. associate-*r/ 85.6%

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

      3. associate-*r/ 85.6%

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

      4. div-sub 85.6%

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

      5. distribute-lft-out-- 85.6%

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

      6. associate-*r/ 85.6%

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

      7. mul-1-neg 85.6%

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

      8. unsub-neg 85.6%

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

      9. distribute-rgt-out-- 85.6%

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

      10. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in z around inf 90.8%

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

   if 1.15e-215 < a < 2.4e125

   1. Initial program 57.3%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 51.2%

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

      1. associate-*r/ 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+51}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a}\\ \end{array} \]

Alternative 7: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z}{t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_3 := \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+216}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ z t))))
        (t_2 (* x (- 1.0 (/ z a))))
        (t_3 (/ y (/ a (- z t)))))
   (if (<= a -1.25e+53)
     t_2
     (if (<= a 2.4e-149)
       t_1
       (if (<= a 6.8e-82)
         t_3
         (if (<= a 1.1e+65) t_1 (if (<= a 1.22e+216) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double t_2 = x * (1.0 - (z / a));
	double t_3 = y / (a / (z - t));
	double tmp;
	if (a <= -1.25e+53) {
		tmp = t_2;
	} else if (a <= 2.4e-149) {
		tmp = t_1;
	} else if (a <= 6.8e-82) {
		tmp = t_3;
	} else if (a <= 1.1e+65) {
		tmp = t_1;
	} else if (a <= 1.22e+216) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x * (z / t))
    t_2 = x * (1.0d0 - (z / a))
    t_3 = y / (a / (z - t))
    if (a <= (-1.25d+53)) then
        tmp = t_2
    else if (a <= 2.4d-149) then
        tmp = t_1
    else if (a <= 6.8d-82) then
        tmp = t_3
    else if (a <= 1.1d+65) then
        tmp = t_1
    else if (a <= 1.22d+216) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * (z / t));
	double t_2 = x * (1.0 - (z / a));
	double t_3 = y / (a / (z - t));
	double tmp;
	if (a <= -1.25e+53) {
		tmp = t_2;
	} else if (a <= 2.4e-149) {
		tmp = t_1;
	} else if (a <= 6.8e-82) {
		tmp = t_3;
	} else if (a <= 1.1e+65) {
		tmp = t_1;
	} else if (a <= 1.22e+216) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * (z / t))
	t_2 = x * (1.0 - (z / a))
	t_3 = y / (a / (z - t))
	tmp = 0
	if a <= -1.25e+53:
		tmp = t_2
	elif a <= 2.4e-149:
		tmp = t_1
	elif a <= 6.8e-82:
		tmp = t_3
	elif a <= 1.1e+65:
		tmp = t_1
	elif a <= 1.22e+216:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(z / t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_3 = Float64(y / Float64(a / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.25e+53)
		tmp = t_2;
	elseif (a <= 2.4e-149)
		tmp = t_1;
	elseif (a <= 6.8e-82)
		tmp = t_3;
	elseif (a <= 1.1e+65)
		tmp = t_1;
	elseif (a <= 1.22e+216)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x * (z / t));
	t_2 = x * (1.0 - (z / a));
	t_3 = y / (a / (z - t));
	tmp = 0.0;
	if (a <= -1.25e+53)
		tmp = t_2;
	elseif (a <= 2.4e-149)
		tmp = t_1;
	elseif (a <= 6.8e-82)
		tmp = t_3;
	elseif (a <= 1.1e+65)
		tmp = t_1;
	elseif (a <= 1.22e+216)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+53], t$95$2, If[LessEqual[a, 2.4e-149], t$95$1, If[LessEqual[a, 6.8e-82], t$95$3, If[LessEqual[a, 1.1e+65], t$95$1, If[LessEqual[a, 1.22e+216], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2500000000000001e53 or 1.22e216 < a

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate-*l/ 90.3%

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

      3. fma-def 90.3%

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

   3. Simplified 90.3%

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

      1. fma-udef 90.3%

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

      2. associate-*l/ 63.4%

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

      3. associate-*r/ 92.5%

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

   5. Applied egg-rr 92.5%

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

   6. Taylor expanded in t around 0 73.7%

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

   7. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   9. Simplified 53.5%

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

   if -1.2500000000000001e53 < a < 2.4000000000000001e-149 or 6.7999999999999995e-82 < a < 1.0999999999999999e65

   1. Initial program 59.5%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. div-sub 76.6%

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

      5. distribute-lft-out-- 76.6%

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

      6. associate-*r/ 76.6%

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

      7. mul-1-neg 76.6%

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

      8. unsub-neg 76.6%

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

      9. distribute-rgt-out-- 76.6%

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

      10. associate-/l* 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in z around inf 74.7%

