Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.5% → 91.5%

Time: 17.0s

Alternatives: 13

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-50} \lor \neg \left(a \leq 7.2 \cdot 10^{-191}\right):\\ \;\;\;\;y \cdot \left(\frac{t - z}{a - t} + 1\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e-50) (not (<= a 7.2e-191)))
   (+ (* y (+ (/ (- t z) (- a t)) 1.0)) x)
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-50) || !(a <= 7.2e-191)) {
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	} else {
		tmp = x - (z * (y / (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 ((a <= (-2.9d-50)) .or. (.not. (a <= 7.2d-191))) then
        tmp = (y * (((t - z) / (a - t)) + 1.0d0)) + x
    else
        tmp = x - (z * (y / (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 ((a <= -2.9e-50) || !(a <= 7.2e-191)) {
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e-50) or not (a <= 7.2e-191):
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e-50) || !(a <= 7.2e-191))
		tmp = Float64(Float64(y * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0)) + x);
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e-50) || ~((a <= 7.2e-191)))
		tmp = (y * (((t - z) / (a - t)) + 1.0)) + x;
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.9e-50], N[Not[LessEqual[a, 7.2e-191]], $MachinePrecision]], N[(N[(y * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.90000000000000008e-50 or 7.20000000000000038e-191 < a

   1. Initial program 81.9%

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

      1. sub-neg 81.9%

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

      2. distribute-frac-neg 81.9%

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

      3. distribute-rgt-neg-out 81.9%

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

      4. associate-/l* 91.0%

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

      5. div-sub 91.0%

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

      6. associate-+r- 91.0%

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

      7. associate-/r/ 91.5%

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

      8. distribute-rgt-neg-out 91.5%

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

      9. associate-/r/ 91.0%

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

      10. distribute-frac-neg 91.0%

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

      11. associate-+l+ 91.0%

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

      12. associate-+r- 91.5%

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

      13. distribute-frac-neg 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. associate--l+ 92.9%

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

      3. div-sub 92.8%

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

   6. Simplified 92.8%

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

   if -2.90000000000000008e-50 < a < 7.20000000000000038e-191

   1. Initial program 72.3%

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

      1. sub-neg 72.3%

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

      2. distribute-frac-neg 72.3%

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

      3. distribute-rgt-neg-out 72.3%

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

      4. associate-/l* 80.2%

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

      5. div-sub 78.8%

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

      6. associate-+r- 78.8%

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

      7. associate-/r/ 80.2%

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

      8. distribute-rgt-neg-out 80.2%

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

      9. associate-/r/ 78.8%

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

      10. distribute-frac-neg 78.8%

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

      11. associate-+l+ 78.8%

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

      12. associate-+r- 86.4%

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

      13. distribute-frac-neg 86.4%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around 0 90.6%

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

      1. +-commutative 90.6%

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

      2. associate--l+ 82.5%

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

      3. div-sub 82.5%

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

   6. Simplified 82.5%

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

      1. add-cube-cbrt 82.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 82.3%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 82.3%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 95.9%

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

       1. mul-1-neg 95.9%

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

       2. associate-/l* 90.7%

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

       3. distribute-frac-neg 90.7%

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

       4. associate-/r/ 97.4%

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

   11. Simplified 97.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-50} \lor \neg \left(a \leq 7.2 \cdot 10^{-191}\right):\\ \;\;\;\;y \cdot \left(\frac{t - z}{a - t} + 1\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-296}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 10^{-44}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (- (/ y (/ a z)) y))))
   (if (<= a -3.8e-16)
     t_1
     (if (<= a -4.7e-296)
       (- x (/ (* y z) (- a t)))
       (if (<= a 1e-44) (- x (/ y (/ t (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a / z)) - y);
	double tmp;
	if (a <= -3.8e-16) {
		tmp = t_1;
	} else if (a <= -4.7e-296) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 1e-44) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / (a / z)) - y)
    if (a <= (-3.8d-16)) then
        tmp = t_1
    else if (a <= (-4.7d-296)) then
        tmp = x - ((y * z) / (a - t))
    else if (a <= 1d-44) then
        tmp = x - (y / (t / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a / z)) - y);
	double tmp;
	if (a <= -3.8e-16) {
		tmp = t_1;
	} else if (a <= -4.7e-296) {
		tmp = x - ((y * z) / (a - t));
	} else if (a <= 1e-44) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a / z)) - y)
	tmp = 0
	if a <= -3.8e-16:
		tmp = t_1
	elif a <= -4.7e-296:
		tmp = x - ((y * z) / (a - t))
	elif a <= 1e-44:
		tmp = x - (y / (t / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a / z)) - y))
	tmp = 0.0
	if (a <= -3.8e-16)
		tmp = t_1;
	elseif (a <= -4.7e-296)
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	elseif (a <= 1e-44)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a / z)) - y);
	tmp = 0.0;
	if (a <= -3.8e-16)
		tmp = t_1;
	elseif (a <= -4.7e-296)
		tmp = x - ((y * z) / (a - t));
	elseif (a <= 1e-44)
		tmp = x - (y / (t / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-16], t$95$1, If[LessEqual[a, -4.7e-296], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-44], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.80000000000000012e-16 or 9.99999999999999953e-45 < a