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

   8. Taylor expanded in y around 0 61.5%

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

      1. associate-*r/ 61.5%

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

      2. mul-1-neg 61.5%

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

      3. distribute-rgt-neg-out 61.5%

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

      4. associate-*r/ 63.6%

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

   10. Simplified 63.6%

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

   if 2.4000000000000001e-149 < a < 6.7999999999999995e-82 or 1.0999999999999999e65 < a < 1.22e216

   1. Initial program 62.1%

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

      1. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in x around 0 46.6%

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

   5. Taylor expanded in a around inf 39.5%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+65}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 8: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-254}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+43}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -5.2e+63)
     t_1
     (if (<= a 5.2e-254)
       (+ y (* x (/ z t)))
       (if (<= a 2e+43)
         (/ (- y) (/ t (- z t)))
         (if (<= a 1.05e+65)
           (/ (- t) (/ (- a t) y))
           (if (<= a 1.25e+216) (/ y (/ a (- z t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -5.2e+63) {
		tmp = t_1;
	} else if (a <= 5.2e-254) {
		tmp = y + (x * (z / t));
	} else if (a <= 2e+43) {
		tmp = -y / (t / (z - t));
	} else if (a <= 1.05e+65) {
		tmp = -t / ((a - t) / y);
	} else if (a <= 1.25e+216) {
		tmp = y / (a / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-5.2d+63)) then
        tmp = t_1
    else if (a <= 5.2d-254) then
        tmp = y + (x * (z / t))
    else if (a <= 2d+43) then
        tmp = -y / (t / (z - t))
    else if (a <= 1.05d+65) then
        tmp = -t / ((a - t) / y)
    else if (a <= 1.25d+216) then
        tmp = y / (a / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -5.2e+63) {
		tmp = t_1;
	} else if (a <= 5.2e-254) {
		tmp = y + (x * (z / t));
	} else if (a <= 2e+43) {
		tmp = -y / (t / (z - t));
	} else if (a <= 1.05e+65) {
		tmp = -t / ((a - t) / y);
	} else if (a <= 1.25e+216) {
		tmp = y / (a / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -5.2e+63:
		tmp = t_1
	elif a <= 5.2e-254:
		tmp = y + (x * (z / t))
	elif a <= 2e+43:
		tmp = -y / (t / (z - t))
	elif a <= 1.05e+65:
		tmp = -t / ((a - t) / y)
	elif a <= 1.25e+216:
		tmp = y / (a / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -5.2e+63)
		tmp = t_1;
	elseif (a <= 5.2e-254)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (a <= 2e+43)
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	elseif (a <= 1.05e+65)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (a <= 1.25e+216)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -5.2e+63)
		tmp = t_1;
	elseif (a <= 5.2e-254)
		tmp = y + (x * (z / t));
	elseif (a <= 2e+43)
		tmp = -y / (t / (z - t));
	elseif (a <= 1.05e+65)
		tmp = -t / ((a - t) / y);
	elseif (a <= 1.25e+216)
		tmp = y / (a / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+63], t$95$1, If[LessEqual[a, 5.2e-254], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+43], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+65], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+216], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.2000000000000002e63 or 1.24999999999999995e216 < a

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate-*l/ 90.3%

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

      3. fma-def 90.3%

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

   3. Simplified 90.3%

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

      1. fma-udef 90.3%

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

      2. associate-*l/ 63.4%

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

      3. associate-*r/ 92.5%

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

   5. Applied egg-rr 92.5%

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

   6. Taylor expanded in t around 0 73.7%

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

   7. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   9. Simplified 53.5%

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

   if -5.2000000000000002e63 < a < 5.2e-254

   1. Initial program 65.3%

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

      1. associate-/l* 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in t around inf 82.7%

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

      1. associate--l+ 82.7%

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

      2. associate-*r/ 82.7%

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

      3. associate-*r/ 82.7%

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

      4. div-sub 82.8%

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

      5. distribute-lft-out-- 82.8%

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

      6. associate-*r/ 82.8%

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

      7. mul-1-neg 82.8%

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

      8. unsub-neg 82.8%

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

      9. distribute-rgt-out-- 82.8%

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

      10. associate-/l* 86.5%

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

   6. Simplified 86.5%

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

   7. Taylor expanded in z around inf 78.1%

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

   8. Taylor expanded in y around 0 63.3%

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

      1. associate-*r/ 63.3%

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

      2. mul-1-neg 63.3%

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

      3. distribute-rgt-neg-out 63.3%

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

      4. associate-*r/ 65.7%

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

   10. Simplified 65.7%

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

   if 5.2e-254 < a < 2.00000000000000003e43

   1. Initial program 56.7%

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

      1. associate-/l* 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in x around 0 53.7%

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

   5. Taylor expanded in a around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. associate-/l* 59.8%

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

      3. distribute-neg-frac 59.8%

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

   7. Simplified 59.8%

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

   if 2.00000000000000003e43 < a < 1.04999999999999996e65

   1. Initial program 69.0%

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

      1. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in x around 0 48.9%

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

   5. Taylor expanded in z around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-/l* 72.5%

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

      3. distribute-neg-frac 72.5%

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

   7. Simplified 72.5%

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

   if 1.04999999999999996e65 < a < 1.24999999999999995e216

   1. Initial program 52.7%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in x around 0 37.0%

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

   5. Taylor expanded in a around inf 30.3%

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

      1. associate-/l* 44.5%

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

   7. Simplified 44.5%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-254}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+43}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 9: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+40}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))))
   (if (<= t -8.2e-9)
     (* y (/ (- z t) (- a t)))
     (if (<= t 6.5e-65)
       t_1
       (if (<= t 1.65e+40)
         (* (- z t) (/ y (- a t)))
         (if (<= t 1.12e+170) t_1 (+ y (* x (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -8.2e-9) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = t_1;
	} else if (t <= 1.65e+40) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.12e+170) {
		tmp = t_1;
	} else {
		tmp = y + (x * (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) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    if (t <= (-8.2d-9)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.5d-65) then
        tmp = t_1
    else if (t <= 1.65d+40) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 1.12d+170) then
        tmp = t_1
    else
        tmp = y + (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (t <= -8.2e-9) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = t_1;
	} else if (t <= 1.65e+40) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.12e+170) {
		tmp = t_1;
	} else {
		tmp = y + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	tmp = 0
	if t <= -8.2e-9:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.5e-65:
		tmp = t_1
	elif t <= 1.65e+40:
		tmp = (z - t) * (y / (a - t))
	elif t <= 1.12e+170:
		tmp = t_1
	else:
		tmp = y + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (t <= -8.2e-9)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.5e-65)
		tmp = t_1;
	elseif (t <= 1.65e+40)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 1.12e+170)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (t <= -8.2e-9)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.5e-65)
		tmp = t_1;
	elseif (t <= 1.65e+40)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 1.12e+170)
		tmp = t_1;
	else
		tmp = y + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-9], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-65], t$95$1, If[LessEqual[t, 1.65e+40], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+170], t$95$1, N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.2000000000000006e-9

   1. Initial program 40.2%

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

      1. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in x around 0 43.3%

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

      1. associate-*r/ 66.8%

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

   6. Simplified 66.8%

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

   if -8.2000000000000006e-9 < t < 6.5e-65 or 1.6499999999999999e40 < t < 1.1200000000000001e170

   1. Initial program 79.5%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 67.3%

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

      1. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

   if 6.5e-65 < t < 1.6499999999999999e40

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-*l/ 86.5%

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

      3. fma-def 86.3%

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

   3. Simplified 86.3%

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

      1. fma-udef 86.5%

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

      2. associate-*l/ 77.7%

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

      3. associate-*r/ 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in y around -inf 55.6%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.4%

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

   8. Simplified 64.4%

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

   if 1.1200000000000001e170 < t

   1. Initial program 25.2%

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

      1. associate-/l* 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r/ 68.2%

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

      3. associate-*r/ 68.2%

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

      4. div-sub 68.2%

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

      5. distribute-lft-out-- 68.2%

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

      6. associate-*r/ 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. distribute-rgt-out-- 68.4%

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

      10. associate-/l* 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in z around inf 79.2%

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

   8. Taylor expanded in y around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. mul-1-neg 67.9%

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

      3. distribute-rgt-neg-out 67.9%

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

      4. associate-*r/ 72.8%

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

   10. Simplified 72.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+40}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e-9)
   (* y (/ (- z t) (- a t)))
   (if (<= t 6.5e-65)
     (+ x (/ (- y x) (/ a z)))
     (if (<= t 2.7e+41)
       (* (- z t) (/ y (- a t)))
       (if (<= t 1.8e+169) (+ x (/ z (/ a (- y x)))) (+ y (* x (/ z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-9) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.7e+41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.8e+169) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + (x * (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 <= (-8.5d-9)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.5d-65) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.7d+41) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 1.8d+169) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = y + (x * (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 <= -8.5e-9) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-65) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.7e+41) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 1.8e+169) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = y + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e-9:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.5e-65:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.7e+41:
		tmp = (z - t) * (y / (a - t))
	elif t <= 1.8e+169:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = y + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e-9)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.5e-65)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.7e+41)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 1.8e+169)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = Float64(y + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e-9)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.5e-65)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.7e+41)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 1.8e+169)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = y + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e-9], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-65], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+41], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.5e-9