   1. Initial program 84.2%

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

      1. sub-neg 84.2%

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

      2. distribute-frac-neg 84.2%

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

      3. distribute-rgt-neg-out 84.2%

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

      4. associate-/l* 93.2%

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

      5. div-sub 93.2%

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

      6. associate-+r- 93.2%

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

      7. associate-/r/ 93.7%

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

      8. distribute-rgt-neg-out 93.7%

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

      9. associate-/r/ 93.2%

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

      10. distribute-frac-neg 93.2%

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

      11. associate-+l+ 93.2%

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

      12. associate-+r- 93.9%

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

      13. distribute-frac-neg 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   if -3.80000000000000012e-16 < a < -4.7e-296

   1. Initial program 67.3%

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

      1. sub-neg 67.3%

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

      2. distribute-frac-neg 67.3%

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

      3. distribute-rgt-neg-out 67.3%

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

      4. associate-/l* 74.6%

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

      5. div-sub 72.5%

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

      6. associate-+r- 72.5%

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

      7. associate-/r/ 74.8%

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

      8. distribute-rgt-neg-out 74.8%

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

      9. associate-/r/ 72.5%

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

      10. distribute-frac-neg 72.5%

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

      11. associate-+l+ 72.5%

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

      12. associate-+r- 80.0%

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

      13. distribute-frac-neg 80.0%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in z around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. associate-*r* 92.0%

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

      3. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

   if -4.7e-296 < a < 9.99999999999999953e-45

   1. Initial program 77.1%

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

      1. sub-neg 77.1%

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

      2. distribute-frac-neg 77.1%

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

      3. distribute-rgt-neg-out 77.1%

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

      4. associate-/l* 86.3%

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

      5. div-sub 86.3%

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

      6. associate-+r- 86.3%

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

      7. associate-/r/ 86.3%

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

      8. distribute-rgt-neg-out 86.3%

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

      9. associate-/r/ 86.3%

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

      10. distribute-frac-neg 86.3%

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

      11. associate-+l+ 86.3%

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

      12. associate-+r- 89.1%

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

      13. distribute-frac-neg 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. associate--l+ 91.8%

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

      3. div-sub 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

      3. associate-/l* 94.7%

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

      4. mul-1-neg 94.7%

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

      5. unsub-neg 94.7%

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

   9. Simplified 94.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-296}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 10^{-44}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \end{array} \]

Alternative 3: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-17} \lor \neg \left(a \leq 8.2 \cdot 10^{-191}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-17) (not (<= a 8.2e-191)))
   (- (+ y x) (* y (/ z (- a t))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-17) || !(a <= 8.2e-191)) {
		tmp = (y + x) - (y * (z / (a - t)));
	} else {
		tmp = x - (z * (y / (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 ((a <= (-1.8d-17)) .or. (.not. (a <= 8.2d-191))) then
        tmp = (y + x) - (y * (z / (a - t)))
    else
        tmp = x - (z * (y / (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 ((a <= -1.8e-17) || !(a <= 8.2e-191)) {
		tmp = (y + x) - (y * (z / (a - t)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-17) or not (a <= 8.2e-191):
		tmp = (y + x) - (y * (z / (a - t)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-17) || !(a <= 8.2e-191))
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-17) || ~((a <= 8.2e-191)))
		tmp = (y + x) - (y * (z / (a - t)));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-17], N[Not[LessEqual[a, 8.2e-191]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999997e-17 or 8.2000000000000004e-191 < a