   1. Initial program 40.2%

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

      1. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in x around 0 43.3%

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

      1. associate-*r/ 66.8%

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

   6. Simplified 66.8%

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

   if -8.5e-9 < t < 6.5e-65

   1. Initial program 84.4%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around 0 79.7%

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

   if 6.5e-65 < t < 2.7e41

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-*l/ 86.5%

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

      3. fma-def 86.3%

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

   3. Simplified 86.3%

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

      1. fma-udef 86.5%

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

      2. associate-*l/ 77.7%

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

      3. associate-*r/ 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in y around -inf 55.6%

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

      1. associate-/l* 64.3%

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

      2. associate-/r/ 64.4%

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

   8. Simplified 64.4%

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

   if 2.7e41 < t < 1.80000000000000005e169

   1. Initial program 54.2%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around 0 51.0%

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

      1. associate-/l* 68.8%

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

   6. Simplified 68.8%

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

   if 1.80000000000000005e169 < t

   1. Initial program 25.2%

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

      1. associate-/l* 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r/ 68.2%

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

      3. associate-*r/ 68.2%

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

      4. div-sub 68.2%

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

      5. distribute-lft-out-- 68.2%

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

      6. associate-*r/ 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. distribute-rgt-out-- 68.4%

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

      10. associate-/l* 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in z around inf 79.2%

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

   8. Taylor expanded in y around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. mul-1-neg 67.9%

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

      3. distribute-rgt-neg-out 67.9%

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

      4. associate-*r/ 72.8%

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

   10. Simplified 72.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+104}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+170}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.32e+104)
   (+ y (* (/ x t) (- z a)))
   (if (<= t 4.1e+170)
     (+ x (* (- z t) (/ (- y x) (- a t))))
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+104) {
		tmp = y + ((x / t) * (z - a));
	} else if (t <= 4.1e+170) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.32d+104)) then
        tmp = y + ((x / t) * (z - a))
    else if (t <= 4.1d+170) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+104) {
		tmp = y + ((x / t) * (z - a));
	} else if (t <= 4.1e+170) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.32e+104:
		tmp = y + ((x / t) * (z - a))
	elif t <= 4.1e+170:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.32e+104)
		tmp = Float64(y + Float64(Float64(x / t) * Float64(z - a)));
	elseif (t <= 4.1e+170)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.32e+104)
		tmp = y + ((x / t) * (z - a));
	elseif (t <= 4.1e+170)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.32e+104], N[(y + N[(N[(x / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+170], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.32000000000000003e104

   1. Initial program 30.9%

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

      1. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in t around inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate-*r/ 69.8%

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

      3. associate-*r/ 69.8%

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

      4. div-sub 69.8%

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

      5. distribute-lft-out-- 69.8%

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

      6. associate-*r/ 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. distribute-rgt-out-- 69.8%

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

      10. associate-/l* 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. associate-/l* 84.2%

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

      3. associate-/r/ 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

   9. Simplified 88.4%

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

   if -1.32000000000000003e104 < t < 4.1e170

   1. Initial program 76.5%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   if 4.1e170 < t

   1. Initial program 25.2%

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

      1. associate-/l* 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-*r/ 68.2%

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

      3. associate-*r/ 68.2%

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

      4. div-sub 68.2%

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

      5. distribute-lft-out-- 68.2%

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

      6. associate-*r/ 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. distribute-rgt-out-- 68.4%

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

      10. associate-/l* 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+104}:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+170}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 12: 35.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5000000000000:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.0)
   y
   (if (<= t -1.08e-88)
     x
     (if (<= t 3.8e-277)
       (* y (/ z a))
       (if (<= t 2.8e-63)
         x
         (if (<= t 5000000000000.0)
           (* y (/ (- z) t))
           (if (<= t 1.8e+169) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.0) {
		tmp = y;
	} else if (t <= -1.08e-88) {
		tmp = x;
	} else if (t <= 3.8e-277) {
		tmp = y * (z / a);
	} else if (t <= 2.8e-63) {
		tmp = x;
	} else if (t <= 5000000000000.0) {
		tmp = y * (-z / t);
	} else if (t <= 1.8e+169) {
		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 <= (-2.0d0)) then
        tmp = y
    else if (t <= (-1.08d-88)) then
        tmp = x
    else if (t <= 3.8d-277) then
        tmp = y * (z / a)
    else if (t <= 2.8d-63) then
        tmp = x
    else if (t <= 5000000000000.0d0) then
        tmp = y * (-z / t)
    else if (t <= 1.8d+169) 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 <= -2.0) {
		tmp = y;
	} else if (t <= -1.08e-88) {
		tmp = x;
	} else if (t <= 3.8e-277) {
		tmp = y * (z / a);
	} else if (t <= 2.8e-63) {
		tmp = x;
	} else if (t <= 5000000000000.0) {
		tmp = y * (-z / t);
	} else if (t <= 1.8e+169) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.0:
		tmp = y
	elif t <= -1.08e-88:
		tmp = x
	elif t <= 3.8e-277:
		tmp = y * (z / a)
	elif t <= 2.8e-63:
		tmp = x
	elif t <= 5000000000000.0:
		tmp = y * (-z / t)
	elif t <= 1.8e+169:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.0)
		tmp = y;
	elseif (t <= -1.08e-88)
		tmp = x;
	elseif (t <= 3.8e-277)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.8e-63)
		tmp = x;
	elseif (t <= 5000000000000.0)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.0)
		tmp = y;
	elseif (t <= -1.08e-88)
		tmp = x;
	elseif (t <= 3.8e-277)
		tmp = y * (z / a);
	elseif (t <= 2.8e-63)
		tmp = x;
	elseif (t <= 5000000000000.0)
		tmp = y * (-z / t);
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.0], y, If[LessEqual[t, -1.08e-88], x, If[LessEqual[t, 3.8e-277], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-63], x, If[LessEqual[t, 5000000000000.0], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2 or 1.80000000000000005e169 < t

   1. Initial program 34.2%

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

      1. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in t around inf 54.1%

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

   if -2 < t < -1.07999999999999995e-88 or 3.79999999999999986e-277 < t < 2.8000000000000002e-63 or 5e12 < t < 1.80000000000000005e169

   1. Initial program 77.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 37.5%

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

   if -1.07999999999999995e-88 < t < 3.79999999999999986e-277

   1. Initial program 85.5%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 50.6%

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

   5. Taylor expanded in t around 0 43.6%

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

      1. associate-/l* 57.8%

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

   7. Simplified 57.8%

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

      1. div-inv 59.5%

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

      2. clear-num 59.6%

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

   9. Applied egg-rr 59.6%

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

   if 2.8000000000000002e-63 < t < 5e12

   1. Initial program 67.5%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in x around 0 48.0%

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

   5. Taylor expanded in a around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. associate-/l* 41.6%

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

      3. distribute-neg-frac 41.6%

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

   7. Simplified 41.6%

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

   8. Taylor expanded in t around 0 35.9%

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

      1. mul-1-neg 35.9%

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

      2. associate-*r/ 35.9%

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

      3. *-commutative 35.9%

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

      4. distribute-rgt-neg-in 35.9%

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

   10. Simplified 35.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5000000000000:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 35.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.24:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.24)
   y
   (if (<= t -1.92e-90)
     x
     (if (<= t 1.4e-277)
       (* y (/ z a))
       (if (<= t 5.6e-75)
         x
         (if (<= t 1.2e+44) (* x (/ z t)) (if (<= t 1.8e+169) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.24) {
		tmp = y;
	} else if (t <= -1.92e-90) {
		tmp = x;
	} else if (t <= 1.4e-277) {
		tmp = y * (z / a);
	} else if (t <= 5.6e-75) {
		tmp = x;
	} else if (t <= 1.2e+44) {
		tmp = x * (z / t);
	} else if (t <= 1.8e+169) {
		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 <= (-0.24d0)) then
        tmp = y
    else if (t <= (-1.92d-90)) then
        tmp = x
    else if (t <= 1.4d-277) then
        tmp = y * (z / a)
    else if (t <= 5.6d-75) then
        tmp = x
    else if (t <= 1.2d+44) then
        tmp = x * (z / t)
    else if (t <= 1.8d+169) 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 <= -0.24) {
		tmp = y;
	} else if (t <= -1.92e-90) {
		tmp = x;
	} else if (t <= 1.4e-277) {
		tmp = y * (z / a);
	} else if (t <= 5.6e-75) {
		tmp = x;
	} else if (t <= 1.2e+44) {
		tmp = x * (z / t);
	} else if (t <= 1.8e+169) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -0.24:
		tmp = y
	elif t <= -1.92e-90:
		tmp = x
	elif t <= 1.4e-277:
		tmp = y * (z / a)
	elif t <= 5.6e-75:
		tmp = x
	elif t <= 1.2e+44:
		tmp = x * (z / t)
	elif t <= 1.8e+169:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.24)
		tmp = y;
	elseif (t <= -1.92e-90)
		tmp = x;
	elseif (t <= 1.4e-277)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 5.6e-75)
		tmp = x;
	elseif (t <= 1.2e+44)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -0.24)
		tmp = y;
	elseif (t <= -1.92e-90)
		tmp = x;
	elseif (t <= 1.4e-277)
		tmp = y * (z / a);
	elseif (t <= 5.6e-75)
		tmp = x;
	elseif (t <= 1.2e+44)
		tmp = x * (z / t);
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.24], y, If[LessEqual[t, -1.92e-90], x, If[LessEqual[t, 1.4e-277], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-75], x, If[LessEqual[t, 1.2e+44], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.23999999999999999 or 1.80000000000000005e169 < t