   1. Initial program 81.9%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around inf 89.3%

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

   if -1.79999999999999997e-17 < a < 8.2000000000000004e-191

   1. Initial program 73.4%

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

      1. sub-neg 73.4%

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

      2. distribute-frac-neg 73.4%

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

      3. distribute-rgt-neg-out 73.4%

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

      4. associate-/l* 80.3%

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

      5. div-sub 79.0%

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

      6. associate-+r- 79.0%

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

      7. associate-/r/ 80.3%

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

      8. distribute-rgt-neg-out 80.3%

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

      9. associate-/r/ 79.0%

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

      10. distribute-frac-neg 79.0%

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

      11. associate-+l+ 79.0%

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

      12. associate-+r- 85.7%

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

      13. distribute-frac-neg 85.7%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in y around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. associate--l+ 82.3%

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

      3. div-sub 82.3%

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

   6. Simplified 82.3%

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

      1. add-cube-cbrt 82.1%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 82.1%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 82.1%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 94.1%

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

       1. mul-1-neg 94.1%

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

       2. associate-/l* 89.3%

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

       3. distribute-frac-neg 89.3%

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

       4. associate-/r/ 95.3%

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

   11. Simplified 95.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-17} \lor \neg \left(a \leq 8.2 \cdot 10^{-191}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e-16)
   (- x (- (/ y (/ a z)) y))
   (if (<= a 1.15e+22)
     (- x (* z (/ y (- a t))))
     (+ x (* y (+ (/ t (- a t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-16) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.15e+22) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d-16)) then
        tmp = x - ((y / (a / z)) - y)
    else if (a <= 1.15d+22) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = x + (y * ((t / (a - t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-16) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.15e+22) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e-16:
		tmp = x - ((y / (a / z)) - y)
	elif a <= 1.15e+22:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = x + (y * ((t / (a - t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e-16)
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	elseif (a <= 1.15e+22)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e-16)
		tmp = x - ((y / (a / z)) - y);
	elseif (a <= 1.15e+22)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = x + (y * ((t / (a - t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e-16], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+22], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6000000000000003e-16

   1. Initial program 85.8%

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

      1. sub-neg 85.8%

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

      2. distribute-frac-neg 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. associate-/l* 95.3%

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

      5. div-sub 95.3%

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

      6. associate-+r- 95.3%

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

      7. associate-/r/ 96.0%

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

      8. distribute-rgt-neg-out 96.0%

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

      9. associate-/r/ 95.3%

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

      10. distribute-frac-neg 95.3%

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

      11. associate-+l+ 95.4%

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

      12. associate-+r- 96.7%

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

      13. distribute-frac-neg 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 85.4%

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

      1. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   if -5.6000000000000003e-16 < a < 1.1500000000000001e22

   1. Initial program 74.2%

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

      1. sub-neg 74.2%

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

      2. distribute-frac-neg 74.2%

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

      3. distribute-rgt-neg-out 74.2%

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

      4. associate-/l* 81.7%

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

      5. div-sub 80.9%

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

      6. associate-+r- 80.9%

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

      7. associate-/r/ 81.8%

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

      8. distribute-rgt-neg-out 81.8%

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

      9. associate-/r/ 80.9%

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

      10. distribute-frac-neg 80.9%

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

      11. associate-+l+ 80.9%

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

      12. associate-+r- 85.2%

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

      13. distribute-frac-neg 85.2%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. associate--l+ 83.6%

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

      3. div-sub 83.6%

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

   6. Simplified 83.6%

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

      1. add-cube-cbrt 83.4%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 83.4%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 83.4%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 87.4%

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

       1. mul-1-neg 87.4%

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

       2. associate-/l* 86.6%

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

       3. distribute-frac-neg 86.6%

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

       4. associate-/r/ 89.3%

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

   11. Simplified 89.3%

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

   if 1.1500000000000001e22 < a

   1. Initial program 81.8%

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

      1. sub-neg 81.8%

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

      2. distribute-frac-neg 81.8%

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

      3. distribute-rgt-neg-out 81.8%

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

      4. associate-/l* 92.2%

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

      5. div-sub 92.2%

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

      6. associate-+r- 92.2%

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

      7. associate-/r/ 92.6%

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

      8. distribute-rgt-neg-out 92.6%

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

      9. associate-/r/ 92.2%

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

      10. distribute-frac-neg 92.2%

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

      11. associate-+l+ 92.2%

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

      12. associate-+r- 92.3%

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

      13. distribute-frac-neg 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 95.1%