   1. Initial program 34.2%

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

      1. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in t around inf 54.1%

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

   if -0.23999999999999999 < t < -1.92000000000000009e-90 or 1.39999999999999988e-277 < t < 5.59999999999999996e-75 or 1.20000000000000007e44 < t < 1.80000000000000005e169

   1. Initial program 77.4%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in a around inf 40.8%

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

   if -1.92000000000000009e-90 < t < 1.39999999999999988e-277

   1. Initial program 85.5%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 50.6%

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

   5. Taylor expanded in t around 0 43.6%

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

      1. associate-/l* 57.8%

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

   7. Simplified 57.8%

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

      1. div-inv 59.5%

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

      2. clear-num 59.6%

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

   9. Applied egg-rr 59.6%

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

   if 5.59999999999999996e-75 < t < 1.20000000000000007e44

   1. Initial program 72.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r/ 60.9%

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

      3. associate-*r/ 60.9%

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

      4. div-sub 61.1%

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

      5. distribute-lft-out-- 61.1%

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

      6. associate-*r/ 61.1%

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

      7. mul-1-neg 61.1%

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

      8. unsub-neg 61.1%

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

      9. distribute-rgt-out-- 61.1%

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

      10. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in y around 0 31.7%

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

      1. associate-/l* 35.4%

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

      2. associate-/r/ 35.3%

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

   9. Simplified 35.3%

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

   10. Taylor expanded in z around inf 23.0%

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

       1. associate-*r/ 26.7%

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

   12. Simplified 26.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.24:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 45.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -6e-9)
     y
     (if (<= t -2.15e-235)
       t_1
       (if (<= t 1.75e-278) (/ y (/ a z)) (if (<= t 7.2e+170) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6e-9) {
		tmp = y;
	} else if (t <= -2.15e-235) {
		tmp = t_1;
	} else if (t <= 1.75e-278) {
		tmp = y / (a / z);
	} else if (t <= 7.2e+170) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-6d-9)) then
        tmp = y
    else if (t <= (-2.15d-235)) then
        tmp = t_1
    else if (t <= 1.75d-278) then
        tmp = y / (a / z)
    else if (t <= 7.2d+170) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6e-9) {
		tmp = y;
	} else if (t <= -2.15e-235) {
		tmp = t_1;
	} else if (t <= 1.75e-278) {
		tmp = y / (a / z);
	} else if (t <= 7.2e+170) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -6e-9:
		tmp = y
	elif t <= -2.15e-235:
		tmp = t_1
	elif t <= 1.75e-278:
		tmp = y / (a / z)
	elif t <= 7.2e+170:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -6e-9)
		tmp = y;
	elseif (t <= -2.15e-235)
		tmp = t_1;
	elseif (t <= 1.75e-278)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 7.2e+170)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -6e-9)
		tmp = y;
	elseif (t <= -2.15e-235)
		tmp = t_1;
	elseif (t <= 1.75e-278)
		tmp = y / (a / z);
	elseif (t <= 7.2e+170)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-9], y, If[LessEqual[t, -2.15e-235], t$95$1, If[LessEqual[t, 1.75e-278], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+170], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999996e-9 or 7.1999999999999999e170 < t

   1. Initial program 34.8%

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

      1. associate-/l* 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in t around inf 53.6%

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

   if -5.99999999999999996e-9 < t < -2.15000000000000012e-235 or 1.74999999999999985e-278 < t < 7.1999999999999999e170

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*l/ 88.7%

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

      3. fma-def 88.7%

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

   3. Simplified 88.7%

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

      1. fma-udef 88.7%

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

      2. associate-*l/ 79.9%

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

      3. associate-*r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in t around 0 69.0%

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

   7. Taylor expanded in x around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

   9. Simplified 49.2%

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

   if -2.15000000000000012e-235 < t < 1.74999999999999985e-278

   1. Initial program 75.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around 0 66.3%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 48.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (- y (* z (/ y t)))))
   (if (<= t -5e-9)
     t_2
     (if (<= t -1.65e-224)
       t_1
       (if (<= t 6.6e-279) (/ y (/ a z)) (if (<= t 1.8e+169) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y - (z * (y / t));
	double tmp;
	if (t <= -5e-9) {
		tmp = t_2;
	} else if (t <= -1.65e-224) {
		tmp = t_1;
	} else if (t <= 6.6e-279) {
		tmp = y / (a / z);
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y - (z * (y / t))
    if (t <= (-5d-9)) then
        tmp = t_2
    else if (t <= (-1.65d-224)) then
        tmp = t_1
    else if (t <= 6.6d-279) then
        tmp = y / (a / z)
    else if (t <= 1.8d+169) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y - (z * (y / t));
	double tmp;
	if (t <= -5e-9) {
		tmp = t_2;
	} else if (t <= -1.65e-224) {
		tmp = t_1;
	} else if (t <= 6.6e-279) {
		tmp = y / (a / z);
	} else if (t <= 1.8e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y - (z * (y / t))
	tmp = 0
	if t <= -5e-9:
		tmp = t_2
	elif t <= -1.65e-224:
		tmp = t_1
	elif t <= 6.6e-279:
		tmp = y / (a / z)
	elif t <= 1.8e+169:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -5e-9)
		tmp = t_2;
	elseif (t <= -1.65e-224)
		tmp = t_1;
	elseif (t <= 6.6e-279)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -5e-9)
		tmp = t_2;
	elseif (t <= -1.65e-224)
		tmp = t_1;
	elseif (t <= 6.6e-279)
		tmp = y / (a / z);
	elseif (t <= 1.8e+169)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-9], t$95$2, If[LessEqual[t, -1.65e-224], t$95$1, If[LessEqual[t, 6.6e-279], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000001e-9 or 1.80000000000000005e169 < t

   1. Initial program 34.8%

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

      1. associate-/l* 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. associate-*r/ 65.2%

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

      3. associate-*r/ 65.2%

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

      4. div-sub 65.2%

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

      5. distribute-lft-out-- 65.2%

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

      6. associate-*r/ 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. distribute-rgt-out-- 65.4%

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

      10. associate-/l* 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in z around inf 71.3%

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

   8. Taylor expanded in y around inf 51.0%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -5.0000000000000001e-9 < t < -1.6500000000000001e-224 or 6.6e-279 < t < 1.80000000000000005e169

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*l/ 88.7%

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

      3. fma-def 88.7%

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

   3. Simplified 88.7%

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

      1. fma-udef 88.7%

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

      2. associate-*l/ 79.9%

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

      3. associate-*r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in t around 0 69.0%

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

   7. Taylor expanded in x around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

   9. Simplified 49.2%

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

   if -1.6500000000000001e-224 < t < 6.6e-279

   1. Initial program 75.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around 0 66.3%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 16: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))))
   (if (<= a -4e+55)
     t_1
     (if (<= a 1.15e-215)
       (+ y (/ (- x y) (/ t z)))
       (if (<= a 3.7e+104) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -4e+55) {
		tmp = t_1;
	} else if (a <= 1.15e-215) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 3.7e+104) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    if (a <= (-4d+55)) then
        tmp = t_1
    else if (a <= 1.15d-215) then
        tmp = y + ((x - y) / (t / z))
    else if (a <= 3.7d+104) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -4e+55) {
		tmp = t_1;
	} else if (a <= 1.15e-215) {
		tmp = y + ((x - y) / (t / z));
	} else if (a <= 3.7e+104) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	tmp = 0
	if a <= -4e+55:
		tmp = t_1
	elif a <= 1.15e-215:
		tmp = y + ((x - y) / (t / z))
	elif a <= 3.7e+104:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -4e+55)
		tmp = t_1;
	elseif (a <= 1.15e-215)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	elseif (a <= 3.7e+104)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (a <= -4e+55)
		tmp = t_1;
	elseif (a <= 1.15e-215)
		tmp = y + ((x - y) / (t / z));
	elseif (a <= 3.7e+104)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+55], t$95$1, If[LessEqual[a, 1.15e-215], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+104], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000004e55 or 3.6999999999999998e104 < a

   1. Initial program 61.6%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in t around 0 55.4%

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

      1. associate-/l* 71.1%

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

   6. Simplified 71.1%

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

   if -4.00000000000000004e55 < a < 1.15e-215

   1. Initial program 63.9%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. associate-*r/ 82.6%

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

      3. associate-*r/ 82.6%

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

      4. div-sub 82.7%

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

      5. distribute-lft-out-- 82.7%

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

      6. associate-*r/ 82.7%

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

      7. mul-1-neg 82.7%

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

      8. unsub-neg 82.7%

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

      9. distribute-rgt-out-- 82.7%

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

      10. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in z around inf 80.6%

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

   if 1.15e-215 < a < 3.6999999999999998e104

   1. Initial program 57.0%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   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/ 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 17: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+123} \lor \neg \left(x \leq 2.4 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.8e+123) (not (<= x 2.4e+122)))
   (* x (- 1.0 (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.8e+123) || !(x <= 2.4e+122)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7.8d+123)) .or. (.not. (x <= 2.4d+122))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.8e+123) || !(x <= 2.4e+122)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.8e+123) or not (x <= 2.4e+122):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.8e+123) || !(x <= 2.4e+122))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7.8e+123) || ~((x <= 2.4e+122)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.8e+123], N[Not[LessEqual[x, 2.4e+122]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.79999999999999986e123 or 2.4000000000000002e122 < x