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

      1. +-commutative 95.1%

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

      2. associate--l+ 94.3%

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

      3. div-sub 94.3%

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

   6. Simplified 94.3%

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

   7. Taylor expanded in z around 0 88.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \]

Alternative 5: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-57} \lor \neg \left(a \leq 5.2 \cdot 10^{-51}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e-57) (not (<= a 5.2e-51)))
   (- x (- (/ y (/ a z)) y))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-57) || !(a <= 5.2e-51)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d-57)) .or. (.not. (a <= 5.2d-51))) then
        tmp = x - ((y / (a / z)) - y)
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-57) || !(a <= 5.2e-51)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e-57) or not (a <= 5.2e-51):
		tmp = x - ((y / (a / z)) - y)
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e-57) || !(a <= 5.2e-51))
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e-57) || ~((a <= 5.2e-51)))
		tmp = x - ((y / (a / z)) - y);
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e-57], N[Not[LessEqual[a, 5.2e-51]], $MachinePrecision]], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.00000000000000001e-57 or 5.2e-51 < a

   1. Initial program 83.5%

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

      1. sub-neg 83.5%

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

      2. distribute-frac-neg 83.5%

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

      3. distribute-rgt-neg-out 83.5%

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

      4. associate-/l* 91.9%

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

      5. div-sub 91.9%

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

      6. associate-+r- 91.9%

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

      7. associate-/r/ 92.4%

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

      8. distribute-rgt-neg-out 92.4%

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

      9. associate-/r/ 91.9%

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

      10. distribute-frac-neg 91.9%

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

      11. associate-+l+ 91.9%

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

      12. associate-+r- 92.5%

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

      13. distribute-frac-neg 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 81.8%

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

      1. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

   if -6.00000000000000001e-57 < a < 5.2e-51

   1. Initial program 72.5%

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

      1. sub-neg 72.5%

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

      2. distribute-frac-neg 72.5%

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

      3. distribute-rgt-neg-out 72.5%

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

      4. associate-/l* 82.0%

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

      5. div-sub 81.0%

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

      6. associate-+r- 81.0%

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

      7. associate-/r/ 81.9%

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

      8. distribute-rgt-neg-out 81.9%

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

      9. associate-/r/ 81.0%

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

      10. distribute-frac-neg 81.0%

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

      11. associate-+l+ 81.0%

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

      12. associate-+r- 86.3%

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

      13. distribute-frac-neg 86.3%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. associate--l+ 84.3%

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

      3. div-sub 84.3%

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

   6. Simplified 84.3%

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

      1. add-cube-cbrt 84.1%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 84.1%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 84.1%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 91.0%

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

       1. mul-1-neg 91.0%

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

       2. associate-/l* 90.2%

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

       3. distribute-frac-neg 90.2%

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

       4. associate-/r/ 93.3%

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

   11. Simplified 93.3%

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

   12. Taylor expanded in a around 0 90.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-57} \lor \neg \left(a \leq 5.2 \cdot 10^{-51}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-51} \lor \neg \left(a \leq 2.05 \cdot 10^{-46}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.3e-51) (not (<= a 2.05e-46)))
   (- x (- (/ y (/ a z)) y))
   (- x (/ y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.3e-51) || !(a <= 2.05e-46)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.3d-51)) .or. (.not. (a <= 2.05d-46))) then
        tmp = x - ((y / (a / z)) - y)
    else
        tmp = x - (y / (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.3e-51) || !(a <= 2.05e-46)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.3e-51) or not (a <= 2.05e-46):
		tmp = x - ((y / (a / z)) - y)
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.3e-51) || !(a <= 2.05e-46))
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.3e-51) || ~((a <= 2.05e-46)))
		tmp = x - ((y / (a / z)) - y);
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.3e-51], N[Not[LessEqual[a, 2.05e-46]], $MachinePrecision]], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2999999999999997e-51 or 2.05e-46 < a

   1. Initial program 84.1%

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

      1. sub-neg 84.1%

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

      2. distribute-frac-neg 84.1%

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

      3. distribute-rgt-neg-out 84.1%

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

      4. associate-/l* 92.4%

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

      5. div-sub 92.4%

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

      6. associate-+r- 92.4%

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

      7. associate-/r/ 93.0%

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

      8. distribute-rgt-neg-out 93.0%

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

      9. associate-/r/ 92.4%

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

      10. distribute-frac-neg 92.4%

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

      11. associate-+l+ 92.4%

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

      12. associate-+r- 93.1%

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

      13. distribute-frac-neg 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around 0 82.3%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

   if -4.2999999999999997e-51 < a < 2.05e-46

   1. Initial program 71.8%

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

      1. sub-neg 71.8%

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

      2. distribute-frac-neg 71.8%

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

      3. distribute-rgt-neg-out 71.8%

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

      4. associate-/l* 81.2%

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

      5. div-sub 80.2%

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

      6. associate-+r- 80.2%

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

      7. associate-/r/ 81.2%

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

      8. distribute-rgt-neg-out 81.2%

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

      9. associate-/r/ 80.2%

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

      10. distribute-frac-neg 80.2%

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

      11. associate-+l+ 80.2%

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

      12. associate-+r- 85.5%

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

      13. distribute-frac-neg 85.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. associate--l+ 83.5%

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

      3. div-sub 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in t around inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. unsub-neg 90.8%

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

      3. associate-/l* 90.0%

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

      4. mul-1-neg 90.0%

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

      5. unsub-neg 90.0%

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

   9. Simplified 90.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-51} \lor \neg \left(a \leq 2.05 \cdot 10^{-46}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 7: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-18} \lor \neg \left(a \leq 1.85 \cdot 10^{+19}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.8e-18) (not (<= a 1.85e+19)))
   (- x (- (/ y (/ a z)) y))
   (- x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.8e-18) || !(a <= 1.85e+19)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x - (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.8d-18)) .or. (.not. (a <= 1.85d+19))) then
        tmp = x - ((y / (a / z)) - y)
    else
        tmp = x - (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.8e-18) || !(a <= 1.85e+19)) {
		tmp = x - ((y / (a / z)) - y);
	} else {
		tmp = x - (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.8e-18) or not (a <= 1.85e+19):
		tmp = x - ((y / (a / z)) - y)
	else:
		tmp = x - (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.8e-18) || !(a <= 1.85e+19))
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.8e-18) || ~((a <= 1.85e+19)))
		tmp = x - ((y / (a / z)) - y);
	else
		tmp = x - (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.8e-18], N[Not[LessEqual[a, 1.85e+19]], $MachinePrecision]], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.8000000000000002e-18 or 1.85e19 < a

   1. Initial program 84.3%

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

      1. sub-neg 84.3%

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

      2. distribute-frac-neg 84.3%

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

      3. distribute-rgt-neg-out 84.3%

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

      4. associate-/l* 94.0%

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

      5. div-sub 94.0%

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

      6. associate-+r- 94.0%

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

      7. associate-/r/ 94.6%

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

      8. distribute-rgt-neg-out 94.6%

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

      9. associate-/r/ 94.0%

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

      10. distribute-frac-neg 94.0%

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

      11. associate-+l+ 94.1%

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

      12. associate-+r- 94.8%

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

      13. distribute-frac-neg 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 84.5%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

   if -9.8000000000000002e-18 < a < 1.85e19

   1. Initial program 73.8%

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

      1. sub-neg 73.8%

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

      2. distribute-frac-neg 73.8%

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

      3. distribute-rgt-neg-out 73.8%

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

      4. associate-/l* 81.5%

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

      5. div-sub 80.6%

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

      6. associate-+r- 80.6%

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

      7. associate-/r/ 81.5%

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

      8. distribute-rgt-neg-out 81.5%

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

      9. associate-/r/ 80.6%

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

      10. distribute-frac-neg 80.6%

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

      11. associate-+l+ 80.6%

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

      12. associate-+r- 85.0%

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

      13. distribute-frac-neg 85.0%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-*r/ 87.3%