   1. Initial program 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-*l/ 71.9%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

      1. fma-udef 71.9%

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

      2. associate-*l/ 46.1%

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

      3. associate-*r/ 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in t around 0 54.1%

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

   7. Taylor expanded in x around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

   9. Simplified 51.0%

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

   if -7.79999999999999986e123 < x < 2.4000000000000002e122

   1. Initial program 69.0%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around 0 54.4%

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

      1. associate-*r/ 69.9%

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

   6. Simplified 69.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+123} \lor \neg \left(x \leq 2.4 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 18: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7)
   y
   (if (<= t 6.8e-75)
     x
     (if (<= t 1.8e+45) (* x (/ z t)) (if (<= t 1.8e+169) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7) {
		tmp = y;
	} else if (t <= 6.8e-75) {
		tmp = x;
	} else if (t <= 1.8e+45) {
		tmp = x * (z / t);
	} else if (t <= 1.8e+169) {
		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 <= (-2.7d0)) then
        tmp = y
    else if (t <= 6.8d-75) then
        tmp = x
    else if (t <= 1.8d+45) then
        tmp = x * (z / t)
    else if (t <= 1.8d+169) 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 <= -2.7) {
		tmp = y;
	} else if (t <= 6.8e-75) {
		tmp = x;
	} else if (t <= 1.8e+45) {
		tmp = x * (z / t);
	} else if (t <= 1.8e+169) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7:
		tmp = y
	elif t <= 6.8e-75:
		tmp = x
	elif t <= 1.8e+45:
		tmp = x * (z / t)
	elif t <= 1.8e+169:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7)
		tmp = y;
	elseif (t <= 6.8e-75)
		tmp = x;
	elseif (t <= 1.8e+45)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7)
		tmp = y;
	elseif (t <= 6.8e-75)
		tmp = x;
	elseif (t <= 1.8e+45)
		tmp = x * (z / t);
	elseif (t <= 1.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7], y, If[LessEqual[t, 6.8e-75], x, If[LessEqual[t, 1.8e+45], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+169], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000002 or 1.80000000000000005e169 < t

   1. Initial program 34.2%

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

      1. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in t around inf 54.1%

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

   if -2.7000000000000002 < t < 6.8000000000000003e-75 or 1.8e45 < t < 1.80000000000000005e169

   1. Initial program 80.7%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 36.2%

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

   if 6.8000000000000003e-75 < t < 1.8e45

   1. Initial program 72.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r/ 60.9%

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

      3. associate-*r/ 60.9%

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

      4. div-sub 61.1%

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

      5. distribute-lft-out-- 61.1%

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

      6. associate-*r/ 61.1%

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

      7. mul-1-neg 61.1%

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

      8. unsub-neg 61.1%

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

      9. distribute-rgt-out-- 61.1%

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

      10. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in y around 0 31.7%

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

      1. associate-/l* 35.4%

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

      2. associate-/r/ 35.3%

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

   9. Simplified 35.3%

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

   10. Taylor expanded in z around inf 23.0%

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

       1. associate-*r/ 26.7%

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

   12. Simplified 26.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19: 37.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.62:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.62) y (if (<= t 2.8e+169) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.62) {
		tmp = y;
	} else if (t <= 2.8e+169) {
		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 <= (-0.62d0)) then
        tmp = y
    else if (t <= 2.8d+169) 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 <= -0.62) {
		tmp = y;
	} else if (t <= 2.8e+169) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -0.62:
		tmp = y
	elif t <= 2.8e+169:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.62)
		tmp = y;
	elseif (t <= 2.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -0.62)
		tmp = y;
	elseif (t <= 2.8e+169)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.62], y, If[LessEqual[t, 2.8e+169], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -0.619999999999999996 or 2.8000000000000002e169 < t

   1. Initial program 34.2%

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

      1. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in t around inf 54.1%

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

   if -0.619999999999999996 < t < 2.8000000000000002e169

   1. Initial program 79.4%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in a around inf 31.5%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.62:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20: 26.0% 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 61.2%

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

   1. associate-/l* 80.4%

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

3. Simplified 80.4%

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

4. Taylor expanded in a around inf 22.9%

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

5. Final simplification 22.9%

   \[\leadsto x \]

Developer target: 87.3% 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 2023310 
(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))))