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

      2. associate-*r* 87.3%

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

      3. neg-mul-1 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

      3. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-18} \lor \neg \left(a \leq 1.85 \cdot 10^{+19}\right):\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 8: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-18)
   (- x (- (/ y (/ a z)) y))
   (if (<= a 1.6e+22) (- x (/ y (/ (- a t) z))) (- (+ y x) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-18) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.6e+22) {
		tmp = x - (y / ((a - t) / z));
	} else {
		tmp = (y + x) - (y * (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 (a <= (-8.5d-18)) then
        tmp = x - ((y / (a / z)) - y)
    else if (a <= 1.6d+22) then
        tmp = x - (y / ((a - t) / z))
    else
        tmp = (y + x) - (y * (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 (a <= -8.5e-18) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.6e+22) {
		tmp = x - (y / ((a - t) / z));
	} else {
		tmp = (y + x) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-18:
		tmp = x - ((y / (a / z)) - y)
	elif a <= 1.6e+22:
		tmp = x - (y / ((a - t) / z))
	else:
		tmp = (y + x) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-18)
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	elseif (a <= 1.6e+22)
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-18)
		tmp = x - ((y / (a / z)) - y);
	elseif (a <= 1.6e+22)
		tmp = x - (y / ((a - t) / z));
	else
		tmp = (y + x) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-18], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+22], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4999999999999995e-18

   1. Initial program 86.0%

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

      1. sub-neg 86.0%

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

      2. distribute-frac-neg 86.0%

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

      3. distribute-rgt-neg-out 86.0%

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

      4. associate-/l* 95.4%

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

      5. div-sub 95.4%

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

      6. associate-+r- 95.4%

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

      7. associate-/r/ 96.1%

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

      8. distribute-rgt-neg-out 96.1%

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

      9. associate-/r/ 95.4%

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

      10. distribute-frac-neg 95.4%

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

      11. associate-+l+ 95.4%

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

      12. associate-+r- 96.7%

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

      13. distribute-frac-neg 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 85.6%

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

      1. associate-/l* 91.0%

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

   6. Simplified 91.0%

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

   if -8.4999999999999995e-18 < a < 1.6e22

   1. Initial program 74.0%

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

      1. sub-neg 74.0%

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

      2. distribute-frac-neg 74.0%

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

      3. distribute-rgt-neg-out 74.0%

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

      4. associate-/l* 81.6%

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

      5. div-sub 80.8%

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

      6. associate-+r- 80.8%

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

      7. associate-/r/ 81.7%

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

      8. distribute-rgt-neg-out 81.7%

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

      9. associate-/r/ 80.8%

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

      10. distribute-frac-neg 80.8%

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

      11. associate-+l+ 80.8%

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

      12. associate-+r- 85.1%

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

      13. distribute-frac-neg 85.1%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-*r/ 87.3%

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

      2. associate-*r* 87.3%

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

      3. neg-mul-1 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

      3. associate-/l* 86.7%

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

   9. Simplified 86.7%

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

   if 1.6e22 < a

   1. Initial program 81.8%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 87.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 9: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-15)
   (- x (- (/ y (/ a z)) y))
   (if (<= a 1.8e+21) (- x (* z (/ y (- a t)))) (- (+ y x) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-15) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.8e+21) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = (y + x) - (y * (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 (a <= (-2.3d-15)) then
        tmp = x - ((y / (a / z)) - y)
    else if (a <= 1.8d+21) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = (y + x) - (y * (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 (a <= -2.3e-15) {
		tmp = x - ((y / (a / z)) - y);
	} else if (a <= 1.8e+21) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = (y + x) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-15:
		tmp = x - ((y / (a / z)) - y)
	elif a <= 1.8e+21:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = (y + x) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-15)
		tmp = Float64(x - Float64(Float64(y / Float64(a / z)) - y));
	elseif (a <= 1.8e+21)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-15)
		tmp = x - ((y / (a / z)) - y);
	elseif (a <= 1.8e+21)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = (y + x) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-15], N[(x - N[(N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+21], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2999999999999999e-15

   1. Initial program 85.8%

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

      1. sub-neg 85.8%

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

      2. distribute-frac-neg 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. associate-/l* 95.3%

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

      5. div-sub 95.3%

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

      6. associate-+r- 95.3%

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

      7. associate-/r/ 96.0%

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

      8. distribute-rgt-neg-out 96.0%

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

      9. associate-/r/ 95.3%

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

      10. distribute-frac-neg 95.3%

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

      11. associate-+l+ 95.4%

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

      12. associate-+r- 96.7%

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

      13. distribute-frac-neg 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 85.4%

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

      1. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   if -2.2999999999999999e-15 < a < 1.8e21

   1. Initial program 74.2%

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

      1. sub-neg 74.2%

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

      2. distribute-frac-neg 74.2%

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

      3. distribute-rgt-neg-out 74.2%

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

      4. associate-/l* 81.7%

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

      5. div-sub 80.9%

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

      6. associate-+r- 80.9%

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

      7. associate-/r/ 81.8%

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

      8. distribute-rgt-neg-out 81.8%

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

      9. associate-/r/ 80.9%

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

      10. distribute-frac-neg 80.9%

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

      11. associate-+l+ 80.9%

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

      12. associate-+r- 85.2%

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

      13. distribute-frac-neg 85.2%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. associate--l+ 83.6%

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

      3. div-sub 83.6%

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

   6. Simplified 83.6%

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

      1. add-cube-cbrt 83.4%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 83.4%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 83.4%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 87.4%

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

       1. mul-1-neg 87.4%

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

       2. associate-/l* 86.6%

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

       3. distribute-frac-neg 86.6%

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

       4. associate-/r/ 89.3%

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

   11. Simplified 89.3%

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

   if 1.8e21 < a

   1. Initial program 81.8%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 87.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;x - \left(\frac{y}{\frac{a}{z}} - y\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 87.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((t - z) / ((a - t) / y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.2%

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

   1. sub-neg 79.2%

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

   2. distribute-frac-neg 79.2%

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

   3. distribute-rgt-neg-out 79.2%

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

   4. associate-/l* 88.0%

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

   5. div-sub 87.6%

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

   6. associate-+r- 87.6%

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

   7. associate-/r/ 88.3%

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

   8. distribute-rgt-neg-out 88.3%

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

   9. associate-/r/ 87.6%

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

   10. distribute-frac-neg 87.6%

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

   11. associate-+l+ 87.6%

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

   12. associate-+r- 90.1%

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

   13. distribute-frac-neg 90.1%

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

3. Simplified 90.5%

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

4. Final simplification 90.5%

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

Alternative 11: 77.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e-18) (+ y x) (if (<= a 3.8e-8) (+ x (* z (/ y t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-18) {
		tmp = y + x;
	} else if (a <= 3.8e-8) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.4d-18)) then
        tmp = y + x
    else if (a <= 3.8d-8) then
        tmp = x + (z * (y / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-18) {
		tmp = y + x;
	} else if (a <= 3.8e-8) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e-18:
		tmp = y + x
	elif a <= 3.8e-8:
		tmp = x + (z * (y / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e-18)
		tmp = Float64(y + x);
	elseif (a <= 3.8e-8)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e-18)
		tmp = y + x;
	elseif (a <= 3.8e-8)
		tmp = x + (z * (y / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e-18], N[(y + x), $MachinePrecision], If[LessEqual[a, 3.8e-8], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.3999999999999997e-18 or 3.80000000000000028e-8 < a

   1. Initial program 83.8%

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

      1. sub-neg 83.8%

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

      2. distribute-frac-neg 83.8%

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

      3. distribute-rgt-neg-out 83.8%

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

      4. associate-/l* 93.0%

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

      5. div-sub 93.0%

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

      6. associate-+r- 93.0%

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

      7. associate-/r/ 93.6%

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

      8. distribute-rgt-neg-out 93.6%

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

      9. associate-/r/ 93.0%

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

      10. distribute-frac-neg 93.0%

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

      11. associate-+l+ 93.0%

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

      12. associate-+r- 93.8%

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

      13. distribute-frac-neg 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 81.9%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 81.9%

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

   6. Simplified 81.9%

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

   if -4.3999999999999997e-18 < a < 3.80000000000000028e-8

   1. Initial program 73.6%

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

      1. sub-neg 73.6%

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

      2. distribute-frac-neg 73.6%

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

      3. distribute-rgt-neg-out 73.6%

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

      4. associate-/l* 81.8%

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

      5. div-sub 80.9%

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

      6. associate-+r- 80.9%

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

      7. associate-/r/ 81.9%

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

      8. distribute-rgt-neg-out 81.9%

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

      9. associate-/r/ 80.9%

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

      10. distribute-frac-neg 80.9%

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

      11. associate-+l+ 80.9%

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

      12. associate-+r- 85.6%

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

      13. distribute-frac-neg 85.6%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. associate--l+ 84.7%

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

      3. div-sub 84.7%

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

   6. Simplified 84.7%

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

      1. add-cube-cbrt 84.4%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{1 + \frac{t - z}{a - t}} \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right) \cdot \sqrt[3]{1 + \frac{t - z}{a - t}}\right)} + x \]

      2. pow3 84.5%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   8. Applied egg-rr 84.5%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{1 + \frac{t - z}{a - t}}\right)}^{3}} + x \]

   9. Taylor expanded in z around inf 88.8%

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

       1. mul-1-neg 88.8%

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

       2. associate-/l* 88.1%

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

       3. distribute-frac-neg 88.1%

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

       4. associate-/r/ 90.8%

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

   11. Simplified 90.8%

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

   12. Taylor expanded in a around 0 85.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12: 63.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-49}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-49) (+ y x) (if (<= a 6.5e-268) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-49) {
		tmp = y + x;
	} else if (a <= 6.5e-268) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d-49)) then
        tmp = y + x
    else if (a <= 6.5d-268) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-49) {
		tmp = y + x;
	} else if (a <= 6.5e-268) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-49:
		tmp = y + x
	elif a <= 6.5e-268:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-49)
		tmp = Float64(y + x);
	elseif (a <= 6.5e-268)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e-49)
		tmp = y + x;
	elseif (a <= 6.5e-268)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-49], N[(y + x), $MachinePrecision], If[LessEqual[a, 6.5e-268], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.39999999999999992e-49 or 6.5000000000000003e-268 < a

   1. Initial program 82.2%

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

      1. sub-neg 82.2%

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

      2. distribute-frac-neg 82.2%

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

      3. distribute-rgt-neg-out 82.2%

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

      4. associate-/l* 91.4%

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

      5. div-sub 91.4%

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

      6. associate-+r- 91.4%

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

      7. associate-/r/ 91.8%

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

      8. distribute-rgt-neg-out 91.8%

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

      9. associate-/r/ 91.4%

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

      10. distribute-frac-neg 91.4%

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

      11. associate-+l+ 91.4%

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

      12. associate-+r- 91.9%

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

      13. distribute-frac-neg 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in a around inf 73.1%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 73.1%

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

   6. Simplified 73.1%

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

   if -2.39999999999999992e-49 < a < 6.5000000000000003e-268

   1. Initial program 67.3%

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

      1. sub-neg 67.3%

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

      2. distribute-frac-neg 67.3%

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

      3. distribute-rgt-neg-out 67.3%

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

      4. associate-/l* 74.4%

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

      5. div-sub 72.4%

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

      6. associate-+r- 72.4%

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

      7. associate-/r/ 74.4%

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

      8. distribute-rgt-neg-out 74.4%

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

      9. associate-/r/ 72.4%

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

      10. distribute-frac-neg 72.4%

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

      11. associate-+l+ 72.4%

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

      12. associate-+r- 83.0%

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

      13. distribute-frac-neg 83.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around inf 64.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-49}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 51.2% 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 79.2%

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

   1. sub-neg 79.2%

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

   2. distribute-frac-neg 79.2%

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

   3. distribute-rgt-neg-out 79.2%

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

   4. associate-/l* 88.0%

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

   5. div-sub 87.6%

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

   6. associate-+r- 87.6%

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

   7. associate-/r/ 88.3%

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

   8. distribute-rgt-neg-out 88.3%

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

   9. associate-/r/ 87.6%

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

   10. distribute-frac-neg 87.6%

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

   11. associate-+l+ 87.6%

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

   12. associate-+r- 90.1%

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

   13. distribute-frac-neg 90.1%

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

3. Simplified 90.5%

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

4. Taylor expanded in x around inf 54.2%

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

5. Final simplification 54.2%

   \[\leadsto x \]

Developer target: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * 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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))